A Correlation Analysis Model of Human Factors in Mine Accidents Based on Apriori Algorithm

Quantitative evaluation of human reliability or HEP can find out the fundamental cause of human error. In this section, the CREAM method of human reliability analysis method is used to trace and analyze the occurred accidents, and to explore the unobservable human factors which caused the accidents. A new human reliability analysis model is established by combining the HEP prediction technology with the error analysis method by using Apriori algorithm.

3.1 Selection of evaluation method

Each human reliability evaluation method has its merits and defects. There is no evaluation method that applies to human reliability in all systems. In many systems, it is necessary to combined two or more evaluation methods. Technique for human error rate prediction (THERP) [18] decomposes each human task into several subtasks, sets up an event tree with the task as the trunk, assigns the failure probability of each subtasks on each branch by looking up the table, and computes the failure probability of the task by weighting those of all branches. This approach can accurately depict the operation features of every task, yet fails to reflect the effect of human cognition on accidents. To makes matters worse, the weighted calculation is easy to accumulate error, and the failure probability table of THERP is not suitable for all kinds of tasks.

CREAM [19] builds up an effective and reasonable failure probability model, which identifies the cognitive control mode of the cognitive behavior in each branch, assigns the failure probability to the identified cognitive control mode by looking up the table, and adjusts the probability based on the performance factors that reflect the features of situational environment (because the situation environment might affect human cognitive behavior). The failure probability evaluation model is well known for its reliability and accuracy in data quantification. As a result, the CREAM has been widely adopted to evaluate human reliability.

The combination of THERP and CREAM can give full play to their merits, and avoid their defects: the task decomposition and event tree construction are realized by THERP, while the failure probability is estimated in the light of the basic failure probability and the performance factors given by CREAM. In this way, the failure probability estimation will be more practical, and the human reliability evaluation will be more accurate.

The THERP-based quantification of failure probability consists of four stages: system familiarization, qualitative analysis, quantitative analysis, and result application. During qualitative analysis, the action types, action objects, and potential human errors of a task are analyzed in details, and the possible wrong actions and their types are identified. On this basis, the task is decomposed into a series of subtasks, and depicted with an event tree of human reliability evaluation.

After task decomposition, the subtasks have two logic relations: series and parallel. If the subtasks are connected in series, then task can succeed only if all subtasks are successful; if the subtasks are in parallel, then the task can succeed if any subtask is successfully. The success and failure probabilities of the task with series subtasks and the task with parallel subtasks can be quantified respectively by:

$\left\{\begin{array}{l}P(S)=u(v \mid u) \\ P(F)=1-u(v \mid u)=u(V \mid u)+U(v \mid U)+U(V \mid U)\end{array}\right.$  (1)

$\left\{\begin{array}{c}P(S)=U(V \mid U)=u(v \mid u)+u(V \mid u)+U(v \mid U) \\ P(F)=U(V \mid U)\end{array}\right.$  (2)

where, S and F are the success and failure of the task, respectively; U and V are two subtasks; u and v are success and success probability of a subtask, respectively.

In the event tree of human reliability evaluation, HEP is affected by operator quality, current state of individuals, hardware reliability, management mechanism, and environmental conditions. The actual HEP of each subtask must be modified based on performance factors. Since the HEP is a conditional probability, it is necessary to consider the correlation between subtasks and operators in the system. Otherwise, the predicted HEP will be seriously distorted. Suppose a task can be logically divided into subtask U and subtask V in time order, that is, subtas U occurs before subtask V. If subtask U k fails, then the failure probability of V falls in one of the five levels according to the correlation between U and V:

Full correlation:

$P(V \mid U)=1$  (3)

High correlation:

$P(V \mid U)=(1+P(V)) / 2$  (4)

Medium correlation:

$P(V \mid U)=(1+6 P(V)) / 7$  (5)

Low correlation:

$P(V \mid U)=(1+19 P(V)) / 20$  (6)

Zero correlation:

$P(V \mid U)=P(V)$  (7)

3.2 Improved evaluation model

CREAM holds that human error arises from incorrect cognition of the situation and wrong decision induced by the environment, in addition to wrong actions. There are four kinds of cognitive control modes in CREAM: scrambled, opportunistic, tactical and strategic [19]. The error probability interval of each mode is given in Table 1.

Table 1. Error probability interval of each mode

Apriori algorithm looks for the frequent item sets in the target dataset by two metrics, namely, support and confidence. Support is the number of occurrences of each member item. The support of the pair of frequent items X and Y can be defined as:

Support $(\mathrm{X}, \mathrm{Y})=\mathrm{P}(\mathrm{XY})=$ Num $(\mathrm{XY}) /$ Num(Allsamples)  (8)

In general, an item with a high support or a too low support does not belong to the frequent item set.

Confidence is the probability that if an item occurs, then another item will also occur. The confidence of X on Y can be defined as:

Confidence $(\mathrm{X} \Leftarrow \mathrm{Y})=\mathrm{P}(\mathrm{X} \mid \mathrm{Y})=P(X Y) / P(Y)$  (9)

Here, Apriori algorithm is introduced to analyze the correlation between human factors. Then, the weighting of cognitive control mode in CREAM was modified based on the historical data on human-induced mine accidents. Based on the mined association rules, six factors were found to have great impact on the occurrence of cognitive error: underground monitoring system, underground personnel positioning system, underground emergency shelter system, underground compressed air self-rescue system, underground water supply rescue system, and underground communication system. Therefore, the six factors were taken as the CPC factors in the mine system.

According to its degree of impact on operator performance, each CPC factor was divided into three levels: improved, reduced and insignificant. Then, the probability of cognitive error leading to human-induced mine accidents was predicted by an improved method: the probability of cognitive failure was calculated based on the å_reduced and å_improved of CPC factors:

$\eta=\Sigma_{\text {reduced}}-\Sigma_{\text {improved}}$  (10)

where, h is the context influence index; å_reduced and å_improved are the number of CPC factors whose level is reduced or improved, respectively.

If there is no context impact, the context influence index $\eta$ is zero. At this time, the probability of cognitive failure is the basic failure probability CFP₀ . The relationship between cognitive failure probability CFP , basic failure probability CFP₀ and context influence index $\eta$ can be expressed as:

$\lg \left(C F P / C F P_{0}\right)=k \eta$  (11)

The basic failure probability CFP₀ depends on CFP  and $\eta_{\max }$, and $\eta_{\min }$:

$\eta_{\max }=\lg \left(C F P_{\max } / C F P_{0}\right) / k$  (12)

$\eta_{\min }=\lg \left(C F P_{\min } / C F P_{0}\right) / k$  (13)

Thus, k and CFP₀  can be respectively expressed as:

$k=\lg \left(C F P_{\max } / C F P_{\min }\right)=\left(\eta_{\max }-\eta_{\min }\right)$  (14)

$C F P_{Q}=C F P_{m a x} / 10^{k \eta_{\max }}$  (15)

Then, the cognitive failure probability CFP can be calculated by:

$\mathrm{CFP}=C F P_{0} \times 10^{\frac{\eta}{4}}$  (16)

The improved evaluation model for human factors in mine accidents involves the following steps:

Step 1. For the subtasks on each branch of the event tree, analyze the cognitive activities in human-induced accident, and determine the cognitive control mode of these activities.

Step 2. Find the basic cognitive failure probability CFP₀ .

Step 3. Under the context of cognitive activities, determine the level of each CPC factor, quantify the effect of each factor, and adjust the weight of the cognitive control mode, using Apriori algorithm.

Step 4. Compute the context influence index, and calculate the cognitive failure probability of each subtask by (16).

Step 5. According to the logic relation of subtasks in event tree, weight or multiply the cognitive failure probabilities of the member subtasks to obtain the cognitive failure probability of each branch.

Table 2 lists the type of cognitive function, cognitive control mode, and basic failure probability of each branch in the event tree, which are obtained by our model.