A study on the development of a novel task complexity measure: TACOM
Jinkyun Park and Wondea Jung,
Integrated Safety Assessment Division, Korea Atomic Energy Research Institute, P.O.Box 105, Duckjin-Dong, Yusong-Ku, Taejon, 305-353, Republic of Korea. 1. Introduction
It is well perceived that human performance related problems would occur due to complicated procedures [1, 2]. Unfortunately a serviceable framework that can be used to systematically evaluate the complexity of procedures is relatively scant. For this reason, in this study, a complexity measure called the TACOM (Task Complexity) measure is suggested to quantify the complexity of emergency tasks that are prescribed in emergency operating procedures (EOPs) of nuclear power plants (NPPs).
2. The development of the TACOM measure The TACOM measure is composed of five sub-measures that cover five kinds of distinctive decisive factors making the performance of emergency tasks complicated. Table 1 summarizes the definition of the TACOM measure with all the five sub-measures.
< Table 1. TACOM with the associated sub-measures > Definition/Meaning TACOM 2 1 2 2 2 2 2 ) ( ) ( ) ( ) ( ) ( ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ × + × + × + × + × EDC AHC SSC SLC SIC ε δ γ β α SIC
Representing the complexity due to the amount of information to be processed by operators.
SLC
Representing the complexity due to the execution logic of the required actions to be sequenced by operators.
SSC
Representing the complexity due to the amount of the required actions to be performed by operators.
AHC
Representing the complexity due to the amount of system knowledge that is necessary to identify the problem space of the required actions.
EDC
Representing the complexity due to the amount of cognitive resources that is necessary to establish proper decision criteria of the required actions.
ε δ γ β α , , ,
, Weighting factors for SIC, SLC, SSC,
AHC and EDC.
Each sub-measure is quantified by graph entropy concepts that have been widely used to measure the complexity of software (i.e., source codes) [3]. Fig. 1 delineates three phases for quantifying the complexity of an emergency task that consists of two procedural steps
(i.e., S1 and S2). 2 2 2 2 2 ( ) ( ) ( ) ( ) )
( SIC SLC SSC AHC EDC
TACOM = α× +β× +γ× +δ× +ε×
S1. IF pressurizer pressure is less than 123.9kg/cm2A,
THEN verify BOTH safety injection actuation signal (SIAS) and containment isolation actuation signal (CIAS) are actuated.
The required information to accomplish each procedural step Step Designation Meaning Type
I1 The value of pressurizer pressure ‘Float’ I2 The status of SIAS alarms ‘Array’ of ‘Boolean’ S1
I3 The status of CIAS alarms ‘Array ‘of ‘Boolean’ I1 The value of pressurizer pressure ‘Float’ I2 The status of SIAS alarms ‘Array’ of ‘Boolean’ I4 RCP control switches ‘Array’ of ‘Boolean’ S2
I5 The value of RCS subcooling margin ‘Float’
The required actions to accomplish each procedural step Step Designation Meaning
AT1 Verifying pressurizer pressure AT2 Verifying the status of SIAS AT3 Verifying the status of CIAS S1
AT7 Go to next procedural step AT1 Verifying pressurizer pressure AT2 Verifying the status of SIAS AT4 Stop one RCP in each loop AT5 Verifying RCS subcooling margin AT6 Stop all RCPs S2
AT7 Go to next procedural step
S1 I1 I2 I3 A21 A31 F B B S2 I1 I2 I4 A21 F B B I5 A41 F S1 AT1 AT2 AT3 AT7 S2 AT1 AT2 AT4 AT7 AT5 AT6 S1 1st 2nd 3rd AT2 AT3 CF CF CF AT1 4th AT7 CF AH11 S2 1st 2nd 3rd AT2 AT4 CF CF CF AT1 4th AT5 CF 5th 6th AT6 AT7 AH11 AH41 AH51 AH61 CF CF S1 1st 2nd 3rd AT2 AT3
ED-1ED-1 ED-1 AT1 4th AT7 ED-1 S2 1st 2nd 3rd AT2 AT4
ED-1 ED-1ED-1 AT1 4th AT5 ED-1 5th 6th AT6 AT7 ED-1 ED-1 Quantifying SIC An arbitrary task Quantifying SLC & SSC Quantifying AHC Quantifying EDC Task analysis & quantifying sub-measures by graph entropy concepts
Quantifying SIC based on information structure graphs. SIC = 3.922
Quantifying SLC and SSC based on action structure graphs. SLC = 2.085, SSC = 3.252
Quantifying AHC based on abstraction hierarchy graphs. AHC = 4.885
Quantifying EDC based on abstraction hierarchy graphs. EDC = 4.563
Quantifying TACOM
Abstraction hierarchy levels Step Designation Level of abstraction
hierarchy AT1 SF AT2 CF AT3 CF S1 AT7 CF AT1 SF AT2 CF AT4 SF AT5 SF AT6 SF S2 AT7 CF
Engineering decision levels Step Designation Level of engineering
decision AT1 ED-1 AT2 ED-1 AT3 ED-1 S1 AT7 ED-1 AT1 ED-1 AT2 ED-1 AT4 ED-1 AT5 ED-1 AT6 ED-1 S2 AT7 ED-1
S2. IF pressurizer pressure is less than 121kg/cm2A AND SIAS is actuated,
THEN perform BOTH of the following:
a. Stop ONE reactor coolant pump (RCP) in each loop. b. IF reactor coolant system (RCS) subcooling margin
is less than 15oC, THEN stop ALL RCPs.
< Figure 1. The quantification scheme of TACOM > 3. Measure validation
The appropriateness of the TACOM measure is briefly verified by comparing the estimated TACOM scores with averaged task performance time data. The task performance times denote an elapsed time to accomplish the required tasks, and these data are extracted from OPERA database developed by KAERI [4].
The OPERA database contains many kinds of plant-specific and domain-plant-specific operators’ performance data obtained under simulated emergencies. To collect operators’ performance data under simulated emergencies,
Transactions of the Korean Nuclear Society Autumn Meeting Busan, Korea, October 27-28, 2005
a full scope simulator installed in the training center of the reference NPP was used. This simulator was designed based on a 1,000MWe pressurized water reactor (PWR), and it has conventional control interfaces, such as switches, indicators, and alarm tiles, etc. Using this simulator, for over a period of three years (from 1999 to 2001), more than 100 audio-visual records were gathered from the re-training sessions of emergency operations. Then both a time-line analysis and a verbal protocol analysis were carried out to extract useful information. As a result, various kinds of operators’ performance data were successfully secured.
For this comparison, as epitomized in Table 2, performance time data for 38 tasks are extracted from the OPERA database.
< Table 2. Averaged task performance time data >
ID TACOM1 Time2 ID TACOM Time
1 1.842 57.0 20 2.005 72.2 2 2.627 280.3 21 2.430 200.1 3 2.104 85.4 22 1.898 77.3 4 2.224 71.2 23 2.441 159.9 5 2.048 90.7 24 2.492 226.0 6 2.362 196.5 25 1.865 64.8 7 2.458 183.7 26 2.360 264.3 8 2.371 139.3 27 1.851 61.9 9 1.842 44.1 28 2.150 155.6 10 2.104 89.0 29 1.419 18.0 11 2.472 169.0 30 0.918 23.7 12 2.528 507.0 31 1.865 130 13 1.842 47.9 32 1.567 69.9 14 2.104 37.1 33 1.477 16.4 15 2.089 130.3 34 1.865 22.4 16 2.493 275.5 35 0.985 11.1 17 2.469 182.5 36 1.459 19.5 18 1.994 152.5 37 1.465 30.7 19 2.016 83.9 38 1.484 51.6
1All the weighting factors used in quantifying TACOM
scores are equivalent.
2Averaged task performance time (s).
From these comparisons, it was observed that the TACOM measure seems to be meaningful for explaining the change of operators’ performance because there is a significant statistical correlation between the averaged task performance time data and the estimated TACOM
scores (see Fig. 2, R2 = 0.775 with p < 0.001).
4. Conclusion
In this study, the TACOM measure that can systematically evaluate the complexity of emergency tasks is developed based on the five sub-measures. These sub-measures cover five kinds of distinctive factors that
can affect the complexity of tasks, and each sub-measure is quantified by a graph entropy concept. In order to demonstrate the appropriateness of the TACOM measure, the estimated TACOM scores are compared with operators’ performance time data obtained from the OPERA database. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 100 200 300 400 500 6000.0 0.5 1.0 1.5 2.0 2.5 3.0 0 100 200 300 400 500 600 Lower 95% prediction line Upper 95% prediction line
Regression line Time = 1.876 X e(1.893 X TACOM) R = 0.880, R2 = 0.775 Aver aged tas k p erformanc e ti me (s)
TACOM score (based on equal weights) < Figure 2. The result of comparisons between averaged task performance time data with the associated
TACOM scores>
As a result, it was observed that the change of task performance time data is susceptible to the change of TACOM scores. Subsequently, although more detailed verification activities are decisive to assure the appropriateness of the TACOM measure, the following conclusion could be drawn without an irrationality – “The TACOM measure can be used to quantify the complexity of tasks stipulated in EOPs.”
References
[1] A. Degani, and E. L. Wiener. Human factors of flight-deck checklists: the normal checklist. National Aeronautics and Space Administration, NASA/CR-177549. 1990.
[2] D. Wieringa, C. Moore, and V. Barnes. Procedure writing principles and practices. Battelle Press, 2nd Edition. 1998. [3] J. S. Davis, and R. J. LeBlanc. A Study of the applicability of complexity measures. IEEE Transactions on Software Engineering 1988;14:9, 1366-1372.
[4] J. Park, W. Jung, J. Kim, and J. Ha. Analysis of human performance observed under simulated emergencies of nuclear power plants. Korea Atomic Energy Research Institute, KAERI/TR-2895/2005. 2005.
