The Management Oversight and Risk Tree (MORT) may be used to assign numerical indicators to risks. This method is a scientific method of ranking hazards and their causal factors for analysis and allocation of resources, including management concern, to resolve them.

The management oversight and risk tree (MORT) is an investigative tool which analyzes the many factors contributing to an accident. It accomplishes this by means of identification of unwanted or potentially hazardous energy sources, along with consideration of the adequacy of the controls and barriers on these energy sources. The analysis proceeds through a chain of cause and effect, examining the sources of energy flow, controls upon such energy flows, and barriers between these energy flows and vulnerable people or objects.

The basic tool is the MORT Chart, which can be used by an analyst to trace the chain of causality linking the accident and its contributing factors. This chart, which is a slight modification from the one published by the Department of Energy, can be downloaded by clicking here. Be advised that the file is 674,742 bytes. This very large chart is intended to be printed in sections and posted on a wall A thumbnail quality version is shown below:

MORT assumes that an accident has a number of interrelated causes. An accident is considered to be an undesired occurrence which causes injury to people or results in property damage. Specifically, an accident is:

(1) An unwanted energy flow or environmental condition. . .

(2) Which, because of lack or failure of barriers or controls. . .

(3) Produces injury or damage to vulnerable persons or objects.

It occurs because of a lack of adequate barriers or controls upon the unwanted energy transfer associated with the undesired occurrence. Accidents are usually preceded by initiating sequences consisting of planning errors and operational errors which result in failures to adjust to changes in human factors or environmental conditions. The failure to adjust satisfactorily leads directly to unsafe conditions and unsafe acts that arise out of the risk associated with that activity. The unsafe conditions and unsafe acts, in turn, provoke the flow of unwanted energy.

MORT assumes that in any industrial accident situation, contributors to the accident can be identified as either assumed risks which management has made a conscious decision to accept, or management oversights or omissions, or both. The emphasis on management as the key factor is because management is by definition responsible for the activities and posture of the organization. Since an accident is an event or condition not desired by management, it represents either a decision that the risk of the potential for harm is acceptably small, or a misunderstanding on the part of management of what the magnitude of the risk is, or that the risk exists at all. In either case, the occurrence of an accident is by its nature a failure of management effectiveness.

The management oversights or omissions resulting in an accident are further divided into specific controls factors which are or were inadequate, and also inadequate management system factors which allow or allowed the specific control factors to exist. Both are needed for management to overlook some hazardous condition which could result in an accident.

Finally, the accident itself, as previously defined, requires the three factors of energy, inadequate controls or barriers, and vulnerable people or objects, to occur.

The events or conditions in the causal chain are identified and arranged in a graphic logic tree which shows the causal relationship between them. Many causes are interrelated in a way which makes it impossible to establish a rigid hierarchy of cause and effect. In other words, there is often more than a single chain of cause and effect between any given basic event and the undesired top event which constitutes the accident. This results in a continual evolution of the tree, which is updated and published every two years by the System Safety Development Center in Pocatello, Idaho.

A companion document to the MORT chart explains the methodology used to develop the tree and the significance of each condition or causal factor. Each item in the tree is identified by the page number and its place in the outline structure in which it appears. For example, item 26e25 is item e25 on page 26, which asks the question, "Were task schedule pressures (as experienced by the individual) held to an acceptable level?"

Basic causal factors are those events or conditions for which subordinate causal factors either cannot be established or cannot be effectively analyzed. Some of these are conditions or events normally expected to occur. Some of them are accepted risks. The ones defined in the 1994 tree are listed as follows. Accepted risks are identified with an asterisk.

These basic causal factors define the following higher-tier events or conditions in the tree.

The relationship between these items is shown graphically in the tree and can be logically defined by the following cut sets:

2c4a requires the simultaneous occurrence of 2c2a AND 3d1a
2c4b requires the simultaneous occurrence of 2c2b AND 3d1b
2c4c requires the simultaneous occurrence of 2c2c AND 3d1c
3b4 requires the occurrence of 3c4 OR 3c5 OR 4c6 OR 4c7
4a5 requires the occurrence of 4b6 OR 4b7
4a6 requires the occurrence of 4b8 OR 5b9 OR 5b10 OR 5b11
5a1 requires the occurrence of 5b1 OR 5b2
5b4 requires the occurrence of 5c1 OR 6c2
6a1 requires the occurrence of 6b1 OR 6b2
7b4 requires the occurrence of 7c1 OR 7c2
10c1 requires the occurrence of 10d1 OR 10d2 OR 10d3 OR 10d4
10c2 requires the occurrence of 10d5 OR 10d6
10c3 requires the occurrence of 10d7 OR 11d8
11a2 requires the occurrence of 11b3 OR 11b4 OR 11b5 OR 11b6 OR 11b7 OR 12b8 OR 12b9 OR 12b10
11c4 requires the occurrence of 11d9 OR 11d10
12a3 requires the occurrence of 12b11 OR 12b12 OR 12b13 OR 12b14 OR 12b15
12a4 requires the occurrence of 13b16 OR 13b17 OR 13b18 OR 13b19 OR 13b20
14a1 requires the occurrence of 14b1 OR 14b2 OR 14b3 OR 14b4 OR 14b5
15b2i requires the occurrence of 15c1i OR 15c2i OR 15c3i
15b2m requires the occurrence of 15c1m OR 15c2m OR 15c3m
17c2 requires the occurrence of 17d1 OR 17d2 OR 17d3 OR 17d4
18c5 requires the occurrence of 18d5 OR 18d6 OR 18d7
20e3 requires the occurrence of 20f1 OR 20f2 OR 20f3 OR 20f4
21e4 requires the occurrence of 21f5 OR 21f6
21f7 requires the occurrence of 21g1 OR 21g2 OR 21g3 OR 21g4
22d11 requires the occurrence of 22e7 OR 23e8 OR 23e9 OR 23e10 OR 23e11 OR 23e12
22e6 requires the occurrence of 22f9 OR 22f10 OR 22f11 OR 22f12
23c11 requires the occurrence of 23d12 OR 23d13
24d14 requires the occurrence of 24e13 OR 24e14
24d15 requires the occurrence of 24e15 OR 24e16 OR 24e17 OR 25e18 OR 25e19
25e22 requires the occurrence of 26f13 OR 26f14
27e29 requires the occurrence of 27f15 OR 27f16
27e31 requires the occurrence of 27f17 OR 27f18 OR 28f19
28b1a requires the occurrence of 29c1a OR 29c2a OR 29c3a OR 29c4a
28b1b requires the occurrence of 29c1c OR 29c2c OR 29c3c OR 29c4c
28b2a requires the occurrence of 29c1b OR 29c2b OR 29c3b OR 29c4b
28b2b requires the occurrence of 29c1d OR 29c2d OR 29c3d OR 29c4d
29b4 requires the occurrence of 29c15 OR 29c16 OR 30c17
31a4 requires the occurrence of 31b1 OR 31b2 OR 31b3 OR 31b4 OR 31b5
35a6 requires the occurrence of 35b1 OR 35b2 OR 35b3 OR 35b4 OR 35b5 OR 35b6 OR 35b7 OR 36b8 OR 36b9
37b1 requires the occurrence of 37c1 OR 37c2
37b2 requires the occurrence of 37c3 OR 38c4 OR 38c5 OR 38c6 OR 38c7 OR 38c8
38b4 requires the occurrence of 38c9 OR 38c10 OR 38c11 OR 39c12 OR 39c13
39b5 requires the occurrence of 39c14 OR 39c15
39b6 requires the occurrence of 39c16 OR 39c17 OR 39c18 OR 39c19
41c30 requires the occurrence of 41d1 OR 41d2 OR 41d3 OR 41d4 OR 41d5
42c31 requires the occurrence of 42d6 OR 42d7 OR 42d8 OR 42d9 OR 42d10
43c34 requires the occurrence of 43d11 OR 43d12 OR 43d13 OR 43d14 OR 44d15 OR 44d16 OR 44d17 OR 44d18 OR 44d19
45b20 requires the occurrence of 45c40 OR 45c41 OR 46c42 OR 46c43 OR 46c44 OR 46c45 OR 46c46 OR 46c47
47a4 requires the occurrence of 47b1 OR 47b2 OR 47b3 OR 47b4 OR 47b5
48a5 requires the occurrence of 48b6 OR 48b7 OR 48b8
10b1 requires the occurrence of 10c1 OR 10c2
10b2 requires the occurrence of 10c3 OR 11c4
28a1 requires the occurrence of 28b1a OR 28b2a
29a2 requires the occurrence of 28b1b OR 28b2b
10a1 requires the occurrence of 10b1 OR 10b2
28d18 requires the occurrence of 28a1 OR 29a2
45c39 is equivalent to 28d18
3a4 requires the occurrence of 3b3 OR 3b4 OR 4b5
26d17 requires the occurrence of 26e24 OR 26e25 OR 26e26 OR 26e27 OR 26e28 OR 27e29 OR 27e30 OR 27e31 OR 28e32
25d16 requires the occurrence of 25e20 OR 25e21 OR 25e23 OR 25e22
20d8 requires the occurrence of 20e1 OR 20e2 OR 20e3
30SD6 requires the occurrence of 30a1 OR 30a2 OR 30a3 OR 31a4 OR 31a5 OR 31a6
13SD2 requires the occurrence of 14a1 OR 14a2 OR 14a3 OR 14a4
17b1 requires the occurrence of 17c1 OR 17c2 OR 17c3
18b2 requires the occurrence of 18c4 OR 18c5 OR 18c6 OR 18c7
15a1m requires the occurrence of 15b1m OR 15b2m
15a1i requires the occurrence of 15b1i OR 15b2i
22f8 requires the occurrence of 10a1 OR 12a3 OR 11a2 OR 12a4 OR 13a5
9SD1 is equivalent to 22f8
37MB2 is equivalent to 22f8
16a4 requires the occurrence of 17b1 OR 18b2
24c14 requires the occurrence of 24d14 OR 24d15 OR 25d16 OR 28d18 OR 26d17
21e5 requires the occurrence of 21f7 OR 10a1
21d10 requires the occurrence of 21e4 OR 22e6 OR 21e5
21c10 requires the occurrence of 22d11 OR 21d10
19c9 requires the occurrence of 20d8 OR 20d9
19b3 requires the occurrence of 19c8 OR 19c9 OR 21c10 OR 23c11 OR 23c12 OR 24c13 OR 24c14
30c18 is equivalent to 19b3
15b3i is equivalent to 19b3
15b3m is equivalent to 19b3
3c3a is equivalent to 19b3
3c3b is equivalent to 19b3
3c3c is equivalent to 19b3
30b5 requires the occurrence of 30c19 OR 30c18
15a2m requires the occurrence of 15b3m OR 15b4m OR 16b5m OR 16b6m
15a2i requires the occurrence of 15b3i OR 15b4i OR 16b5i OR 16b6i
2b2a requires the occurrence of 2c1a OR 2c4a OR 3c3a
2b2b requires the occurrence of 2c1b OR 2c4b OR 3c3b
2b2c requires the occurrence of 2c1c OR 2c4c OR 3c3c
2a1 requires the occurrence of 2b1a OR 2b2a
3a2 requires the occurrence of 2b1b OR 2b2b
3a3 requires the occurrence of 2b1c OR 2b2c
46b21 requires the occurrence of 4a5 OR 2a1 OR 3a2 OR 3a3 OR 3A4 OR 4a6
2SA2 is equivalent to 46b21
14SD4 requires the occurrence of 15a1i OR 15a2i
14SD3 requires the occurrence of 15a1m OR 15a2m
19a5 requires the occurrence of 19b3 OR 29b4 OR 30b5
41b8 requires the occurrence of 41c27 OR 41c28 OR 41c29 OR 41c30 OR 42c31
16SD5 requires the occurrence of 16a1 OR 16a2 OR 16a3 OR 16a4 OR 19a5
7SC1 requires the occurrence of 30SD6 OR 13SD2 OR 16SD5 OR 9SD1 OR 14SD3 OR 14SD4
9c2a is equivalent to 19b3
9c2b is equivalent to 19b3
9c2c is equivalent to 19b3
9c2d is equivalent to 19b3
8b3a requires the occurrence of 8c1a OR 9c2a
8b3b requires the occurrence of 8c1b OR 9c2b
8b3c requires the occurrence of 8c1c OR 9c2c
8b3d requires the occurrence of 8c1d OR 9c2d
43b13 requires the occurrence of 43c32 OR 43c33 OR 43c34 OR 44c35 OR 44c36 OR 44c37 OR 44c38 OR 45c39
8a1 requires the occurrence of 8b1a OR 8b2a OR 8b3a
8a2 requires the occurrence of 8b1b OR 8b2b OR 8b3b
8a3 requires the occurrence of 8b1c OR 8b2c OR 8b3c
9a4 requires the occurrence of 8b1d OR 8b2d OR 8b3d
5a2 requires the occurrence of 5b3 OR 5b4
7SC2 requires the occurrence of 8a1 OR 8a2 OR 8a3 OR 9a4
7a2 requires the occurrence of 7b3 OR 7b4
37a1 requires the occurrence of 37b1 OR 37b2 OR 38b3 OR 38b4 OR 39b5 OR 39b6
6SB3 requires the occurrence of 6a1 OR 7a2
5SB1 requires the occurrence of 5a1 OR 5a2
6SB2 requires the occurrence of 7SC1 OR 7SC2
9SC3 is equivalent to 6SB2
40c26 is equivalent to 6SB2
40b7 requires the occurrence of 40c26 OR 40c20 OR 40c21 OR 40c22 OR 40c23 OR 40c24 OR 40c25
42b9 is equivalent to 15a1m
42b10 is equivalent to 15a1i
40a2 requires the occurrence of 42b9 OR 42b10 OR 40b7 OR 42b11 OR 43b12 OR 41b8 OR 43b13 OR 45b14 OR 45b15 OR 45b16 OR 45b17 OR 45b18 OR 45b19 OR 45b20 OR 2SA2
7SB4 requires the simultaneous occurrence of 5SB1 AND 6SB2
9SC4 is equivalent to 7SB4
2SA1 requires the simultaneous occurrence of 5SB1 AND 7SB4 AND 6SB3
37MB3 requires the occurrence of 37a1 OR 40a2
48a6 is equivalent to 30SD6
35a6 is equivalent to 30SD6
46MB4 requires the occurrence of 47a1 OR 47a2 OR 47a3 OR 47a4 OR 48a5 OR 48a6
32a4 is equivalent to 10a1
37MB2 is equivalent to 22f8
32MA1 requires the occurrence of 32a1 OR 32a2 OR 32a3 OR 32a4 OR 33a5 OR 33a6 OR 33a7 OR 33a8 OR 33a9 OR 33a10 OR 34a11
36a10 is equivalent to 26e24
34MA2 requires the occurrence of 34a1 OR 34a2 OR 34a3 OR 34a4 OR 34a5 OR 35a6 OR 36a7 OR 36a8 OR 36a9 OR 36a10
36MA3 requires the occurrence of 37MB1 OR 37MB2 OR 37MB3 OR 46MB4
1S requires the occurrence of 2SA1 OR 2SA2
32M requires the occurrence of 32MA1 OR 34MA2 OR 37MA3
1S/M requires the simultaneous occurrence of 1S AND 32M
48R requires the occurrence of 6c2 OR 5b2 OR 6b2 OR 8b1a OR 8c1a OR 8b1b OR 8c1b OR 8b1c OR 8c1c OR 8b1d OR 8c1d OR 7c2 OR 20d9 OR 26e24 OR 28f19 OR 4c7
1T requires the occurrence of 1S/M OR 48R

One way of mathematically interpreting these sets is to assume that each basic causal factor identifies the probability of occurrence of an undesired event or, in the case of conditions which are always expected to occur, the probability that the occurrence will contribute the an undesirable event. The probabilities of events defined by basic causal factors is then established by the following system of equations:

[2c4a] = ([2c2a] x [3d1a])
[2c4b] = ([2c2b] x [3d1b])
[2c4c] = ([2c2c] x [3d1c])
[3b4] = (1-((1-[3c4]) x (1-[3c5]) x (1-[4c6]) x (1-[4c7])))
[4a5] = (1-((1-[4b6]) x (1-[4b7])))
[4a6] = (1-((1-[4b8]) x (1-[5b9]) x (1-[5b10]) x (1-[5b11])))
[5a1] = (1-((1-[5b1]) x (1-[5b2])))
[5b4] = (1-((1-[5c1]) x (1-[6c2])))
[6a1] = (1-((1-[6b1]) x (1-[6b2])))
[7b4] = (1-((1-[7c1]) x (1-[7c2])))
[10c1] = (1-((1-[10d1]) x (1-[10d2]) x (1-[10d3]) x (1-[10d4])))
[10c2] = (1-((1-[10d5]) x (1-[10d6])))
[10c3] = (1-((1-[10d7]) x (1-[11d8])))
[11a2] = (1-((1-[11b3]) x (1-[11b4]) x (1-[11b5]) x (1-[11b6]) x (1-[11b7]) x (1-[12b8]) x (1-[12b9]) x (1-[12b10])))
[11c4] = (1-((1-[11d9]) x (1-[11d10])))
[12a3] = (1-((1-[12b11]) x (1-[12b12]) x (1-[12b13]) x (1-[12b14]) x (1-[12b15])))
[12a4] = (1-((1-[13b16]) x (1-[13b17]) x (1-[13b18]) x (1-[13b19]) x (1-[13b20])))
[14a1] = (1-((1-[14b1]) x (1-[14b2]) x (1-[14b3]) x (1-[14b4]) x (1-[14b5])))
[15b2i] = (1-((1-[15c1i]) x (1-[15c2i]) x (1-[15c3i])))
[15b2m] = (1-((1-[15c1m]) x (1-[15c2m]) x (1-[15c3m])))
[17c2] = (1-((1-[17d1]) x (1-[17d2]) x (1-[17d3]) x (1-[17d4])))
[18c5] = (1-((1-[18d5]) x (1-[18d6]) x (1-[18d7])))
[20e3] = (1-((1-[20f1]) x (1-[20f2]) x (1-[20f3]) x (1-[20f4])))
[21e4] = (1-((1-[21f5]) x (1-[21f6])))
[21f7] = (1-((1-[21g1]) x (1-[21g2]) x (1-[21g3]) x (1-[21g4])))
[22d11] = (1-((1-[22e7]) x (1-[23e8]) x (1-[23e9]) x (1-[23e10]) x (1-[23e11]) x (1-[23e12])))
[22e6] = (1-((1-[22f9]) x (1-[22f10]) x (1-[22f11]) x (1-[22f12])))
[23c11] = (1-((1-[23d12]) x (1-[23d13])))
[24d14] = (1-((1-[24e13]) x (1-[24e14])))
[24d15] = (1-((1-[24e15]) x (1-[24e16]) x (1-[24e17]) x (1-[25e18]) x (1-[25e19])))
[25e22] = (1-((1-[26f13]) x (1-[26f14])))
[27e29] = (1-((1-[27f15]) x (1-[27f16])))
[27e31] = (1-((1-[27f17]) x (1-[27f18]) x (1-[28f19])))
[28b1a] = (1-((1-[29c1a]) x (1-[29c2a]) x (1-[29c3a]) x (1-[29c4a])))
[28b1b] = (1-((1-[29c1c]) x (1-[29c2c]) x (1-[29c3c]) x (1-[29c4c])))
[28b2a] = (1-((1-[29c1b]) x (1-[29c2b]) x (1-[29c3b]) x (1-[29c4b])))
[28b2b] = (1-((1-[29c1d]) x (1-[29c2d]) x (1-[29c3d]) x (1-[29c4d])))
[29b4] = (1-((1-[29c15]) x (1-[29c16]) x (1-[30c17])))
[31a4] = (1-((1-[31b1] x (1-[31b2]) x (1-[31b3]) x (1-[31b4]) x (1-[31b5])))
[35a6] = (1-((1-[35b1]) x (1-[35b2]) x (1-[35b3]) x (1-[35b4]) x (1-[35b5]) x (1-[35b6]) x (1-[35b7]) x (1-[36b8]) x (1-[36b9])))
[37b1] = (1-((1-[37c1]) x (1-[37c2])))
[37b2] = (1-((1-[37c3]) x (1-[38c4]) x (1-[38c5]) x (1-[38c6]) x (1-[38c7]) x (1-[38c8])))
[38b4] = (1-((1-[38c9]) x (1-[38c10]) x (1-[38c11]) x (1-[39c12]) x (1-[39c13])))
[39b5] = (1-((1-[39c14]) x (1-[39c15])))
[39b6] = (1-((1-[39c16]) x (1-[39c17]) x (1-[39c18]) x (1-[39c19])))
[41c30] = (1-((1-[41d1]) x (1-[41d2]) x (1-[41d3]) x (1-[41d4]) x (1-[41d5])))
[42c31] = (1-((1-[42d6]) x (1-[42d7]) x (1-[42d8]) x (1-[42d9]) x (1-[42d10])))
[43c34] = (1-((1-[43d11]) x (1-[43d12]) x (1-[43d13]) x (1-[43d14]) x (1-[44d15]) x (1-[44d16]) x (1-[44d17]) x (1-[44d18]) x (1-[44d19])))
[45b20] = (1-((1-[45c40]) x (1-[45c41]) x (1-[46c42]) x (1-[46c43]) x (1-[46c44]) x (1-[46c45]) x (1-[46c46]) x (1-[46c47])))
[47a4] = (1-((1-[47b1]) x (1-[47b2]) x (1-[47b3]) x (1-[47b4]) x (1-[47b5])))
[48a5] = (1-((1-[48b6]) x (1-[48b7]) x (1-[48b8])))
[10b1] = (1-((1-[10c1]) x (1-[10c2])))
[10b2] = (1-((1-[10c3]) x (1-[11c4])))
[28a1] = (1-((1-[28b1a]) x (1-[28b2a])))
[29a2] = (1-((1-[28b1b]) x (1-[28b2b])))
[10a1] = (1-((1-[10b1]) x (1-[10b2])))
[28d18] = (1-((1-[ 28a1]) x (1-[29a2])))
[45c39] = [28d18]
[3a4] = (1-((1-[3b3]) x (1-[3b4]) x (1-[4b5])))
[26d17] = (1-((1-[26e24]) x (1-[26e25]) x (1-[26e26]) x (1-[26e27]) x (1-[26e28]) x (1-[27e29]) x (1-[27e30]) x (1-[27e31]) x (1-[28e32])))
[25d16] = (1-((1-[25e20]) x (1-[25e21]) x (1-[25e23]) x (1-[25e22])))
[20d8] = (1-((1-[20e1]) x (1-[20e2]) x (1-[20e3])))
[30SD6] = (1-((1-[30a1]) x (1-[30a2]) x (1-[30a3]) x (1-[31a4]) x (1-[31a5]) x (1-[31a6])))
[13SD2] = (1-((1-[14a1]) x (1-[14a2]) x (1-[14a3]) x (1-[14a4])))
[17b1] = (1-((1-[17c1]) x (1-[17c2]) x (1-[17c3])))
[18b2] = (1-((1-[18c4]) x (1-[18c5]) x (1-[18c6]) x (1-[18c7])))
[15a1m] = (1-((1-[15b1m]) x (1-[15b2m])))
[15a1i] = (1-((1-[15b1i]) x (1-[15b2i])))
[22f8] = (1-((1-[10a1]) x (1-[12a3]) x (1-[11a2]) x (1-[12a4]) x (1-[13a5])))
[9SD1] = [22f8]
[37MB2] = [22f8]
[16a4] = (1-((1-[17b1]) x (1-[18b2])))
[24c14] = (1-((1-[24d14]) x (1-[24d15]) x (1-[25d16]) x (1-[28d18]) x (1-[26d17])))
[21e5] = (1-((1-[21f7]) x (1-[10a1])))
[21d10] = (1-((1-[21e4]) x (1-[22e6]) x (1-[21e5])))
[21c10] = (1-((1-[22d11]) x (1-[21d10])))
[19c9] = (1-((1-[20d8]) x (1-[20d9])))
[19b3] = (1-((1-[19c8]) x (1-[19c9]) x (1-[21c10]) x (1-[23c11]) x (1-[23c12]) x (1-[24c13]) x (1-[24c14])))
[30c18] = [19b3]
[15b3i] = [19b3]
[15b3m] = [19b3]
[3c3a] = [19b3]
[3c3b] = [19b3]
[3c3c] = [19b3]
[30b5] = (1-((1-[30c19]) x (1-[30c18])))
[15a2m] = (1-((1-[15b3m]) x (1-[15b4m]) x (1-[16b5m]) x (1-[16b6m])))
[15a2i] = (1-((1-[15b3i]) x (1-[15b4i]) x (1-[16b5i]) x (1-[16b6i])))
[2b2a] = (1-((1-[2c1a]) x (1-[2c4a]) x (1-[3c3a])))
[2b2b] = (1-((1-[2c1b]) x (1-[2c4b]) x (1-[3c3b])))
[2b2c] = (1-((1-[2c1c]) x (1-[2c4c]) x (1-[3c3c])))
[2a1] = (1-((1-[2b1a]) x (1-[2b2a])))
[3a2] = (1-((1-[2b1b]) x (1-[2b2b])))
[3a3] = (1-((1-[2b1c]) x (1-[2b2c])))
[46b21] = (1-((1-[4a5]) x (1-[2a1]) x (1-[3a2]) x (1-[3a3]) x (1-[3A4]) x (1-[4a6])))
[2SA2] = (1-((1-[46b21])))
[14SD4] = (1-((1-[15a1i]) x (1-[15a2i])))
[14SD3] = (1-((1-[15a1m]) x (1-[15a2m])))
[19a5] = (1-((1-[19b3]) x (1-[29b4]) x (1-[30b5])))
[41b8] = (1-((1-[41c27]) x (1-[41c28]) x (1-[41c29]) x (1-[41c30]) x (1-[42c31])))
[16SD5] = (1-((1-[16a1]) x (1-[16a2]) x (1-[16a3]) x (1-[16a4]) x (1-[19a5])))
[7SC1] = (1-((1-[30SD6]) x (1-[13SD2]) x (1-[16SD5]) x (1-[9SD1]) x (1-[14SD3]) x (1-[14SD4])))
[9c2a] = [19b3]
[9c2b] = [19b3]
[9c2c] = [19b3]
[9c2d] = [19b3]
[8b3a] = (1-((1-[8c1a]) x (1-[9c2a])))
[8b3b] = (1-((1-[8c1b]) x (1-[9c2b])))
[8b3c] = (1-((1-[8c1c]) x (1-[9c2c])))
[8b3d] = (1-((1-[8c1d]) x (1-[9c2d])))
[43b13] = (1-((1-[43c32]) x (1-[43c33]) x (1-[43c34]) x (1-[44c35]) x (1-[44c36]) x (1-[44c37]) x (1-[44c38]) x (1-[45c39])))
[8a1] = (1-((1-[8b1a]) x (1-[8b2a]) x (1-[8b3a])))
[8a2] = (1-((1-[8b1b]) x (1-[8b2b]) x (1-[8b3b])))
[8a3] = (1-((1-[8b1c]) x (1-[8b2c]) x (1-[8b3c])))
[9a4] = (1-((1-[8b1d]) x (1-[8b2d]) x (1-[8b3d])))
[5a2] = (1-((1-[5b3]) x (1-[5b4])))
[7SC2] = (1-((1-[8a1]) x (1-[8a2]) x (1-[8a3]) x (1-[9a4])))
[7a2] = (1-((1-[7b3]) x (1-[7b4])))
[37a1] = (1-((1-[37b1]) x (1-[37b2]) x (1-[38b3]) x (1-[38b4]) x (1-[39b5]) x (1-[39b6])))
[6SB3] = (1-((1-[6a1]) x (1-[7a2])))
[5SB1] = (1-((1-[5a1]) x (1-[5a2])))
[6SB2] = (1-((1-[7SC1]) x (1-[7SC2])))
[9SC3] = [6SB2]
[40c26] = [6SB2]
[40b7] = (1-((1-[40c26]) x (1-[40c20]) x (1-[40c21]) x (1-[40c22]) x (1-[40c23]) x (1-[40c24]) x (1-[40c25])))
[42b9] = [15a1m]
[42b10] = [15a1i]
[40a2] = (1-((1-[42b9]) x (1-[42b10]) x (1-[40b7]) x (1-[42b11]) x (1-[43b12]) x (1-[41b8]) x (1-[43b13]) x (1-[45b14]) x (1-[45b15]) x (1-[45b16]) x (1-[45b17]) x (1-[45b18]) x (1-[45b19]) x (1-[45b20]) x (1-[2SA2])))
[7SB4] = ([5SB1] x [6SB2])
[9SC4] = [7SB4]
[2SA1] = ([5SB1] x [7SB4] x [6SB3])
[37MB3] = (1-((1-[37a1]) x (1-[40a2])))
[48a6] = [30SD6]
[35a6] = [30SD6]
[46MB4] = (1-((1-[47a1]) x (1-[47a2]) x (1-[47a3]) x (1-[47a4]) x (1-[48a5]) x (1-[48a6])))
[32a4] = [10a1]
[37MB2] = [22f8]
[32MA1] = (1-((1-[32a1]) x (1-[32a2]) x (1-[32a3]) x (1-[32a4]) x (1-[33a5]) x (1-[33a6]) x (1-[33a7]) x (1-[33a8]) x (1-[33a9]) x (1-[33a10]) x (1-[34a11])))
[36a10] = [26e24]
[34MA2] = (1-((1-[34a1]) x (1-[34a2]) x (1-[34a3]) x (1-[34a4]) x (1-[34a5]) x (1-[35a6]) x (1-[36a7]) x (1-[36a8]) x (1-[36a9]) x (1-[36a10])))
[36MA3] = (1-((1-[37MB1]) x (1-[37MB2]) x (1-[37MB3]) x (1-[46MB4])))
[1S] = (1-((1-[2SA1]) x (1-[2SA2])))
[32M] = (1-((1-[32MA1]) x (1-[34MA2]) x (1-[36MA3])))
[1S/M] = ([1S] x [32M])
[48R] = (1-((1-[6c2]) x (1-[5b2]) x (1-[6b2]) x (1-[8b1a]) x (1-[8c1a]) x (1-[8b1b]) x (1-[8c1b]) x (1-[8b1c]) x (1-[8c1c]) x (1-[8b1d]) x (1-[8c1d]) x (1-[7c2]) x (1-[20d9]) x (1-[26e24]) x (1-[28f19]) x (1-[4c7])))
[1T] = (1-((1-[1S/M]) x (1-[48R])))

Since the value assigned to each element is either an independent variable or the range of a function, the entire MORT tree can be thought of as defining a vector whose elements consist of the values of each of the elements of the tree, in a space which has the same number of dimensions as the number of elements. Any hazard can then be represented as a unique point in this space.

This system of equations can be used to analyze the potential for an accident by analysis of the causal factors involved. The following is a hypothetical situation.

A large manufacturing plant employs a process which uses a highly hazardous liquid as defined by the process safety management paragraph of OSHA, 29 CFR 1910.119. The liquid is delivered and stored in storage drums which nominally contain 3000 pounds of the liquid when filled. The amount of liquid in the drum is determined by weighing the drum and subtracting the tare weight of the drum. The liquid in the drums is highly volatile, because of which the drums are always under internal pressure.

One or more filled storage drums are kept on hand, and are exchanged for nearly empty ones when the weight of the drum in use falls below a minimum value. Although considered empty, the used storage drums contain a small quantity of liquid which could become a hazardous vapor if a leak occurs. The storage drums are delivered by truck. The vendor delivers filled storage drums and removes the empty ones on a regular schedule so that a filled drum is always available when needed. The plumbing and piping system meets all commercial and industrial standards, but failure of one or more of the components of the system is still possible and could result in a leak of the liquid into the environment with a resulting vapor cloud having concentrations above the permissible exposure limit.

The plant is located in an industrial park, surrounded by other manufacturing plants, small shops, and office buildings. Parts of it are generally open to the public, and official visits by school children and other groups are frequent. There is a retirement community condominium adjacent to the site. The plant has an aggressive safety program and an excellent safety record, and encourages safety suggestions from its employees. It strives for continuous improvement in its safety posture, and full compliance with OSHA and other regulatory requirements. In addition, it operates according to an extensive body of internal procedures, which specify in detail what actions to take in case of a leak or spill. A rapid response and remediation team is maintained on call and can be activated at any time by a telephone call to a designated emergency number.

As part of the employee suggestion program, an employee suggested the use of a non-hazardous solid in place of the highly hazardous liquid. Rational for this suggestion included the fact that a solid removes the risk of atmospheric contamination from a leak. A second consideration was that the solid is not covered by 29 CFR 1910.119. Substitution of the solid would thus reduce the cost of OSHA compliance management. After administrative evaluation, the plant safety manager tentatively approved the suggestion for an implementation test.

A pilot program was established to determine the effectiveness of the suggestion. While the solid worked equally as well as the liquid in the process, employees using the material objected on the grounds that use of the granular solid rather than the liquid involved the hard work of lifting the heavy bags of the solid to dump them into a hopper. The production manager of the process agreed with his employees and decided upon the continued use of the highly hazardous liquid as an effective and user-friendly chemical, but agreed to install electrical leak detectors in the vicinity of the tank scales to warn of a leak.

The dispute between the safety manager and the production manager on this issue was resolved by higher management in favor of production. The general manager decided that the potential health risk to people and the contamination risk to the environment was acceptably small, and that the cost of process safety management of the liquid was also acceptable.

The factors identified in the MORT tree associated with this situation are indicated below. Each basic causal factor is assigned a subjective score from zero to one which can be interpreted either as the probability that the event will occur within a specified time frame, or the extent, from 0 to 100 percent, to which a given condition or event can be assumed to contribute to the undesired top event in the same time frame. The scores for events or conditions which are not basic causal factors are to be determined by the MORT analysis.

1T Top Event: Accidental release of highly hazardous liquid into the atmosphere, with consequent potential for injury to exposed persons and unfavorable publicity for the company. (The score is to be determined by the MORT analysis.)

5a1 Nonfunctional environmental condition: Stored filled drums awaiting use or nominally empty drums awaiting pickup. (The score is to be determined by the MORT analysis.)

5a2 Functional environmental condition: Drums containing pressurized liquid connected to the process system. (The score is to be determined by the MORT analysis.)

5b1 Inadequate control on condition: Drums can be delivered too soon or picked up too late. (Subjective score assigned=0.1)

5b2 Impracticability of control: Drums are not delivered "just in time," but by a schedule convenient to the vendor. (Subjective score assigned=0.1)

5SB1 Potentially harmful environmental condition: hazardous liquid under pressure is a potential toxicity source. (The score is to be determined by the MORT analysis.)

6a1 Nonfunctional vulnerable people: Retirement community & the public. (The score is to be determined by the MORT analysis.)

6b1 Inadequate control of nonfunctional vulnerable people: Visitors to the plant are not normally briefed on the evacuation plan. (Subjective score assigned=0.2)

6b2 Impracticability of control of nonfunctional vulnerable people: It is not practical to exclude the public from the plant site. (Subjective score assigned=0.2)

6c2 Diversion impractical: Effective diversion of leaking liquid is not possible. (Subjective score assigned=0.3)

6SB2 Barriers & controls LTA: The system consists of drums and other plumbing. (The score is to be determined by the MORT analysis.)

6SB3 Vulnerable people: Workers, residents of the retirement community and the public. (The score is to be determined by the MORT analysis.)

7a2 Functional vulnerable people: Workers and official visitors. (The score is to be determined by the MORT analysis.)

7b3 Administrative controls LTA: Notification of a leak to the retirement community may be untimely or may not allow sufficient time for evacuation. (Subjective score assigned=0.2)

7c2 Evasion impractical: The retirement community is located adjacent to the plant boundary. (Subjective score assigned=0.3)

7SB4 Events & energy flows: Potential for leak of highly hazardous liquid into atmosphere. (The score is to be determined by the MORT analysis.)

8a1 Barriers ON the energy source: Drums and Piping. (The score is to be determined by the MORT analysis.)

8a2 Barriers BETWEEN the energy source: Isolated storage and use facility. (The score is to be determined by the MORT analysis.)

8a3 Barriers ON persons: Personal Protective Equipment is available, but is not normally used due to the small likelihood of a hazardous leak. (The score is to be determined by the MORT analysis.)

8b1d Separation impossible: It is not practical to separate workers from the site of the process. (Subjective score assigned=0.1)

8b2a Barrier failure: Leak is possible due to loss of system integrity. (Subjective score assigned=0.1)

8c1b Barriers not provided: Low probability of leak does not justify expense of additional barriers. (Subjective score assigned=0.2)

8c1c Barrier not provided: There is no established requirement for the workers to use PPE. (Subjective score assigned=0.1)

9a4 Barriers in TIME or SPACE: Workers can evacuate the area if a leak is detected. (The score is to be determined by the MORT analysis.)

9c2a Task performance errors System not properly operated. (The score is to be determined by the MORT analysis.)

18c7 Supervisory judgment: Management decision to use the highly hazardous liquid in lieu of the non-hazardous granular solid. (Subjective score assigned=0.3)

21g4 Employee suggestion not used: Suggestion to use the less hazardous material was not implemented. (Subjective score assigned=0.3)

23d12 Safety analysis controls not used: a highly hazardous liquid is used instead of a non-hazardous solid. (Subjective score assigned=0.3)

26e24 Management concern, vigor and example LTA: In this case, management did not demonstrate sufficient concern for hazardous liquid release. (Subjective score assigned=0.4)

26e27 Nonperformance is rewarding: Worker objection to use of more safe product was supported by higher management. (Subjective score assigned=0.2)

30a3 Standards & directives LTA: No written standard exists for quantity limitation. (Subjective score assigned=0.4)

32a3 Policies not based on adequate risk assessment: The risk of potential injury and the consequences of unfavorable public reaction to a leak do not appear to justify the management decision. (Subjective score assigned=0.4)

33a5 Conformance to codes, standards & regulations LTA: Decision does not fulfill the hazard reduction precedence sequence established by its internal procedures. (Subjective score assigned=0.6)

33a7 Policies not consistent: The decision to continue to use the highly hazardous liquid is not consistent with the plant manager's stated safety philosophy. (Subjective score assigned=0.6)

37c1 Safety goals and risks not defined: This decision demonstrates an inadequate definition of process safety goals. (Subjective score assigned=0.3)

38c10 OSHA regulations not adequately called out: Insufficient consideration of 29 CFR 1910.119. (Subjective score assigned=0.6)

39c13 Internal standards LTA: Violation of company safety precedence sequence. (Subjective score assigned=0.6)

39c17 Analysis of environmental impact LTA: Inadequate consideration of potential release consequences. (Subjective score assigned=0.6)

40c20 Did not substitute safer energy: the less hazardous granular solid is not used in the process. (Subjective score assigned=0.4)

43c34 Task procedures do not meet criteria: Written task procedures to limit quantities do not exist. (NOTE - Since the procedures do not exist at all, the contribution to risk is considered to be 1.0)

48b8 Completion criteria LTA: There is no criteria for completion of quantity limitation controls. (Subjective score assigned=0.7)

The MORT items identified above are located as shown in bold face below.

[2c4a] = ([2c2a] x [3d1a])
[2c4b] = ([2c2b] x [3d1b])
[2c4c] = ([2c2c] x [3d1c])
[3b4] = (1-((1-[3c4]) x (1-[3c5]) x (1-[4c6]) x (1-[4c7])))
[4a5] = (1-((1-[4b6]) x (1-[4b7])))
[4a6] = (1-((1-[4b8]) x (1-[5b9]) x (1-[5b10]) x (1-[5b11])))
[5a1] = (1-((1-[5b1]) x (1-[5b2])))
[5b4] = (1-((1-[5c1]) x (1-[6c2])))
[6a1] = (1-((1-[6b1]) x (1-[6b2])))
[7b4] = (1-((1-[7c1]) x (1-[7c2])))
[10c1] = (1-((1-[10d1]) x (1-[10d2]) x (1-[10d3]) x (1-[10d4])))
[10c2] = (1-((1-[10d5]) x (1-[10d6])))
[10c3] = (1-((1-[10d7]) x (1-[11d8])))
[11a2] = (1-((1-[11b3]) x (1-[11b4]) x (1-[11b5]) x (1-[11b6]) x (1-[11b7]) x (1-[12b8]) x (1-[12b9]) x (1-[12b10])))
[11c4] = (1-((1-[11d9]) x (1-[11d10])))
[12a3] = (1-((1-[12b11]) x (1-[12b12]) x (1-[12b13]) x (1-[12b14]) x (1-[12b15])))
[12a4] = (1-((1-[13b16]) x (1-[13b17]) x (1-[13b18]) x (1-[13b19]) x (1-[13b20])))
[14a1] = (1-((1-[14b1]) x (1-[14b2]) x (1-[14b3]) x (1-[14b4]) x (1-[14b5])))
[15b2i] = (1-((1-[15c1i]) x (1-[15c2i]) x (1-[15c3i])))
[15b2m] = (1-((1-[15c1m]) x (1-[15c2m]) x (1-[15c3m])))
[17c2] = (1-((1-[17d1]) x (1-[17d2]) x (1-[17d3]) x (1-[17d4])))
[18c5] = (1-((1-[18d5]) x (1-[18d6]) x (1-[18d7])))
[20e3] = (1-((1-[20f1]) x (1-[20f2]) x (1-[20f3]) x (1-[20f4])))
[21e4] = (1-((1-[21f5]) x (1-[21f6])))
[21f7] = (1-((1-[21g1]) x (1-[21g2]) x (1-[21g3]) x (1-[21g4])))
[22d11] = (1-((1-[22e7]) x (1-[23e8]) x (1-[23e9]) x (1-[23e10]) x (1-[23e11]) x (1-[23e12])))
[22e6] = (1-((1-[22f9]) x (1-[22f10]) x (1-[22f11]) x (1-[22f12])))
[23c11] = (1-((1-[23d12]) x (1-[23d13])))
[24d14] = (1-((1-[24e13]) x (1-[24e14])))
[24d15] = (1-((1-[24e15]) x (1-[24e16]) x (1-[24e17]) x (1-[25e18]) x (1-[25e19])))
[25e22] = (1-((1-[26f13]) x (1-[26f14])))
[27e29] = (1-((1-[27f15]) x (1-[27f16])))
[27e31] = (1-((1-[27f17]) x (1-[27f18]) x (1-[28f19])))
[28b1a] = (1-((1-[29c1a]) x (1-[29c2a]) x (1-[29c3a]) x (1-[29c4a])))
[28b1b] = (1-((1-[29c1c]) x (1-[29c2c]) x (1-[29c3c]) x (1-[29c4c])))
[28b2a] = (1-((1-[29c1b]) x (1-[29c2b]) x (1-[29c3b]) x (1-[29c4b])))
[28b2b] = (1-((1-[29c1d]) x (1-[29c2d]) x (1-[29c3d]) x (1-[29c4d])))
[29b4] = (1-((1-[29c15]) x (1-[29c16]) x (1-[30c17])))
[31a4] = (1-((1-[31b1]) x (1-[31b2]) x (1-[31b3]) x (1-[31b4]) x (1-[31b5])))
[35a6] = (1-((1-[35b1]) x (1-[35b2]) x (1-[35b3]) x (1-[35b4]) x (1-[35b5]) x (1-[35b6]) x (1-[35b7]) x (1-[36b8]) x (1-[36b9])))
[37b1] = (1-((1-[37c1]) x (1-[37c2])))
[37b2] = (1-((1-[37c3]) x (1-[38c4]) x (1-[38c5]) x (1-[38c6]) x (1-[38c7]) x (1-[38c8])))
[38b4] = (1-((1-[38c9]) x (1-[38c10]) x (1-[38c11]) x (1-[39c12]) x (1-[39c13])))
[39b5] = (1-((1-[39c14]) x (1-[39c15])))
[39b6] = (1-((1-[39c16]) x (1-[39c17]) x (1-[39c18]) x (1-[39c19])))
[41c30] = (1-((1-[41d1]) x (1-[41d2]) x (1-[41d3]) x (1-[41d4]) x (1-[41d5])))
[42c31] = (1-((1-[42d6]) x (1-[42d7]) x (1-[42d8]) x (1-[42d9]) x (1-[42d10])))
[43c34] = (1-((1-[43d11]) x (1-[43d12]) x (1-[43d13]) x (1-[43d14]) x (1-[44d15]) x (1-[44d16]) x (1-[44d17]) x (1-[44d18]) x (1-[44d19])))
[45b20] = (1-((1-[45c40]) x (1-[45c41]) x (1-[46c42]) x (1-[46c43]) x (1-[46c44]) x (1-[46c45]) x (1-[46c46]) x (1-[46c47])))
[47a4] = (1-((1-[47b1]) x (1-[47b2]) x (1-[47b3]) x (1-[47b4]) x (1-[47b5])))
[48a5] = (1-((1-[48b6]) x (1-[48b7]) x (1-[48b8])))
[10b1] = (1-((1-[10c1]) x (1-[10c2])))
[10b2] = (1-((1-[10c3]) x (1-[11c4])))
[28a1] = (1-((1-[28b1a]) x (1-[28b2a])))
[29a2] = (1-((1-[28b1b]) x (1-[28b2b])))
[10a1] = (1-((1-[10b1]) x (1-[10b2])))
[28d18] = (1-((1-[ 28a1]) x (1-[29a2])))
[45c39]=[28d18]
[3a4] = (1-((1-[3b3]) x (1-[3b4]) x (1-[4b5])))
[26d17] = (1-((1-[26e24]) x (1-[26e25]) x (1-[26e26]) x (1-[26e27]) x (1-[26e28]) x (1-[27e29]) x (1-[27e30]) x (1-[27e31]) x (1-[28e32])))
[25d16] = (1-((1-[25e20]) x (1-[25e21]) x (1-[25e23]) x (1-[25e22])))
[20d8] = (1-((1-[20e1]) x (1-[20e2]) x (1-[20e3])))
[30SD6] = (1-((1-[30a1]) x (1-[30a2]) x (1-[30a3]) x (1-[31a4]) x (1-[31a5]) x (1-[31a6])))
[13SD2] = (1-((1-[14a1]) x (1-[14a2]) x (1-[14a3]) x (1-[14a4])))
[17b1] = (1-((1-[17c1]) x (1-[17c2]) x (1-[17c3])))
[18b2] = (1-((1-[18c4]) x (1-[18c5]) x (1-[18c6]) x (1-[18c7])))
[15a1m] = (1-((1-[15b1m]) x (1-[15b2m])))
[15a1i] = (1-((1-[15b1i]) x (1-[15b2i])))
[22f8] = (1-((1-[10a1]) x (1-[12a3]) x (1-[11a2]) x (1-[12a4]) x (1-[13a5])))
[9SD1]=[22f8]
[37MB2]=[22f8]
[16a4] = (1-((1-[17b1]) x (1-[18b2])))
[24c14] = (1-((1-[24d14]) x (1-[24d15]) x (1-[25d16]) x (1-[28d18]) x (1-[26d17])))
[21e5] = (1-((1-[21f7]) x (1-[10a1])))
[21d10] = (1-((1-[21e4]) x (1-[22e6]) x (1-[21e5])))
[21c10] = (1-((1-[22d11]) x (1-[21d10])))
[19c9] = (1-((1-[20d8]) x (1-[20d9])))
[19b3] = (1-((1-[19c8]) x (1-[19c9]) x (1-[21c10]) x (1-[23c11]) x (1-[23c12]) x (1-[24c13]) x (1-[24c14])))
[30c18]=[19b3]
[15b3i]=[19b3]
[15b3m]=[19b3]
[3c3a]=[19b3]
[3c3b]=[19b3]
[3c3c]=[19b3]
[30b5] = (1-((1-[30c19]) x (1-[30c18])))
[15a2m] = (1-((1-[15b3m]) x (1-[15b4m]) x (1-[16b5m]) x (1-[16b6m])))
[15a2i] = (1-((1-[15b3i]) x (1-[15b4i]) x (1-[16b5i]) x (1-[16b6i])))
[2b2a] = (1-((1-[2c1a]) x (1-[2c4a]) x (1-[3c3a])))
[2b2b] = (1-((1-[2c1b]) x (1-[2c4b]) x (1-[3c3b])))
[2b2c] = (1-((1-[2c1c]) x (1-[2c4c]) x (1-[3c3c])))
[2a1] = (1-((1-[2b1a]) x (1-[2b2a])))
[3a2] = (1-((1-[2b1b]) x (1-[2b2b])))
[3a3] = (1-((1-[2b1c]) x (1-[2b2c])))
[46b21] = (1-((1-[4a5]) x (1-[2a1]) x (1-[3a2]) x (1-[3a3]) x (1-[3A4]) x (1-[4a6])))
[2SA2] = (1-((1-[46b21])))
[14SD4] = (1-((1-[15a1i]) x (1-[15a2i])))
[14SD3] = (1-((1-[15a1m]) x (1-[15a2m])))
[19a5] = (1-((1-[19b3]) x (1-[29b4]) x (1-[30b5])))
[41b8] = (1-((1-[41c27]) x (1-[41c28]) x (1-[41c29]) x (1-[41c30]) x (1-[42c31])))
[16SD5] = (1-((1-[16a1]) x (1-[16a2]) x (1-[16a3]) x (1-[16a4]) x (1-[19a5])))
[7SC1] = (1-((1-[30SD6]) x (1-[13SD2]) x (1-[16SD5]) x (1-[9SD1]) x (1-[14SD3]) x (1-[14SD4])))
[9c2a] = [19b3]
[9c2b] = [19b3]
[9c2c] = [19b3]
[9c2d] = [19b3]
[8b3a] = (1-((1-[8c1a]) x (1-[9c2a])))
[8b3b] = (1-((1-[8c1b]) x (1-[9c2b])))
[8b3c] = (1-((1-[8c1c]) x (1-[9c2c])))
[8b3d] = (1-((1-[8c1d]) x (1-[9c2d])))
[43b13] = (1-((1-[43c32]) x (1-[43c33]) x (1-[43c34]) x (1-[44c35]) x (1-[44c36]) x (1-[44c37]) x (1-[44c38]) x (1-[45c39])))
[8a1] = (1-((1-[8b1a]) x (1-[8b2a]) x (1-[8b3a])))
[8a2] = (1-((1-[8b1b]) x (1-[8b2b]) x (1-[8b3b])))
[8a3] = (1-((1-[8b1c]) x (1-[8b2c]) x (1-[8b3c])))
[9a4] = (1-((1-[8b1d]) x (1-[8b2d]) x (1-[8b3d])))
[5a2] = (1-((1-[5b3]) x (1-[5b4])))
[7SC2] = (1-((1-[8a1]) x (1-[8a2]) x (1-[8a3]) x (1-[9a4])))
[7a2] = (1-((1-[7b3]) x (1-[7b4])))
[37a1] = (1-((1-[37b1]) x (1-[37b2]) x (1-[38b3]) x (1-[38b4]) x (1-[39b5]) x (1-[39b6])))
[6SB3] = (1-((1-[6a1]) x (1-[7a2])))
[5SB1] = (1-((1-[5a1]) x (1-[5a2])))
[6SB2] = (1-((1-[7SC1]) x (1-[7SC2])))
[9SC3]=[6SB2]
[40c26]=[6SB2]
[40b7] = (1-((1-[40c26]) x (1-[40c20]) x (1-[40c21]) x (1-[40c22]) x (1-[40c23]) x (1-[40c24]) x (1-[40c25])))
[42b9] = [15a1m]
[42b10] = [15a1i]
[40a2] = (1-((1-[42b9]) x (1-[42b10]) x (1-[40b7]) x (1-[42b11]) x (1-[43b12]) x (1-[41b8]) x (1-[43b13]) x (1-[45b14]) x (1-[45b15]) x (1-[45b16]) x (1-[45b17]) x (1-[45b18]) x (1-[45b19]) x (1-[45b20]) x (1-[2SA2])))
[7SB4] = ([5SB1] x [6SB2])
[9SC4] = [7SB4]
[2SA1] = ([5SB1] x [7SB4] x [6SB3])
[37MB3] = (1-((1-[37a1]) x (1-[40a2])))
[48a6] = [30SD6]
[35a6] = [30SD6]
[46MB4] = (1-((1-[47a1]) x (1-[47a2]) x (1-[47a3]) x (1-[47a4]) x (1-[48a5]) x (1-[48a6])))
[32a4] = [10a1]
[37MB2] = [22f8]
[32MA1] = (1-((1-[32a1]) x (1-[32a2]) x (1-[32a3]) x (1-[32a4]) x (1-[33a5]) x (1-[33a6]) x (1-[33a7]) x (1-[33a8]) x (1-[33a9]) x (1-[33a10]) x (1-[34a11])))
[36a10] = [26e24]
[34MA2] = (1-((1-[34a1]) x (1-[34a2]) x (1-[34a3]) x (1-[34a4]) x (1-[34a5]) x (1-[35a6]) x (1-[36a7]) x (1-[36a8]) x (1-[36a9]) x (1-[36a10])))
[36MA3] = (1-((1-[37MB1]) x (1-[37MB2]) x (1-[37MB3]) x (1-[46MB4])))
[1S] = (1-((1-[2SA1]) x (1-[2SA2])))
[32M] = (1-((1-[32MA1]) x (1-[34MA2]) x (1-[36MA3])))
[1S/M] = ([1S] x [32M])
[48R] = (1-((1-[6c2]) x (1-[5b2]) x (1-[6b2]) x (1-[8b1a]) x (1-[8c1a]) x (1-[8b1b]) x (1-[8c1b]) x (1-[8b1c]) x (1-[8c1c]) x (1-[8b1d]) x (1-[8c1d]) x (1-[7c2]) x (1-[20d9]) x (1-[26e24]) x (1-[28f19]) x (1-[4c7])))
[1T] = (1-((1-[1S/M]) x (1-[48R])))

In an investigation of an actual accident or incident, (after the fact), a thorough analysis will consider all basic causal factors in the MORT tree. This is done to identify those system operation factors and management control system factors which were significant contributors to the undesired event. Such an analysis takes place after the occurrence of a specific accident, and therefore if the analysis is conducted reasonably close in time to the accident, it can be considered relevant to that accident and none other (since no other accidents have occurred in that time frame.). If multiple accidents have occurred, such an investigation and analysis will apply to all of them equally.

Assigning values to all of the basic causal factors thus shows the safety posture of the organization. If one or more accidents have already occurred, an analysis of this scope will show the most significant contributors to the accident(s) and the elements of the MORT tree most in need of management concern. If no accidents have occurred, the complete analysis will show the potential for an accident of an unspecified nature. A general idea of the types of accidents which might occur, and their severity and consequences, can be determined by analysis of the basic and subsequent causal factors leading to them.

When analyzing a specific hypothetical accident, however, one must select only those basic causal factors which are relevant to the accident. Such a selection is simply an extension of the subjective assignment of either the probability that the event will occur within a specified time frame, or the extent, from 0 to 100 percent, to which the given condition or event can be assumed to contribute to the accident under consideration. The assignment of a score of zero implies that the the given basic causal factor is not relevant to the accident under discussion, although it may well be relevant to some other accident, or to the overall safety posture of the organization in general.

Most of the foregoing MORT equations contain elements which are not relevant to this particular case. On the other hand, a number of intermediate elements must be defined to determine the computed values for the items of interest. The relevant equations are shown below. To determine which equations are relevant, we need to identify which unknowns in the equation are basic causal factors for which scores have been assigned, and which unknowns are defined by previous equations. The former are in bold face type, and the latter are in italic.

[5a1] = (1-((1-[5b1]) x (1-[5b2])))
[5b4] = (1-((1-[5c1]) x (1-[6c2])))
[6a1] = (1-((1-[6b1]) x (1-[6b2])))
[7b4] = (1-((1-[7c1]) x (1-[7c2])))
[21f7] = (1-((1-[21g1]) x (1-[21g2]) x (1-[21g3]) x (1-[21g4])))
[23c11] = (1-((1-[23d12]) x (1-[23d13])))
[37b1] = (1-((1-[37c1]) x (1-[37c2])))
[38b4] = (1-((1-[38c9]) x (1-[38c10]) x (1-[38c11]) x (1-[39c12]) x (1-[39c13])))
[39b6] = (1-((1-[39c16]) x (1-[39c17]) x (1-[39c18]) x (1-[39c19])))
[48a5] = (1-((1-[48b6]) x (1-[48b7]) x (1-[48b8])))
[26d17] = (1-((1-[26e24]) x (1-[26e25]) x (1-[26e26]) x (1-[26e27]) x (1-[26e28]) x (1-[27e29]) x (1-[27e30]) x (1-[27e31]) x (1-[28e32])))
[30SD6] = (1-((1-[30a1]) x (1-[30a2]) x (1-[30a3]) x (1-[31a4]) x (1-[31a5]) x (1-[31a6])))
[18b2] = (1-((1-[18c4]) x (1-[18c5]) x (1-[18c6]) x (1-[18c7])))
[16a4] = (1-((1-[17b1]) x (1-[18b2])))
[24c14] = (1-((1-[24d14]) x (1-[24d15]) x (1-[25d16]) x (1-[28d18]) x (1-[26d17])))
[21e5] = (1-((1-[21f7]) x (1-[10a1])))
[21d10] = (1-((1-[21e4]) x (1-[22e6]) x (1-[21e5])))
[21c10] = (1-((1-[22d11]) x (1-[21d10])))
[19b3] = (1-((1-[19c8]) x (1-[19c9]) x (1-[21c10]) x (1-[23c11]) x (1-[23c12]) x (1-[24c13]) x (1-[24c14])))
[30c18] = [19b3]
[15b3i] = [19b3]
[15b3m] = [19b3]
[3c3a] = [19b3]
[3c3b] = [19b3]
[3c3c] = [19b3]
[30b5] = (1-((1-[30c19]) x (1-[30c18])))
[15a2m] = (1-((1-[15b3m]) x (1-[15b4m]) x (1-[16b5m]) x (1-[16b6m])))
[15a2i] = (1-((1-[15b3i]) x (1-[15b4i]) x (1-[16b5i]) x (1-[16b6i])))
[2b2a] = (1-((1-[2c1a]) x (1-[2c4a]) x (1-[3c3a])))
[2b2b] = (1-((1-[2c1b]) x (1-[2c4b]) x (1-[3c3b])))
[2b2c] = (1-((1-[2c1c]) x (1-[2c4c]) x (1-[3c3c])))
[2a1] = (1-((1-[2b1a]) x (1-[2b2a])))
[3a2] = (1-((1-[2b1b]) x (1-[2b2b])))
[3a3] = (1-((1-[2b1c]) x (1-[2b2c])))
[46b21] = (1-((1-[4a5]) x (1-[2a1]) x (1-[3a2]) x (1-[3a3]) x (1-[3A4]) x (1-[4a6])))
[2SA2] = (1-((1-[46b21])))
[14SD4] = (1-((1-[15a1i]) x (1-[15a2i])))
[14SD3] = (1-((1-[15a1m]) x (1-[15a2m])))
[19a5] = (1-((1-[19b3]) x (1-[29b4]) x (1-[30b5])))
[16SD5] = (1-((1-[16a1]) x (1-[16a2]) x (1-[16a3]) x (1-[16a4]) x (1-[19a5])))
[7SC1] = (1-((1-[30SD6]) x (1-[13SD2]) x (1-[16SD5]) x (1-[9SD1]) x (1-[14SD3]) x (1-[14SD4])))
[9c2a] = [19b3]
[9c2b] = [19b3]
[9c2c] = [19b3]
[9c2d] = [19b3]
[8b3a] = (1-((1-[8c1a]) x (1-[9c2a])))
[8b3b] = (1-((1-[8c1b]) x (1-[9c2b])))
[8b3c] = (1-((1-[8c1c]) x (1-[9c2c])))
[8b3d] = (1-((1-[8c1d]) x (1-[9c2d])))
[43b13] = (1-((1-[43c32]) x (1-[43c33]) x (1-[43c34]) x (1-[44c35]) x (1-[44c36]) x (1-[44c37]) x (1-[44c38]) x (1-[45c39])))
[8a1] = (1-((1-[8b1a]) x (1-[8b2a]) x (1-[8b3a])))
[8a2] = (1-((1-[8b1b]) x (1-[8b2b]) x (1-[8b3b])))
[8a3] = (1-((1-[8b1c]) x (1-[8b2c]) x (1-[8b3c])))
[9a4] = (1-((1-[8b1d]) x (1-[8b2d]) x (1-[8b3d])))
[5a2] = (1-((1-[5b3]) x (1-[5b4])))
[7SC2] = (1-((1-[8a1]) x (1-[8a2]) x (1-[8a3] x (1-[9a4])))
[7a2] = (1-((1-[7b3]) x (1-[7b4])))
[37a1] = (1-((1-[37b1]) x (1-[37b2]) x (1-[38b3]) x (1-[38b4]) x (1-[39b5]) x (1-[39b6])))
[6SB3] = (1-((1-[6a1]) x (1-[7a2])))
[5SB1] = (1-((1-[5a1]) x (1-[5a2])))
[6SB2] = (1-((1-[7SC1]) x (1-[7SC2])))
[9SC3] = [6SB2]
[40c26] = [6SB2]
[40b7] = (1-((1-[40c26]) x (1-[40c20]) x (1-[40c21]) x (1-[40c22]) x (1-[40c23]) x (1-[40c24]) x (1-[40c25])))
[40a2] = (1-((1-[42b9]) x (1-[42b10]) x (1-[40b7]) x (1-[42b11]) x (1-[43b12]) x (1-[41b8]) x (1-[43b13]) x (1-[45b14]) x (1-[45b15]) x (1-[45b16]) x (1-[45b17]) x (1-[45b18]) x (1-[45b19]) x (1-[45b20]) x (1-[2SA2])))
[7SB4] = ([5SB1] x [6SB2])
[9SC4] = [7SB4]
[2SA1] = ([5SB1] x [7SB4] x [6SB3])
[37MB3] = (1-((1-[37a1]) x (1-[40a2])))
[48a6] = [30SD6]
[35a6] = [30SD6]
[46MB4] = (1-((1-[47a1]) x (1-[47a2]) x (1-[47a3]) x (1-[47a4]) x (1-[48a5]) x (1-[48a6])))
[32MA1] = (1-((1-[32a1]) x (1-[32a2]) x (1-[32a3]) x (1-[32a4]) x (1-[33a5]) x (1-[33a6]) x (1-[33a7]) x (1-[33a8]) x (1-[33a9]) x (1-[33a10]) x (1-[34a11])))
[36a10] = [26e24]
[34MA2] = (1-((1-[34a1]) x (1-[34a2]) x (1-[34a3]) x (1-[34a4]) x (1-[34a5]) x (1-[35a6]) x (1-[36a7]) x (1-[36a8]) x (1-[36a9]) x (1-[36a10])))
[36MA3] = (1-((1-[37MB1]) x (1-[37MB2]) x (1-[37MB3]) x (1-[46MB4])))
[1S] = (1-((1-[2SA1]) x (1-[2SA2])))
[32M] = (1-((1-[32MA1]) x (1-[34MA2]) x (1-[36MA3])))
[1S/M] = ([1S] x [32M])
[48R] = (1-((1-[6c2]) x (1-[5b2]) x (1-[6b2]) x (1-[8b1a]) x (1-[8c1a]) x (1-[8b1b]) x (1-[8c1b]) x (1-[8b1c]) x (1-[8c1c]) x (1-[8b1d]) x (1-[8c1d]) x (1-[7c2]) x (1-[20d9]) x (1-[26e24]) x (1-[28f19]) x (1-[4c7])))
[1T] = (1-((1-[1S/M]) x (1-[48R])))

Basic causal factors which are not considered significant contributors to this hazard are set equal to zero. Any basic causal factor which is zero results in a factor of 1 in an OR equation and a product of zero in an AND equation. This allows simplification of the equations containing these factors, and elimination of equations which equal zero. The result of this process of elimination is the set of equations shown below.

[5a1] = (1-((1-[5b1]) x (1-[5b2])))
[5b4] = [6c2]
[6a1] = (1-((1-[6b1]) x (1-[6b2])))
[7b4] = [7c2]
[21f7] = [21g4]
[23c11] = [23d12]
[37b1] = [37c1]
[38b4] = (1-((1-[38c10]) x (1-[39c13])))
[39b6] = [39c17]
[48a5] = [48b8]
[26d17] = (1-((1-[26e24]) x (1-[26e27])))
[30SD6] = [30a3]
[18b2] = [18c7]
[16a4] = [18b2]
[24c14] = [26d17]
[21e5] = [21f7]
[21d10] = [21e5]
[21c10] = [21d10]
[19b3] = (1-((1-[21c10]) x (1-[23c11]) x (1-[24c14])))
[30c18] = [19b3]
[15b3i] = [19b3]
[15b3m] = [19b3]
[3c3a] = [19b3]
[3c3b] = [19b3]
[3c3c] = [19b3]
[30b5] = [30c18]
[15a2m] = [15b3m]
[15a2i] = [15b3i]
[2b2a] = [3c3a]
[2b2b] = [3c3b]
[2b2c] = [3c3c]
[2a1] = [2b2a]
[3a2] = [2b2b]
[3a3] = [2b2c]
[46b21] = (1-((1-[2a1]) x (1-[3a2]) x (1-[3a3])))
[2SA2] = [46b21]
[14SD4] = [15a2i]
[14SD3] = [15a2m]
[19a5] = (1-((1-[19b3]) x (1-[30b5])))
[16SD5] = (1-((1-[16a4]) x (1-[19a5])))
[7SC1] = (1-((1-[30SD6]) x (1-[16SD5]) x (1-[14SD3]) x (1-[14SD4])))
[9c2a] = [19b3]
[9c2b] = [19b3]
[9c2c] = [19b3]
[9c2d] = [19b3]
[8b3a] = [9c2a]
[8b3b] = (1-((1-[8c1b]) x (1-[9c2b])))
[8b3c] = (1-((1-[8c1c]) x (1-[9c2c])))
[8b3d] = [9c2d]
[43b13] = [43c34]
[8a1] = (1-((1-[8b2a]) x (1-[8b3a])))
[8a2] = [8b3b]
[8a3] = [8b3c]
[9a4] = (1-((1-[8b1d]) x (1-[8b3d])))
[5a2] = [5b4]
[7SC2] = (1-((1-[8a1]) x (1-[8a2]) x (1-[8a3]) x (1-[9a4])))
[7a2] = (1-((1-[7b3]) x (1-[7b4])))
[37a1] = (1-((1-[37b1]) x (1-[38b4]) x (1-[39b6])))
[6SB3] = (1-((1-[6a1]) x (1-[7a2])))
[5SB1] = (1-((1-[5a1]) x (1-[5a2])))
[6SB2] = (1-((1-[7SC1]) x (1-[7SC2])))
[9SC3] = [6SB2]
[40c26] = [6SB2]
[40b7] = (1-((1-[40c26]) x (1-[40c20])))
[40a2] = (1-((1-[40b7]) x (1-[41b8]) x (1-[43b13]) x (1-[2SA2])))
[7SB4] = ([5SB1] x [6SB2])
[9SC4] = [7SB4]
[2SA1] = ([5SB1] x [7SB4] x [6SB3])
[37MB3] = (1-((1-[37a1]) x (1-[40a2])))
[48a6] = [30SD6]
[35a6] = [30SD6]
[46MB4] = (1-((1-[48a5]) x (1-[48a6])))
[32MA1] = (1-((1-[32a3]) x (1-[33a5]) x (1-[33a7])))
[36a10] = [26e24]
[34MA2] = [36a10]
[36MA3] = (1-((1-[37MB3]) x (1-[46MB4])))
[1S] = (1-((1-[2SA1]) x (1-[2SA2])))
[32M] = (1-((1-[32MA1]) x (1-[34MA2]) x (1-[36MA3])))
[1S/M] = ([1S] x [32M])
[48R] = (1-((1-[6c2]) x (1-[5b2]) x (1-[6b2]) x (1-[8c1b]) x (1-[8c1c]) x (1-[8b1d]) x (1-[7c2]) x (1-[26e24])))
[1T] = (1-((1-[1S/M]) x (1-[48R])))

The independent variables are those to which subjective scores have been assigned:

5b1 Inadequate control on condition: Drums can be delivered too soon or picked up too late. (Score=0.1)

5b2 Impracticability of control: Drums are not delivered "just in time," but by a schedule convenient to the vendor. (Score=0.1)

6b1 Inadequate control of nonfunctional vulnerable people: Visitors to the plant are not normally briefed on the evacuation plan. (Score=0.2)

6b2 Impracticability of control of nonfunctional vulnerable people: It is not practical to exclude the public from the plant site. (Score=0.2)

6c2 Diversion impractical: Effective diversion of leaking liquid is not possible. (Score=0.3)

7b3 Administrative controls LTA: Notification of a leak to the retirement community may be untimely or may not allow sufficient time for evacuation. (Score=0.2)

7c2 Evasion impractical: The retirement community is located adjacent to the plant boundary. (Score=0.3)

8b1d Separation impossible: It is not practical to separate workers from the site of the process. (Score=0.1)

8b2a Barrier failure: Leak is possible due to loss of system integrity. (Score=0.1)

8c1b Barriers not provided: Low probability of leak does not justify expense of additional barriers. (Score=0.2)

8c1c Barrier not provided: There is no established requirement for the workers to use PPE. (Score=0.1)

18c7 Supervisory judgment: Management decision to use the highly hazardous liquid in lieu of the non-hazardous granular solid. (Score=0.3)

21g4 Employee suggestion not used: Suggestion to use the less hazardous material was not implemented. (Score=0.3)

23d12 Safety analysis controls not used: a highly hazardous liquid is used instead of a non-hazardous solid. (Score=0.3)

26e24 Management concern, vigor and example LTA: In this case, management did not demonstrate sufficient concern for hazardous liquid release. (Score=0.4)

26e27 Nonperformance is rewarding: Worker objection to use of more safe product was supported by higher management. (Score=0.2)

30a3 Standards & directives LTA: No written standard exists for quantity limitation. (Score=0.4)

32a3 Policies not based on adequate risk assessment: The risk of potential injury and the consequences of unfavorable public reaction to a leak do not appear to justify the management decision. (Score=0.4)

33a5 Conformance to codes, standards & regulations LTA: Decision does not fulfill the hazard reduction precedence sequence established by its internal procedures. (Score=0.6)

33a7 Policies not consistent: The decision to continue to use the highly hazardous liquid is not consistent with the plant manager's stated safety philosophy. (Score=0.6)

37c1 Safety goals and risks not defined: This decision demonstrates an inadequate definition of process safety goals. (Score=0.3)

38c10 OSHA regulations not adequately called out: Insufficient consideration of 29 CFR 1910.119. (Score=0.6)

39c13 Internal standards LTA: Violation of company safety precedence sequence. (Score=0.6)

39c17 Analysis of environmental impact LTA: Inadequate consideration of potential release consequences. (Score=0.6)

40c20 Did not substitute safer energy: the less hazardous granular solid is not used in the process. (Score=0.4)

43c34 Task procedures do not meet criteria: Written task procedures to limit quantities do not exist. (NOTE - Since the procedures do not exist at all, the contribution to risk is considered to be 1.0)

48b8 Completion criteria LTA: There is no criteria for completion of quantity limitation controls. (Score=0.7)

Substituting the values assigned to the input factors into the equation generates numerical solutions for the items for which the score was to be determined by the MORT analysis. The scores all fall between zero and one, inclusive, with larger numbers indicating proportionately greater risk.

1T Top Event: Accidental release of hazardous liquid into the atmosphere, with consequent potential for injury to exposed persons and unfavorable publicity for the company. (Score=0.99843)

5a1 Nonfunctional environmental condition: Stored filled drums awaiting use or nominally empty drums awaiting pickup. (Score=0.19)

5a2 Functional environmental condition: Drums containing pressurized liquid connected to the process system. (Score=0.3)

5SB1 Potentially harmful environmental condition: hazardous liquid under pressure is a potential toxicity source. (Score=0.433)

6a1 Nonfunctional vulnerable people: Retirement community & the public. (Score=0.36)

6SB3 Vulnerable people: Workers, residents of the retirement community and the public. (Score=0.6416)

7a2 Functional vulnerable people: Workers and official visitors. (Score=0.44)

7SB4 Events & energy flows: Potential for leak of highly hazardous liquid into atmosphere. (Score=0.433)

8a1 Barriers ON the energy source: Drums and piping. (Score=0.78832)

8a2 Barriers BETWEEN the energy source: Isolated storage and use facility. (Score=0.81184)

8a3 Barriers ON persons: Personal Protective Equipment is available, but is not normally used to the small likelihood of a hazardous leak. (Score=0.78832)

9a4 Barriers in TIME or SPACE: Workers can evacuate the area if a leak is detected. (Score=0.78832)

9c2a Task performance errors System not properly operated. (Score=0.7648)

The numerical evaluation of the MORT cut sets generates intermediate numerical products which are events or conditions which were not initially considered, but which the analysis shows have a numerical score which can be interpreted as an indicator of the need for management concern. These intermediate items, not previously identified as candidates for consideration, are:

1S Specific controls factors overlooked or omitted. (Score=0.9885542)

1S/M Management oversights or omissions. (Score=0.9885542)

2a1 Inadequate likelihood of prevention of injuries after leak occurs. (Score=0.7648)

2b2a Potential for inadequate second accident prevention activities. (Score=0.7648)

2b2b Potential for inadequate execution of emergency action activities. (Score=0.7648)

2b2c Potential for inadequate execution of rescue activities. (Score=0.7648)

2SA1 Likelihood of accident. (Score=0.1202929)

2SA2 Likelihood of ameliorative activity inadequacies. (Score=0.986989)

3a2 Inadequate emergency response effectiveness posture. (Score=0.7648)

3a3 Inadequate rescue effectiveness posture. (Score=0.7648)

3c3a Contribution of task performance errors to ameliorative activities. (Score=0.7648)

3c3b Contribution of task performance errors to emergency response activities. (Score=0.7648)

3c3c Contribution of task performance errors to rescue activities. (Score=0.7648)

5b4 Inability to divert energy flow. (Score=0.3)

7b4 Inadequate evasive action in the event of leak. (Score=0.3)

7SC1 Control inadequacies. (Score=0.9987148)

7SC2 Barrier inadequacies. (Score=0.9982154)

8b3a Barriers on energy source not used. (Score=0.7648)

8b3b Barriers between vulnerable people and objects and energy source not used. (Score=0.81184)

8b3c Barriers on vulnerable people and objects are not used. (Score=0.78832)

8b3d Barriers in time and space not used. (Score=0.7648)

9c2b Task performance errors in employment of barriers between people and source. (Score=0.7648)

9c2c Task performance errors in employment of barriers on vulnerable persons. (Score=0.7648)

9c2d Task performance errors in separation of vulnerable people from leak in time or space. (Score=0.7648)

9SC3 Barrier and control inadequacies . (Score=1.0)

9SC4 Potential for undesired events and energy flows. (Score=0.433)

14SD3 Inadequate maintenance. (Score=0.7648)

14SD4 Inadequate inspection(s). (Score=0.7648)

15a2i Inadequate execution of inspection activities. (Score=0.7648)

15a2m Inadequate execution of maintenance activities. (Score=0.7648)

15b3i Inspection task performance errors. (Score=0.7648)

15b3m Maintenance task performance errors. (Score=0.7648)

16a4 Supervisory failures to detect or correct hazards. (Score=0.3)

16SD5 Supervision inadequacies. (Score=0.9612767)

18b2 Failure of supervision/management to correct known hazards. (Score=0.3)

19a5 Potential for work level performance errors. (Score=0.944681)

19b3 Potential for specific task performance errors. (Score=0.7648)

21c10 Inadequate task safety analysis. (Score=0.3)

21d10 Inadequate task safety analysis preparation. (Score=0.3)

21e5 Inadequate task safety analysis knowledge. (Score=0.3)

21f7 Inadequate employee suggestion inputs. (Score=0.3)

23c11 Failure to use safety analysis recommended controls. (Score=0.3)

24c14 Personnel performance discrepancies. (Score=0.52)

26d17 Inadequate employee motivation. (Score=0.52)

30b5 Potential for emergency shutoff errors. (Score=0.7648)

30c18 Emergency shutoff task performance errors. (Score=0.7648)

30SD6 Inadequate higher supervision services. (Score=0.4)

32M Inadequate management system factors. (Score=1.0)

32MA1 Inadequate policies. (Score=0.904)

34MA2 Inadequate policy implementation. (Score=0.4)

35a6 Inadequate management services. (Score=0.4)

36a10 Management concern, vigor and example LTA. (Score=0.4)

36MA3 Risk assessment system inadequacies. (Score=1.0)

37a1 Hazard analysis process concept and requirement inadequacies. (Score=0.9552)

37b1 Inadequate definition of goals and tolerable risks. (Score=0.3)

37MB3 Hazard analysis process inadequacies. (Score=1.0)

38b4 Inadequate specification of safety requirements. (Score=0.84)

39b6 Inadequate analysis of system life cycle. (Score=0.6)

40a2 Inadequate design and development plan. (Score=1.0)

40b7 Inadequate energy control procedures. (Score=1.0)

40c26 Inadequate barriers and controls. (Score=1.0)

43b13 Inadequate operational specifications. (Score=1.0)

46b21 Inadequate amelioration plan. (Score=0.986989)

46MB4 Program review inadequacies. (Score=0.82)

48a5 Block function and work schematic inadequacies. (Score=0.7)

48a6 Environmental, safety and quality program inadequacies. (Score=0.4)

48R Management decision to accept risks. (Score=0.8628314)

The equations defined by the MORT logic establish strict mathematical probabilities only if the scores assigned to the basic causal factors (including those assigned a score of zero) are valid, and then only if the logic is valid. Neither of these conditions can be demonstrated. While the MORT logic is reasonable, the evolution of the tree over the years demonstrates that accident causality analysis is not an exact science. In addition, the assignment of scores to the basic causal factors is highly subjective. The scores which result from the MORT analysis are therefore influenced both by subjectivity and imprecision of the causal relationships which are assumed for the analysis.

Nevertheless, the scores arrived at by use of the MORT tree determine a unique score assigned to each event which is a mathematical function of the assigned scores. Each of these unique scores may be interpreted (loosely) as the probability of occurrence of undesired events during the time frame for which the scores for the basic causal factors are valid, or else the contribution of intermediate events to the top undesired event, which is accidental release of hazardous liquid into the atmosphere, with consequent potential for injury to exposed persons and unfavorable publicity for the company (1T). The score for this event of 0.99843 indicates that such an event, if it occurs, is highly undesirable.

Other events may be interpreted as follows:

Elements 9SC3 (Barrier and control inadequacies), 43b13 (Inadequate operational specifications), 40c26 (Inadequate barriers and controls), 40b7 (Inadequate energy control procedures), 40a2 (Inadequate design and development plan), 37MB3 (Hazard analysis process inadequacies), 36MA3 (Risk assessment system inadequacies), and 32M (Inadequate management system factors) all have a score of 1.0. Taken together, these elements indicate a serious lack of management control on this hazard.

Elements 7SC2 (Barrier inadequacies) (Score=0.9982154), and 7SC1 Control inadequacies) (Score=0.9987148), indicate that the most serious contributors to the undesirability of the top event are lack of control on the highly hazardous liquid. The most serious management concerns are:

1S/M Management oversights or omissions (Score=0.9885542),

1S Specific controls factors overlooked or omitted (Score=0.9885542),

46b21 Inadequate amelioration plan (Score=0.986989),

2SA2 Likelihood of ameliorative activity inadequacies (Score=0.986989),

16SD5 Supervision inadequacies (Score=0.9612767),

37a1 Hazard analysis process concept and requirement inadequacies (Score=0.9552),

19a5 Potential for work level performance errors (Score=0.944681), and

32MA1 Inadequate policies (Score=0.904).

Of slightly less concern, but still significant from a management standpoint, are the following items, which indicate a need for an increase in management appreciation for the possible risks associated with release of the highly hazardous liquid:

48R Management decision to accept risks (Score=0.8628314)

38b4 Inadequate specification of safety requirements (Score=0.84)

46MB4 Program review inadequacies (Score=0.82)

8b3b Barriers between vulnerable people and objects and energy source not used (Score=0.81184)

8a2 Barriers BETWEEN the energy source: Isolated storage and use facility (Score=0.81184)

The following indicate a need for improvement in the reliability of the process containment and the need for improvement in lower tier supervision and worker task performance:

9a4 Barriers in TIME or SPACE: Workers can evacuate the area if a leak is detected (Score=0.78832)

8b3c Barriers on vulnerable people and objects are not used (Score=0.78832)

8a3 Barriers ON persons: Personal Protective Equipment is available, but is not normally used to the small likelihood of a hazardous leak (Score=0.78832)

8a1 Barriers ON the energy source: Drums and Piping (Score=0.78832)

9c2d Task performance errors in separation of vulnerable people from leak in time or space (Score=0.7648)

9c2c Task performance errors in employment of barriers on vulnerable persons (Score=0.7648)

9c2b Task performance errors in employment of barriers between people and source (Score=0.7648)

9c2a Task performance errors System not properly operated (Score=0.7648)

8b3d Barriers in time and space not used (Score=0.7648)

8b3a Barriers on energy source not used (Score=0.7648)

3c3c Contribution of task performance errors to rescue activities (Score=0.7648)

3c3b Contribution of task performance errors to emergency response activities (Score=0.7648)

3c3a Contribution of task performance errors to ameliorative activities (Score=0.7648)

3a3 Inadequate rescue effectiveness posture (Score=0.7648)

3a2 Inadequate emergency response effectiveness posture (Score=0.7648)

30c18 Emergency shutoff task performance errors (Score=0.7648)

30b5 Potential for emergency shutoff errors (Score=0.7648)

2b2c Potential for inadequate execution of rescue activities (Score=0.7648)

2b2b Potential for inadequate execution of emergency action activities (Score=0.7648)

2b2a Potential for inadequate second accident prevention activities (Score=0.7648)

2a1 Inadequate likelihood of prevention of injuries after leak occurs (Score=0.7648)

19b3 Potential for specific task performance errors (Score=0.7648)

15b3m Maintenance task performance errors (Score=0.7648)

15b3i Inspection task performance errors (Score=0.7648)

15a2m Inadequate execution of maintenance activities (Score=0.7648)

15a2i Inadequate execution of inspection activities (Score=0.7648)

14SD4 Inadequate inspection(s) (Score=0.7648)

14SD3 Inadequate maintenance (Score=0.7648)

48a5 Block function and work schematic inadequacies (Score=0.7)

The score of 0.6416 for element 6SB3, (Vulnerable people: Workers, residents at the retirement community and the public), suggests that improvements might be made in personnel access. While it is probably not reasonable to restrict workers from the hazardous liquid storage area, relocation of the retirement community and restriction of public access are factors over which management may have more discretion.

The score of 0.6 for element 39b6 (Inadequate analysis of system life cycle) suggests that thought should be given to reanalyzing the process to determine if safety improvements should be made.

The score of 0.52 for element 26d17 (Inadequate employee motivation) suggests that not taking the employee's suggestion, which is valid as far as safety is concerned, might be a demotivating factor.

Also, the same score for element 24c14 (Personnel performance discrepancies) suggests that potential failure of workers to perform their jobs properly may be a cause for management concern.

The following scores do not indicate the need for drastic improvement, but a need for increased management attention, and possible imposition of a method for tracking these elements to permit timely awareness of any increase in their contribution to overall risk.

7a2 Functional vulnerable people: Workers and official visitors (Score=0.44)

9SC4 Potential for undesired events and energy flows (Score=0.433)

7SB4 Events & energy flows: Potential for leak of highly hazardous liquid into atmosphere (Score=0.433)

5SB1 Potentially harmful environmental condition: highly hazardous liquid under pressure is a potential toxicity source (Score=0.433)

48a6 Environmental, safety and quality program inadequacies (Score=0.4)

35a6 Inadequate management services (Score=0.4)

36a10 Management concern, vigor and example LTA (Score=0.4)

34MA2 Inadequate policy implementation (Score=0.4)

30SD6 Inadequate higher supervision services (Score=0.4)

6a1 Nonfunctional vulnerable people: Retirement community & the public (Score=0.36)

7b4 Inadequate evasive action in the event of leak (Score=0.3)

5b4 Inability to divert energy flow (Score=0.3)

5a2 Functional environmental condition: Drums containing pressurized highly hazardous liquid connected to the process system (Score=0.3)

37b1 Inadequate definition of goals and tolerable risks (Score=0.3)

23c11 Failure to use safety analysis recommended controls (Score=0.3)

21f7 Inadequate employee suggestion inputs (Score=0.3)

21e5 Inadequate task safety analysis knowledge (Score=0.3)

21d10 Inadequate task safety analysis preparation (Score=0.3)

21c10 Inadequate task safety analysis (Score=0.3)

18b2 Failure of supervision/management to correct known hazards (Score=0.3)

16a4 Supervisory failures to detect or correct hazards (Score=0.3)

As expected, element 5a1 (Nonfunctional environmental condition: Stored filled drums awaiting use or nominally empty drums awaiting pickup) (Score=0.19) is not a significant contributor to the risk of a leak. The drums are least likely to leak when they are not connected to anything.

What is perhaps surprising is that element 2SA1 (Likelihood of accident) has a score of only 0.1202929. This may be interpreted as showing that the main problem here is not the likelihood of an accident, which is small, but the management environment which permits the risk to exist in light of a possibility of implementing the safer alternative. This environment may subject the company to severe public criticism, as well as possible OSHA violation penalties and litigation, if an accident occurs. These are precisely the MORT elements which have been determined to have a score of 0.9 or greater. The descriptions of these elements are almost word for word what might be contained in a legal indictment of the company for negligence if an accident with significant public impact does occur. It is up to management to decide if the low probability of the accident occurrence justifies the risk of its potential consequences.

As a continuation of the hypothetical example, we assume that the safety manager has presented the foregoing analysis to management and has pointed out the conclusions noted above. As a result, management has decided to establish and implement a procedure which requires that drums be delivered containing not more than 1999 pounds of liquid. This reduces the amount of liquid in any one drum to below the threshold quantity for process safety management defined in 29 CFR 1910.119. The situation here is that management has recognized and corrected what could become a perception on the part of public and OSHA inspectors (as well as their lawyers) that compliance with 29 CFR 1910.119 has not received sufficient management attention. Correction of this perception changes the scores assigned to the following basic causal factors:

26e24 Management concern, vigor and example LTA: The imposition of quantity limitation controls demonstrates a greater management concern for hazardous liquid release, which changes the score from 0.4 to 0.2.

30a3 Standards & directives LTA: The written standard for quantity limitation changes this score from 0.4 to zero.

37c1 Safety goals and risks not defined: This decision demonstrates a somewhat more adequate definition of process safety goals, changing the score from 0.3 to 0.2

38c10 OSHA regulations not adequately called out: The imposition of quantity limitation controls demonstrates increased consideration of 29 CFR 1910.119. The score in this case is reduced from 0.6 to 0.3

43c34 Task procedures do not meet criteria: The contribution to risk was considered to be 1.0 because task procedures to limit quantities did not exist at all. Imposition of these procedures effectively reduces this score to zero.

48b8 Completion criteria LTA: The criteria for completion of quantity limitation controls reduces this score also to zero.

The other scores stay the same.

5b1 Inadequate control on condition: Drums can be delivered too soon or picked up too late. (Score=0.1)

5b2 Impracticability of control: Drums are not delivered "just in time," but by a schedule convenient to the vendor. (Score=0.1)

6b1 Inadequate control of nonfunctional vulnerable people: Visitors to the plant are not normally briefed on the evacuation plan. (Score=0.2)

6b2 Impracticability of control of nonfunctional vulnerable people: It is not practical to exclude the public from the plant site. (Score=0.2)

6c2 Diversion impractical: Effective diversion of leaking liquid is not possible. (Score=0.3)

7b3 Administrative controls LTA: Notification of a leak to the retirement community may be untimely or may not allow sufficient time for evacuation. (Score=0.2)

7c2 Evasion impractical: The retirement community is located adjacent to the plant boundary. (Score=0.3)

8b1d Separation impossible: It is not practical to separate workers from the site of the process. (Score=0.1)

8b2a Barrier failure: Leak possible due to loss of system integrity. (Score=0.1)

8c1b Barriers not provided: Low probability of leak does not justify expense of additional barriers. (Score=0.2)

8c1c Barrier not provided: There is no established requirement for the workers to use PPE. (Score=0.1)

18c7 Supervisory judgment: Management decision to use the highly hazardous liquid in lieu of the non-hazardous granular solid. (Score=0.3)

21g4 Employee suggestion not used: Suggestion to use the less hazardous material was not implemented. (Score=0.3)

23d12 Safety analysis controls not used: a highly hazardous liquid is used instead of a non-hazardous solid. (Score=0.3)

26e27 Nonperformance is rewarding: Worker objection to use of more safe product was supported by higher management. (Score=0.2)

32a3 Policies not based on adequate risk assessment: The risk of potential injury and the consequences of unfavorable public reaction to a leak do not appear to justify the management decision. (Score=0.4)

33a5 Conformance to codes, standards & regulations LTA: Decision does not fulfill the hazard reduction precedence sequence established by its internal procedures. (Score=0.6)

33a7 Policies not consistent: The decision to continue to use the highly hazardous liquid is not consistent with the plant manager's stated safety philosophy. (Score=0.6)

39c13 Internal standards LTA: Violation of company safety precedence sequence. (Score=0.6)

39c17 Analysis of environmental impact LTA: Inadequate consideration of potential release consequences. (Score=0.6)

40c20 Did not substitute safer energy: the less hazardous granular solid is not used in the process. (Score=0.4)

Substituting the newer values assigned to the input factors into the equation generates new solutions for some of the equations. The input and computed values for the new equations are:

Reduction in the risk defined by the assigned values of the basic causal factors results in a reduction in the risk associated with most of the events in the MORT tree, as noted below. The greatest reduction in risk is associated with those elements which are most affected by the removal of the 29 CFR 1910.119 process safety management requirement on the quaintly of highly hazardous liquid. In no case is a risk associated with any element in the tree increased. The differences in the scores determined by the foregoing equations are:

1T Top Event: Accidental release of hazardous liquid into the atmosphere, with consequent potential for injury to exposed persons and unfavorable publicity for the company. (Score is reduced from 0.99843 to 0.995038.)

1S Specific controls factors overlooked or omitted. (Score is reduced from 0.9885542 to 0.9728691.)

1S/M Management oversights or omissions. (Score is reduced from 0.9885542 to 0.9728691.)

2a1 Inadequate likelihood of prevention of injuries after leak occurs. (Score is reduced from 0.7648 to 0.6864.)

2b2a Potential for inadequate second accident prevention activities. (Score is reduced from 0.7648 to 0.6864.)

2b2b Potential for inadequate execution of emergency action activities. (Score is reduced from 0.7648 to 0.6864.)

2b2c Potential for inadequate execution of rescue activities. (Score is reduced from 0.7648 to 0.6864.)

2SA2 Likelihood of ameliorative activity inadequacies. (Score is reduced from 0.986989 to 0.9691591.)

3a2 Inadequate emergency response effectiveness posture. (Score is reduced from 0.7648 to 0.6864.)

3a3 Inadequate rescue effectiveness posture. (Score is reduced from 0.7648 to 0.6864.)

3c3a Contribution of task performance errors to ameliorative activities. (Score is reduced from 0.7648 to 0.6864.)

3c3b Contribution of task performance errors to emergency response activities. (Score is reduced from 0.7648 to 0.6864.)

3c3c Contribution of task performance errors to rescue activities. (Score is reduced from 0.7648 to 0.6864.)

7SC1 Control inadequacies. (Score is reduced from 0.9987148 to 0.9932299.)

7SC2 Barrier inadequacies. (Score is reduced from 0.9982154 to 0.9943595.)

8a1 Barriers ON the energy source: Drums and Piping. (Score is reduced from 0.78832 to 0.71776.)

8a2 Barriers BETWEEN the energy source: Isolated storage and use facility. (Score is reduced from 0.81184 to 0.74912.)

8a3 Barriers ON persons: Personal Protective Equipment is available, but is not normally used to the small likelihood of a hazardous leak. (Score is reduced from 0.78832 to 0.71776.)

8b3a Barriers on energy source not used. (Score is reduced from 0.7648 to 0.6864.)

8b3b Barriers between vulnerable people and objects and energy are not used. (Score is reduced from 0.81184 to 0.74912.)

8b3c Barriers on vulnerable people and objects are not used. (Score is reduced from 0.78832 to 0.71776.)

8b3d Barriers in time and space not used. (Score is reduced from 0.7648 to 0.6864.)

9a4 Barriers in TIME or SPACE: Workers can evacuate the area if a leak is detected. (Score is reduced from 0.78832 to 0.71776.)

9c2a Task performance errors System not properly operated. (Score is reduced from 0.7648 to 0.6864.)

9c2b Task performance errors in employment of barriers between people and source. (Score is reduced from 0.7648 to 0.6864.)

9c2c Task performance errors in employment of barriers on vulnerable persons. (Score is reduced from 0.7648 to 0.6864.)

9c2d Task performance errors in separation of vulnerable people from leak in time or space. (Score is reduced from 0.7648 to 0.6864.)

14SD3 Inadequate maintenance. (Score is reduced from 0.7648 to 0.6864.)

14SD4 Inadequate inspection(s). (Score is reduced from 0.7648 to 0.6864.)

15a2i Inadequate execution of inspection activities. (Score is reduced from 0.7648 to 0.6864.)

15a2m Inadequate execution of maintenance activities. (Score is reduced from 0.7648 to 0.6864.)

15b3i Inspection task performance errors. (Score is reduced from 0.7648 to 0.6864.)

15b3m Maintenance task performance errors. (Score is reduced from 0.7648 to 0.6864.)

16SD5 Supervision inadequacies. (Score is reduced from 0.9612767 to 0.9311586.)

19a5 Potential for work level performance errors. (Score is reduced from 0.944681 to 0.9016551.)

19b3 Potential for specific task performance errors. (Score is reduced from 0.7648 to 0.6864.)

24c14 Personnel performance discrepancies. (Score is reduced from 0.52 to 0.36.)

26d17 Inadequate employee motivation. (Score is reduced from 0.52 to 0.36.)

30b5 Potential for emergency shutoff errors. (Score is reduced from 0.7648 to 0.6864.)

30c18 Emergency shutoff task performance errors. (Score is reduced from 0.7648 to 0.6864.)

30SD6 Inadequate higher supervision services. (Score is reduced from 0.4 to zero.)

34MA2 Inadequate policy implementation. (Score is reduced from 0.4 to 0.2.)

35a6 Inadequate management services. (Score is reduced from 0.4 to zero.)

36a10 Management concern, vigor and example LTA. (Score is reduced from 0.4 to 0.2.)

37a1 Hazard analysis process concept and requirement inadequacies. (Score is reduced from 0.9552 to 0.9104.)

37b1 Inadequate definition of goals and tolerable risks. (Score is reduced from 0.3 to 0.2.)

38b4 Inadequate specification of safety requirements. (Score is reduced from 0.84 to 0.72.)

43b13 Inadequate operational specifications. (Score is reduced from 1.0 to zero.)

46b21 Inadequate amelioration plan. (Score is reduced from 0.986989 to 0.9691591.)

46MB4 Program review inadequacies. (Score is reduced from 0.82 to zero.)

48a5 Block function and work schematic inadequacies. (Score is reduced from 0.7 to zero.)

48a6 Environmental, safety and quality program inadequacies. (Score is reduced from 0.4 to zero.)

48R Management decision to accept risks. (Score is reduced from 0.8628314 to 0.8171085.)

Not surprisingly, the imposition of quantity controls on the liquid containers does not affect the following elements.

2SA1 Likelihood of accident. (Score remains 0.1202929.)

5a1 Nonfunctional environmental condition: Stored filled drums awaiting use or nominally empty drums awaiting pickup. (Score remains 0.19.)

5a2 Functional environmental condition: Drums containing pressurized liquid connected to the process system. (Score remains 0.3.)

5b4 Inability to divert energy flow. (Score remains 0.3.)

5SB1 Potentially harmful environmental condition: hazardous liquid under pressure is a potential toxicity source. (Score remains 0.433.)

6a1 Nonfunctional vulnerable people: Retirement community & the public. (Score remains 0.36.)

6SB3 Vulnerable people: Workers, residents of the retirement community and the public. (Score remains 0.6416.)

7a2 Functional vulnerable people: Workers and official visitors. (Score remains 0.44.)

7b4 Inadequate evasive action in the event of leak. (Score remains 0.3.)

7SB4 Events & energy flows: Potential for leak of highly hazardous liquid into atmosphere. (Score remains 0.433.)

9SC3 Barrier and control inadequacies . (Score remains 1.0.)

9SC4 Potential for undesired events and energy flows. (Score remains 0.433.)

16a4 Supervisory failures to detect or correct hazards. (Score remains 0.3.)

18b2 Failure of supervision/management to correct known hazards. (Score remains 0.3.)

21c10 Inadequate task safety analysis. (Score remains 0.3.)

21d10 Inadequate task safety analysis preparation. (Score remains 0.3.)

21e5 Inadequate task safety analysis knowledge. (Score remains 0.3.)

21f7 Inadequate employee suggestion inputs. (Score remains 0.3.)

23c11 Failure to use safety analysis recommended controls. (Score remains 0.3.)

32M Inadequate management system factors. (Score remains 1.0.)

32MA1 Inadequate policies. (Score remains 0.904.)

36MA3 Risk assessment system inadequacies. (Score remains 1.0.)

37MB3 Hazard analysis process inadequacies. (Score remains 1.0.)

39b6 Inadequate analysis of system life cycle. (Score remains 0.6.)

40a2 Inadequate design and development plan. (Score remains 1.0.)

40b7 Inadequate energy control procedures. (Score remains 1.0.)

40c26 Inadequate barriers and controls. (Score remains 1.0.)

The foregoing analysis and example demonstrates that the MORT tree is an effective tool which can be used to assign realistic numerical values to a given hazardous condition. Each of these values is a function of the values subjectively assigned to the basic causal factors. The numerical value of each element of the tree is therefore highly dependent upon the subjectivity associated with the assignment of these values. It is also dependent upon the logic defined by the tree, which cannot be considered as an exact representation of the actual causal relationships, which are often not precisely known.

In spite of its limitations, the use of the MORT tree to assign numerical indicators of risk is a logical, consistent, and scientific method of ranking hazards and their causal factors for analysis and allocation of resources, including management concern, to resolve them.

John Lindorfer