CN109241583B - Human-computer interaction system reliability solving method based on Markov - Google Patents

Abstract

The invention relates to a human-computer interaction system reliability solving method based on Markov, which comprises the following steps: the method comprises the following steps: analyzing a human-computer interaction system, an environment and a task scene, and analyzing fault logic to determine a bottom event set causing a human-computer system fault; step two: determining a complete set of state space, and drawing a system state transition diagram according to system fault logic; step three: calculating to obtain the transfer rate between states, and constructing a transfer rate matrix; step four: listing a state equation, and solving to obtain the instantaneous reliability of the human-computer system; through the steps, the fault logic in the human-computer interaction process is analyzed, the set of system fault bottom events is determined, and the instantaneous reliability of the human-computer system is finally solved, so that the effects of accurately solving the reliability of the human-computer system and searching system defects are achieved, and the problem that the multi-factor coupling characteristic of the human-computer system is difficult to describe in the conventional human-computer system reliability modeling is solved.

Description

A Markov-based Reliability Solution for Human-Computer Interaction System

technical field

The invention provides a Markov-based reliability solution method for a human-computer interaction system, which can deeply consider human cognitive characteristics, scene task characteristics and human-computer coupling characteristics, and belongs to the field of human-computer interaction reliability quantitative modeling and prediction.

Background technique

The purpose of human-computer interaction modeling is to describe the dynamic process of human-computer interaction under task requirements by taking human, machine, and environment as a whole while fully considering the existence of environmental disturbances, system failures and human errors. information transfer between, and analysis of potential risk scenarios that may lead to accidents. Human-computer interaction modeling is classified according to the implementation, and can be divided into two categories: logic-based methods and simulation-based methods. The first type of method is to model the elements of the human-machine loop in the system and the relationship between them through logical analysis to obtain element combinations or sequences; the second type of method is to use simulation technology to actually simulate the human-computer interaction process. Environmental disturbances, system failures and human errors are added to the human-machine system to analyze the human-machine interaction behavior under abnormal conditions.

In terms of logic modeling, Bell Labs first proposed the Fault Tree Analysis (FTA) method in 1961. Dugan introduced dynamic logic gates such as function-related gates, priority AND gates, and spare parts gates, thus forming dynamic faults. Tree analysis (Dynamic Fault Tree Analysis, DFTA) method, and proposed the use of Markov model for quantitative analysis, many scholars have improved its shortcomings, and has been widely cited. However, this kind of method only treats people as the bottom event without taking into account the cognitive characteristics, scene task characteristics and human-machine coupling characteristics. The Event Tree Analysis (ETA) method is a logical deductive, bottom-up analysis method, which can describe the human-computer interaction process from the causal logical relationship. The modeling process is simple, but it can only be used in a linear chain. However, the combined events (human-machine loop) cannot be analyzed in the way of description, and the description ability is insufficient. In terms of simulation modeling, the Risk and Reliability Center of the University of Maryland has developed a team information, decision, and action in CrewContext (IDAC) simulation analysis system; Taffy Institute, Massachusetts Institute of Technology, University of Chicago , University of Birmingham and other foreign research institutions have carried out research on multi-agent (MA) simulation technology and are developing corresponding platforms. Simulation-based modeling methods need to construct simulation models for various cognitive failure models and failure mechanism models in different task scenarios, and traversing event combinations or time sequences is very time-consuming, so the workload is huge and the versatility is poor. Simultaneous simulation The results are difficult to check.

At present, the man-machine system with complex automation has been widely used in many important fields. To a certain extent, people have been transformed from operators to monitors and controllers in ordinary scenarios, handlers in important scenarios, and emergency handlers in emergency scenarios. In various scenarios, people often have different information acquisition channels, continuously acquire information from highly dense information groups in different ways of perception, understand information, filter and organize information, analyze and process information, and make decisions and corresponding operations. Complete missions and stay safe at the same time. Complex cognitive processing activities within a certain period of time will lead to an increase in human cognitive load and reduce human cognitive behavioral ability and operational performance. When the cognitive load is too high and the flight faces complex meteorological conditions, information acquisition and analysis Errors may occur, and may also lead to the failure of tasks or system failures and lead to accidents. Therefore, it is very important to analyze the reliability of human-computer interaction of complex systems from the level of information cognition.

Cognitive overload and pattern confusion are two typical cognitive-level human errors. Cognitive overload refers to the state in which people fail to perceive all the information they need due to limited cognitive resources under the premise of limited time. That is to say, the cognitive overload failure is related to the adequacy of time, the limit of cognitive resources and the required perception information, resulting in the selective abandonment of completing a certain task and perceiving information related to the task, thus failing to perceive to some information or forget to perform an action. Pattern confusion refers to the lack of perceptual information (the information required for perceptual fault diagnosis is abandoned due to cognitive overload, or the information required for fault diagnosis due to equipment failure/harsh environment is completely missing), and the perceptual information is incomplete (partial missing means interaction. Incomplete information) or perceptual information errors (that is, interactive information errors, including false alarms), resulting in a state of erroneous judgment on the system failure mode. These two human error modes can explain most of the human-computer interaction faults. Therefore, if these two fault logics can be completely described when modeling and analyzing the human-computer interaction system, the reliability of the system can be analyzed more accurately. .

SUMMARY OF THE INVENTION

(1. Purpose:

The invention provides a Markov-based method for solving reliability of human-computer interaction system, which starts from the cognitive level of human to information in the process of human-computer interaction, and fully considers human cognitive characteristics, scene task characteristics and human-computer interaction. The coupling characteristics improve the system fault logic, so as to measure the reliability of the complex human-machine system more accurately. Through analysis, it is possible to find scenarios and design defects that are easy to induce human error, which plays an important role in improving the level of human performance capabilities and enhancing the reliability and safety of human-machine systems.

(2) Technical solution:

The invention is a Markov-based man-machine system reliability solution method, which includes four steps of determining system fault bottom event set, drawing system state transition diagram, determining state transition rate matrix and solving system instantaneous reliability. This method can more accurately solve the reliability of complex human-machine systems, and can find scenarios and design defects that are easy to induce human errors, which plays an important role in improving the level of human performance capabilities and enhancing the reliability and safety of human-machine systems.

A method for solving the reliability of a Markov-based man-machine system of the present invention, and its specific steps are introduced as follows:

Step 1: Analyze the human-computer interaction system, environment and task scenarios, analyze the fault logic and determine the bottom event set that causes the human-computer system failure;

Step 2: Determine the complete set of the state space, and draw a system state transition diagram according to the system fault logic;

Step 3: Calculate the transition rate between states and construct a transition rate matrix;

Step 4: List the state equation and solve to obtain the instantaneous reliability of the man-machine system;

Through the above steps, the fault logic in the human-computer interaction process is analyzed, the set of system fault bottom events is determined, and the instantaneous reliability of the human-computer system is finally solved, which achieves the accuracy of solving the reliability of the human-computer system and finding system defects. As a result, it solves the problem that the multi-factor coupling characteristics of the human-machine system is difficult to describe in the past reliability modeling of the human-machine system.

Among them, the "determination of the bottom event set that causes the human-machine system failure" described in step 1 is the basis of the entire analysis and calculation process; when analyzing the system failure logic, it should be divided into two parts: independent failure and human-machine interaction failure. , and determine the bottom event sets of the two parts respectively, and obtain the bottom event set of the human-machine system failure by summing the union set, including the following steps:

Step 1): Determine the set of independent failure partial bottom events

The fault tree or FTA method is used to determine the bottom event set of the independent failure part, which has been widely used in engineering practice and is a relatively mature method. The system fault is logically analyzed from the top to the bottom, and the bottom event set of the independent failure part can be obtained by constructing the fault tree; the human-computer interaction fault in this set is passed to the next step as the basis of the analysis;

Step 2): Determine the bottom event set of the human-computer interaction fault part

This part of the analysis is based on the fault tree (FTA) analysis. According to the definition and fault logic of two types of human-computer interaction faults, cognitive overload and mode confusion, the human-computer interaction system, environment and task scenarios that occur in the current human-computer interaction system are analyzed. Interaction fault, so as to determine the bottom event set of the human-computer interaction fault part; first, determine the triggering event, which is the task of identifying the mechanical fault of the system under the current situation, as the bottom event of cognitive overload fault; secondly, analyze The factors that cause people to perceive the lack, error or incompleteness of information, and the equipment failure to be identified are regarded as the bottom event of the mode confusion failure; the combination of the two is the bottom event set of the human-computer interaction failure part; finally, by finding the independent failure part The union of the bottom event set of the human-computer interaction fault part obtains the bottom event set of the human-computer system fault.

Wherein, "drawing a system state transition diagram" described in step 2 includes the following steps:

Step 1): Define System State

The random combination of all the states of the bottom event constitutes the state of the system, so the state of the bottom event should be defined first; generally, the occurrence state of the bottom event is defined as normal (represented by 0) and fault (represented by 1), then all the bottom events The zero-one combination of the state of the event constitutes the different states of the system, and the collection of all system states is called the state space;

Step 2): Draw a system state transition diagram

Taking the bottom event failure number as the abscissa, list all the states of the system from top to bottom; then connect the state points with a directed line according to the state transition logic of the system, and the line represents the transition between states;

The trigger condition of cognitive overload is that the number of input events a satisfies a ≥ 2, and the probability of occurrence of output events corresponding to different input events is different. Therefore, cognitive overload may be triggered more than once in the same chain in the Markov state transition diagram. For example, in a certain situation, in the human-machine system, a cognitive overload failure occurs when a person undertakes three tasks, A, B, and C, resulting in giving up some tasks or giving up perception of information D and E related to these tasks. In this case, two cognitive overload faults are triggered;

The triggering condition of the pattern confusion is the occurrence of a conditional judgment event, so the occurrence of the triggering condition in the state transition diagram should be combined with the pattern confusion; for example, when a fault M occurs, the fault M is mistakenly identified as a fault N due to the event P; Finally, a two-dimensional network structure diagram is formed;

Step 3): Model Simplification

Determine the fault state point and non-fault state point of the system according to the analysis of the fault logic in step 1; combine multiple states in the system fault state set F and non-fault state set NF to simplify the model and reduce the number of system states; simplify The latter state space is numbered from 0 to n, and it is input to the next step to simplify the solution process.

Among them, the method of "calculating the transition rate between states and constructing a transition rate matrix" described in step 3 is as follows: calculating the transition rate between states should be classified according to the form of transition between states, including independent failure parts, cognitive overload There are three types of faults and mode confusion faults; therefore, the transition rate between two different states should be classified and discussed; the transition rate of the independent failure part between states is given by experts based on actual experience and theoretical basis, and the state transition rate of the human-computer interaction part is given by Calculated; finally, the transition rate between states is expressed in the form of a matrix to construct a transition rate matrix; the calculation steps of the transition rate between states are as follows:

Step 1) Solution of transition rate from state i to state j (i≠j)

If the transition from state i to state j is not related to the human-computer interaction fault logic and i≠j, the transition between states only includes the independent failure part, and the transition rate between states is:

q _ij =λ _ij (1)

In the formula: λ _ij is the state transition rate of the independent failure part from state i to state j (i≠j);

If the transition from state i to state j is related to the output event of cognitive overload and i≠j, the transition between states includes the independent failure part and the cognitive overload-related part, and the transition rate between states is:

where P _c is the conditional probability that the cognitive overload output event occurs when the input event occurs;

If the transition from state i to state j is related to the output event of mode confusion and i≠j, that is, the occurrence state of the input event corresponding to the output event must lead to the occurrence of the output event, then the state i and state j are combined, according to formula (1)( 4.5) make calculations;

Step 2) Solution of the transition rate from state i to state j (i=j)

When state i transitions to the remaining n states, there may be multiple state transition processes related to cognitive overload, then the transition rate from state i to state j (i=j) is:

where m (m≤n) is the number of processes related to cognitive overload when state i transitions to the other n states; P _cb is the bth (i=1, 2, 3Λm) process related to cognitive overload The conditional probability that the output event of cognitive overload occurs when the input event occurs;

From this, the transition rates between all states are obtained, and they are expressed in matrix form to obtain the transition rate matrix Q, as follows:

；

;

Among them, the method of "listing the state equation and solving to obtain the instantaneous reliability of the man-machine system" described in step 4 is as follows: the solution of the instantaneous reliability of the system is actually solving the linear differential equation. According to the solution process, it includes: Follow the steps below:

Step 1): Determine the initial state distribution of the system

Denote the probability that the system is in state i at time t as P _i (t), let P(t)=(P ₀ (t), P ₁ (t), Λ, P _n (t)), then according to the state The equation has P(t)=P(0)·e ^Qt ; the transition rate matrix Q has been determined in step 2, so the initial state distribution of the system should be determined first, that is, at t=0 time P ₀ (t), P ₁ ( t), Λ, P _n (t) values to determine P(0), and then list the system state equation;

Step 2): Solve the system state equation

First, the transition rate matrix Q is diagonalized as in formula (4). To simplify the expression, each column in X is denoted as n+1 n+1-order column vectors A ₀ , A ₁ , ΛA _n , and each row in X ^-1 Denoted as n+1 n+1 order row vectors B ₀ , B ₁ , ΛB _n ;

In the formula: Q is the transfer rate matrix;

X is the transformation matrix;

X ^-1 is the inverse matrix of X;

D is a diagonal matrix similar to Q;

A ₀ , A ₁ , ΛA _n are n+1 rows in matrix X;

B ₀ , B ₁ , ΛB _n are the n+1 columns in the matrix X ^-1 ;

n is the order of the matrix Q minus 1;

d ₀ , d ₁ ......d _n is the n+1 characteristic root of Q;

Next, calculate the exponent e ^Qt of the transition rate matrix:

Then the instantaneous probability of each state is:

Step 3): Determine the instantaneous reliability of the system

The instantaneous probability value of all states of the system is obtained through the solution of step 2); the instantaneous failure probability of the system can be obtained by summing all the state probabilities in the failure state set F of the system; therefore, the probability of the system failure at time t is:

in,

In the formula: P(t) is the instantaneous failure rate of the system;

t is time, in s;

F is the fault set;

Then the instantaneous reliability of the system can be known as:

R(t)=1-P(t) (8)

In the formula: R(t) is the instantaneous reliability;

This step is the process of solving the equation, and the solving process is clear and concise, and manual solution can be replaced by MATLAB, VB, C language or C++ programming.

(3) Efficacy and advantages

The invention proposes a Markov-based human-computer interaction system reliability calculation method, which considers human cognitive characteristics, scene task characteristics and human-computer coupling characteristics, completely describes the system fault logic, and can adapt to complex human-computer systems. Quantitative modeling analysis of reliability requirements. At the same time, a calculation method of the transition rate between system states is proposed, which can more accurately calculate the reliability of the man-machine system.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention.

Figure 2. Analysis of the crash accident tree of a twin-engine carrier-based helicopter.

Figure 3. A simplified diagram of the crash accident tree of a twin-engine carrier-based helicopter.

Figure 4. Markov state transition diagram.

Figure 5 Simplified diagram of Markov state transition.

Figure 6. Comparison of accident analysis results.

The serial numbers, symbols and codes in the figure are explained as follows:

Fig. 2 and Fig. 3 Chinese and English letters plus numbers are the event codes, M represents the middle event, X represents the bottom event, and FDEP is the function-related logic gate in the fault tree;

In Figure 4 and Figure 5, X plus a number represents the code of the bottom event, the ellipse represents the state of the system composed of the bottom event, the numbers 0 and 1 represent the occurrence state of the bottom event, 0 represents the event occurs, 1 represents the event does not occur, and the arrow represents the system In the direction of transition, the solid line represents the state transition caused by the independent failure of the equipment, and the dotted line represents the state transition caused by human error.

Detailed ways

The present invention provides a Markov-based man-machine system reliability solution method, as shown in FIG. 1 ; the method is carried out in sequence according to the following four steps; the present invention uses a twin-engine ship-based helicopter as a case, in this case The aircraft is in the landing stage and the altitude is low. When the auto-throttle system is turned on, and one of the helicopter's engines has a throttle jam failure, the aircraft automatically compensates for the asymmetric thrust caused by maintaining the approach speed, and automatically retracts the other. The throttle handle of the engine, while the parameters of the engine drop rapidly. The crew members easily misjudged the throttle jamming failure of the engine as another engine failure, and manually shut down the normal engine, causing the aircraft to lose power and crash.

A method for solving the reliability of a Markov-based man-machine system of the present invention is shown in Figure 1, and the specific implementation is described in detail as follows:

Step 1: Identify the bottom set of events that lead to the failure of the human-machine system

Divided into the following two steps:

Step 1): Determine the set of independent failure partial bottom events

Using the FTA method to model and analyze the system, the set of independent failure partial bottom events can be obtained. In this example, the crash of a dual-engine carrier-based helicopter is taken as the top event, and an accident tree is constructed through top-down logic analysis, as shown in Figure 2, which does not include the two fault logics of cognitive overload and mode confusion. In order to simplify the calculation process, the intermediate events (M4, M5, M9, M11) are omitted, and the simplified model is shown in Figure 3. Then the bottom events of the independent failure part can be obtained as shown in the following table:

Table 1 Bottom event table of independent failure parts

Numbering event X1 Throttle stuck X2 Manual error shutting down the No. 2 engine X3 Engine parameters not checked X4 No. 2 engine throttle handle retracted

Step 2): Determine the bottom event set of the human-computer interaction fault part

This case includes both cognitive overload failure and pattern confusion failure caused by cognitive overload. First of all, the logic of cognitive analysis overload fault should be analyzed. In this case, people undertake normal flight tasks, communication tasks, and tasks of identifying and identifying mechanical faults. This fault is characterized by the retraction of the No. 2 engine handle. These three tasks all need to occupy human cognitive resources, leading to cognitive overload failure, which leads people to give up identifying engine parameters. Combined with the fault characterization, the resulting pattern confusion led people to mistake the No. 1 engine failure as the No. 2 engine fault and erroneously shut down the No. 2 engine. According to the definition of cognitive overload and mode confusion bottom events, the two bottom events are listed in Table 2:

Table 2 The bottom event set of the human-computer interaction fault part

Numbering event X4 No. 2 engine throttle handle retracted

Thus it can be known that the set of system fault bottom events is {X1, X4, X2, X3}.

Step 2: Draw the system state transition diagram including the following steps

Step 1): Define System State

The definition of the system state should first define the state of the bottom event, record the occurrence of the bottom event as state 1, and record the occurrence of the bottom event as state 0, so that the states of the bottom event can be clearly distinguished. There are four bottom events in this case, and the zero-one combination of these four event states constitutes the complete set of the state space of the system, and there are 16 state points in this set.

Step 2): Draw a system state transition diagram

Take the number of bottom events as the abscissa, and list the system states from top to bottom. According to the analysis of the fault logic in step 1, connect the system state points with directional lines in turn. , forming a network logic diagram, as shown in Figure 4.

Step 3): Model Simplification

According to the analysis of the fault logic in step 1, the fault state point and the non-fault state point of the system are determined. The multiple states in the system fault state set F and the non-fault state set NF are merged, and 12 state spaces remain, as shown in Figure 5. The simplified state space is numbered from 0 to 11 and input to the next step to simplify the solution process.

Step 3: Calculate the transition rate between states

For the calculation of the state transition rate between systems, the state transition rate of the independent failure part should be determined first. The independent failure part of the system state transition is caused by the occurrence of the bottom event, so the state transition rate of the independent failure part is equal to the occurrence rate of the bottom event that causes the system state transition. Make the following assumptions:

λ _X1 =λ _X2 =λ _X3 =λ _X4 =1×10 ⁻⁴ (9)

where λ _X1 , λ _X2 , λ _X3 , and λ _X4 are the occurrence rates of the bottom events X1, X2, X3, and X4.

Step 1) Solution of transition rate from state i to state j (i≠j)

First of all, the fault classification of system state transition should be analyzed. In this case, it includes the independent failure part and the human-computer interaction fault part. In the human-computer interaction fault part, the mode confusion is caused by cognitive overload, and the two faults can be combined into one overall analysis. After analysis, the state transition relationship between systems is listed in Table 3:

Table 3 Classification of state transitions between systems

Then there is a transition rate between states containing only independent failure parts:

q ₀₁ =q ₂₁ =q ₃₉ =q ₄₅ =q ₆₅ =q ₇₉ =q _8,11 =q _10,11 =λ _X1

q ₀₂ =q ₃₇ =q ₄₆ =q _8,11 =λ _X4

q ₀₃ =q ₁₉ =q ₂₇ =q ₄₈ =q _5,11 =q _6,10 =λ _X2

q ₀₄ =q ₁₅ =q ₂₆ =q ₃₈ =q _7,10 =q _9,11 =λ _X2

For the part containing human-computer interaction faults, the conditional probability that the cognitive overload output event occurs at the input event should be determined first. In this case, the input events of cognitive overload are normal flight tasks, communication tasks and tasks of identifying and identifying mechanical faults undertaken by humans, and the output events are abandoning the identification of engine parameters. Assuming this conditional probability P _c =0.8, the transition rate between states of the human-computer interaction fault part is:

q _1,11 =(λ _X2 +λ _X3 )P _c

q _2,10 =(λ _X1 +λ _X2 +λ _X3 )P _c

Step 2) Solution of the transition rate from state i to state j (i=j)

It is known that among all 12 states of the system, only state 1 and state 2 have cognitive overload failures in the process of transitioning to other states. The input and output events of cognitive overload were the same in both processes, with a conditional probability of P _c =0.8. Then there is the transition rate between states:

q ₀₀ =-(λ _X1 +λ _X4 +λ _X2 +λ _X3 )

q ₁₁ =-(λ _X2 +λ _X3 )(1-p _c )

q ₂₂ =-(λ _X1 +λ _X2 +λ _X3 )(1-p _c )

q ₃₃ =-(λ _X1 +λ _X4 +λ _X3 )

q ₄₄ =-(λ _X1 +λ _X4 +λ _X2 )

q ₅₅ =-λ _X2

q ₆₆ = -λ _X1 -λ _X2

q ₇₇ = -λ _X1 -λ _X3

q ₈₈ = -λ _X1 -λ _X4

q ₉₉ = -λ _X3

q _10,10 = -λ _X1

The other inter-system state transition rates are all 0, then the inter-system state transition rate matrix is:

Step 4: Solve the instantaneous reliability of the system

First of all, the state distribution at the initial time of the system should be determined. In this case, the state where the bottom events are all occurrences is defined as the initial state of the system, that is, the state point (0000), then it can be known that the initial state distribution of the system is P(0)=(1 ,0,Λ,0) ₁₂ , and then the system reliability can be solved by means of programming. In order to compare the effect of the method, the instantaneous reliability of the system considering only the independent failure part is solved in this case as follows:

Draw a comparison chart of the instantaneous reliability of the system considering both independent failures and human-computer interaction failures and the instantaneous reliability of the system when only considering independent failures, as shown in Figure 6. It can be seen that the former is significantly greater than the latter.

Claims (2)

1. A human-computer interaction system reliability solving method based on Markov is characterized in that: the method comprises the following steps:

the method comprises the following steps: analyzing a human-computer interaction system, an environment and a task scene, and analyzing fault logic to determine a bottom event set causing a human-computer system fault;

step two: determining a complete set of state space, and drawing a system state transition diagram according to system fault logic;

step three: calculating to obtain the transfer rate between states, and constructing a transfer rate matrix;

step four: listing a state equation, and solving to obtain the instantaneous reliability of the human-computer system;

the step one of determining a bottom event set causing the man-machine system fault is the basis of the whole analysis and calculation process; when analyzing system fault logic, the method is divided into two parts of independent failure and man-machine interaction fault, bottom event sets of the two parts are respectively determined, and the bottom event set of the man-machine system fault can be obtained by solving a union set, and the method comprises the following steps:

step 1.1): determining a set of independent failure partial bottom events

Determining the independent failure part bottom event set by adopting a Fault Tree (FTA) method, and performing top-to-bottom logic analysis on system faults by combining the current man-machine system, environment and task situation to construct a fault tree, namely obtaining the independent failure part bottom event set; transmitting the man-machine interaction faults in the set to the next step to serve as a basis for analysis;

step 1.2): determining a set of partial bottom events of human-computer interaction faults

The analysis of the part is established on the basis of Fault Tree (FTA) analysis, and human-computer interaction faults occurring under the current human-computer interaction system, environment and task situations are analyzed according to the definition and fault logic of cognitive overload and mode confusion of two human-computer interaction faults, so that a bottom event set of the human-computer interaction fault part is determined; firstly, determining a trigger event, namely a task of identifying a system mechanical fault borne by a person under the current situation, and taking the trigger event as a bottom event of the cognitive overload fault; secondly, analyzing factors causing human perception information missing, errors and incompleteness, and taking the factors and equipment faults needing to be identified as bottom events of mode confusion faults; the union set of the two events is a bottom event set of the human-computer interaction fault part; finally, obtaining a bottom event set of the man-machine system fault by solving a union set of bottom event sets of the independent failure part and the man-machine interaction fault part;

the step two of drawing the system state transition diagram comprises the following steps:

step 2.1): defining system states

The random combination of all the states of the bottom event constitutes the state of the system, so the state of the bottom event should be defined first; the occurrence state of the bottom event is represented as normal by '0', and the occurrence state of the bottom event is represented as fault by '1', so that zero combination of the states of all the bottom events forms different states of the system, and a set of all the states of the system is called as a state space;

step 2.2): drawing a system state transition diagram

Taking the number of faults of the bottom event as an abscissa, and sequentially listing all states of the system from top to bottom; then, according to the state transition logic of the system, connecting state points by using a directed line, wherein the line represents the transition between states;

the cognitive overload triggering condition is that the number a of input events is more than or equal to 2, and the occurrence probability of output events corresponding to different input events is different, so that the cognitive overload is triggered for multiple times in the same chain in the Markov state transition diagram;

the trigger condition of the mode confusion is that a condition judgment event occurs, so the occurrence of the trigger condition in the state transition diagram should be merged with the mode confusion; if a fault M occurs, a person mistakenly identifies the fault M as a fault N due to an event P; thereby finally forming a two-dimensional mesh structure diagram;

step 2.3): model simplification

Determining fault state points and non-fault state points of the system according to the analysis of the fault logic in the step one; combining a plurality of states in a system fault state set F and a non-fault state set NF, simplifying a model and reducing the number of system states; the simplified state space is marked with serial numbers from 0 to n and is input into the next step, so that the aim of simplifying the solving process is fulfilled;

the "calculating inter-state transition rates, constructing the transition rate matrix" described in step three is performed as follows: calculating the transfer rate among the states, and classifying the transfer rate among the states according to the transfer form among the states, wherein the transfer rate includes three types, namely an independent failure part, a cognitive overload fault and a mode confusion fault; therefore, the transition rate between two different states should be discussed in a classification way; the transfer rate of the independent failure part between the states is given by experts according to actual experience and theoretical basis, and the state transfer rate of the human-computer interaction part is obtained by calculation; finally, expressing the transition rate between states in a matrix form to construct a transition rate matrix; the calculation steps of the transition rate between states are as follows:

step 3.1) solving the transition rate from the state i to the state j;

if the state i is transferred to the state j which is not related to the man-machine interaction fault logic and i is not equal to j, the transfer between the states only comprises an independent failure part, and the transfer rate between the states is as follows:

q _ij ＝λ _ij (1)

in the formula: lambda _ij The state transition rate of the independent failure part from the state i to the state j;

if the state i is transferred to the state j and is related to the output event of the cognitive overload, and i is not equal to j, the inter-state transfer comprises an independent failure part and a cognitive overload related part, and the inter-state transfer rate is as follows:

in the formula: p is _c Outputting a conditional probability of an event occurring at the time of an input event for cognitive overload;

if the state i is transferred to the state j and is related to the mode-confused output event and i is not equal to j, namely the output event is generated because the input event generating state corresponding to the output event definitely causes the output event, combining the state i and the state j, and calculating according to a formula (1);

step 3.2) solving the transfer rate from the state i to the state j;

when the state i is transferred to the rest n states, a plurality of state transfer processes related to cognitive overload exist, and the transfer rate from the state i to the state j is as follows:

in the formula: m is the number of processes related to cognitive overload when the state i is transferred to the other n states, wherein m is less than or equal to n; i =1,2,3 … m; p _cb The conditional probability of the cognitive overload output event occurring when the input event occurs in the process related to the cognitive overload is the b < th > process;

therefore, the transition rate among all states is obtained, and the transition rate matrix Q is expressed in a matrix form and is in the form of:

。

2. the markov-based human-computer interaction system reliability solution method of claim 1, wherein: "list the state equations and solve to get the instantaneous reliability of the human-machine system" described in step four, which is done as follows: the solution of the system instantaneous reliability is actually to solve a linear differential equation, and the solution process comprises the following steps:

step 4.1): determining system initial state distribution

Let P denote the probability that the system is in state i at time t _i (t), let P (t) = (P) ₀ (t),P ₁ (t),…,P _n (t)), then there is P (t) = P (0) · e) according to the equation of state ^Qt (ii) a The transfer rate matrix Q has been determined in step two, so the initial state distribution of the system should be determined first, i.e. at time P when t =0 ₀ (t),P ₁ (t),…,P _n (t) to determine P (0), and then listing the system equation of state;

step 4.2): solving system state equation

First, the transfer rate matrix Q is diagonalized as shown in formula (4), and each column in X is recorded as n +1 order column vectors A for simplifying expression ₀ ,A ₁ ,…A _n Is mixing X ^-1 The middle lines are marked as n +1 order line vectors B ₀ ,B ₁ ,…B _n ；

In the formula: q is a transfer rate matrix;

x is a transformation matrix;

X ^-1 an inverse matrix of X;

d is a diagonal matrix similar to Q;

A ₀ ,A ₁ ,…A _n is n +1 rows in the matrix X;

B ₀ ,B ₁ ,…B _n is a matrix X ^-1 N +1 columns of (1);

n is the order of the matrix Q minus 1;

d ₀ ,d ₁ ……d _n n +1 characteristic roots for Q;

second, the index e of the transfer rate matrix is calculated ^Qt ：

Then the transient probability of each state is:

step 4.3): determining system instantaneous reliability

Obtaining instantaneous probability values of all states of the system through the solution of the step 4.2); summing all the state probabilities in the failure state set F of the system to obtain the instantaneous failure probability of the system; the probability of the system failing at time t is therefore:

wherein,

in the formula: p (t) is the instantaneous failure rate of the system;

t is time, unit s;

f is a fault set;

then the instantaneous reliability of the system is known as:

R(t)＝1-P(t) (8)

in the formula: r (t) is the instantaneous reliability.

Images