JP3445517B2 - System reliability design apparatus and method, and recording medium recording system reliability design software - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an improvement in a technique for designing the reliability of a system, and more specifically, a fault tree of a target system and a given occurrence of an upper event. The probability of occurrence of a subordinate event is calculated based on the probability.

[0002]

2. Description of the Related Art As a technique for analyzing and designing the reliability of various systems such as computer systems and various plants, FTA (Fault tree
A method called lysis (fault tree analysis) is known.
Where Fault tree = fault tree
This data represents the structure of the system reliability, and represents the events such as individual failures that affect the system reliability and the relationships between the events using a tree structure tree. .

As an example of such a fault tree,
For example, a root node representing the entire system of interest is linked to a node representing each constituent element, and a node indicating what kind of failure is possible for each node of each constituent element. Although linked ones are possible, the actual structure can be freely determined for each system.

In such a fault tree, the probability of occurrence can be set for each of the events that make up the fault tree, and when an event is composed of another event that is more detailed, the former is a tree structure. It is represented by the node on the root side and is called the upper event. The latter is represented by a node at the end of the tree structure and is called a sub event. It should be noted that the terms “higher-order event” and “lower-order event” include cases where components corresponding to the high-order event or low-order event are represented.

For example, when the entire system does not fail unless both of the two subsystems in parallel fail, the upper event of the failure of the entire system is connected with the lower event of the failure of each individual subsystem by AND. in this case,
For example, if the failure probability of each individual partial system is 0.1, the failure probability of the entire system is 0.1 * 0.1 = 0.01.

Further, when the whole system fails when either one of the two subsystems in series fails, the lower event of the failure of each individual subsystem is connected by OR with the upper event of the failure of the overall system. . In this case, for example, the probability of occurrence of failure of each subsystem is 0.
If 1, the probability of failure of the entire system is 1- (1-0.1) * (1-0.1) = 0.19.

Since 1-fault occurrence probability = operating rate (reliability), it is meaningless if the failure occurrence rate and the operating rate are exchanged and the types of logical operators are reversed accordingly. Is the same.

Then, if such a fault tree is used and the occurrence probability is set for each lower event, AN
By sequentially calculating the occurrence probabilities of upper events according to D, OR, etc., the failure occurrence rate of the entire system, that is, the degree of reliability can be calculated as the occurrence probability of the top event.

Therefore, by using the fault tree, for example, it is possible to perform a trial calculation to evaluate how the overall reliability changes when the configuration of the partial system is changed between serial and parallel, or to evaluate the overall reliability. It is possible to perform a design work such as rationalizing the cost by increasing or decreasing the reliability of the lowest event, for example, within a range that can satisfy the reliability required as.

[0010]

However, conventionally, as described above, it is not possible to calculate the reliability of the upper event or the entire system in a bottom-up manner from the occurrence probability, that is, the reliability that is known for the lower event. Although it was possible, on the contrary, from the reliability required for the entire system and upper events,
A technique for calculating the occurrence probability that each sub-event should satisfy in a top-down manner has not been known.

Therefore, conventionally, when there is an undetermined probability of occurrence of a subordinate event, the reliability of the entire system is calculated by temporarily using an appropriate approximate value or ignoring it, and the calculation result is calculated. The designer had to decide the probability of occurrence of subordinate events while checking. As a result, not only is it difficult to calculate reliability accurately, but the calculation result may change each time the probability of occurrence of some lower-order events is replenished, improving the efficiency and accuracy of reliability design. Was difficult.

In particular, in order to design efficiently, it is necessary to reduce the occurrence probability of a low-order event that has a great influence on the overall reliability, that is, a significant degree of importance. Repeating the above procedure was complicated and difficult.

The present invention has been proposed in order to solve the problems of the prior art as described above, and its purpose is to provide a fault tree of a target system and an occurrence probability given to an upper event. PROBLEM TO BE SOLVED: To provide a system reliability design device and method for effectively supporting system reliability design by calculating the occurrence probability of a subordinate event based on the above, and a recording medium recording system reliability design software. Is.

[0014]

In order to achieve the above object, the invention of claim 1 provides a reliability design of a system for designing the reliability of a system having a plurality of components. In the device, a plurality of configurations included in the system
Set the factors based on their impact on system reliability.
It is divided into rank events and sub-events, and these relationships are hierarchically organized.
Enter the structure of the fault tree expressed as a tree structure.
Input means and trust regarding the reliability of each component
Means for pre-storing sex data, said inputting means
By analyzing the fault tree input from the
Therefore, at least for each sub-event whose occurrence probability is unknown
An importance calculation method for calculating importance and a higher-level event
Using the occurrence probability and the importance given for
By generating the original equation and finding the solution,
Probability calculation means for calculating the raw probability and each sub-event
Corresponding to the occurrence probability calculated for
Means for comparing reliability data of said component
And are provided. The invention of claim 4, which is assumed from a viewpoint that the method invention of claim 1, co
A computer with multiple components using a computer.
System reliability for designing system reliability
In the design method, the system input by the user is used.
System components that contribute to system reliability.
Based on the influence of
Fault tree that represents these relationships in a hierarchical tree structure
By analyzing the structure of
Importance calculation that calculates importance for each unknown sub-event
Steps and upper events entered by the user
Using the probability of occurrence and the calculated importance, multidimensional
By generating the equation and finding the solution,
Probability calculation step for calculating probability and
Occurrence probability calculated by
Reliability data on the reliability of each component that corresponds to
Comparing the data with the data. The invention of claim 7 is obtained by considering the inventions of claims 1 and 4 as a recording medium in which software of a computer is recorded, and the reliability of the system for designing the reliability of the system using the computer. a recording medium which records sex design software, the software in the software the computer, Yu
User-entered multiple configurations included in the system.
Based on the impact of the components on the reliability of the system,
It is divided into rank events and sub events, and these relationships are hierarchically
-Analyzing the structure of the fault tree represented by the structure
At least for each sub-event whose probability of occurrence is unknown.
The higher level event entered by the user
Occurrence probability and the calculated importance
By generating a multidimensional equation and finding a solution,
Let the probability of occurrence of the event be calculated and calculated for each sub event.
Occurrence probability and the lower event given by the user
Reliability data about the reliability of each corresponding component
The feature is that they are compared . According to the inventions of claims 1, 4, and 7, even if a given fault tree has a lower event whose occurrence probability is unknown, each lower event calculated from the occurrence probability designated for the upper event and the structure of the fault tree. By generating and solving a multidimensional equation using the importance of and, it is possible to calculate or estimate the unknown occurrence probability of the lower event, and output it. In other words, the occurrence probability of a lower event corresponding to the target occurrence probability of the upper event can be calculated in a top-down manner, effectively supporting the design related to the reliability of the system such as the device corresponding to the lower event. . In addition, a different approach for each system component
The expected occurrence probability and expected occurrence probability
The reliability data such as standards are stored in a database.
Prepared, the calculated probability of occurrence and their reliability
Component and output the comparison result
The probability of occurrence for each
It becomes easy to judge whether the element is a problem.

The present invention includes a mode in which the importance is used for calculating the probability of occurrence of a lower event from the solution of the equation, not the equation generation. In particular, such top-down calculations are performed upstream of system design, that is, at the stage where the components have not yet been specifically determined in the initial stage, so that the reliability required for each component can be easily determined in advance. It can be expected to have great effects such as rational resource allocation and prevention of stage reversion. In addition, as a representative example of the upper-level events, there is a peak event that represents the reliability of the entire system at the root of the fault tree, and as a representative example of the lower-level events, at the end of the fault tree, which affects the system reliability. Mention may be made of the bottom event, which represents the most subdivided event. Further, the present invention generates a multidimensional equation based on the occurrence probability given to the upper event and the occurrence probability of each of the lower events, obtains the solution of this multidimensional equation, and based on this solution and the importance. It also includes the case where the unknown occurrence probability is calculated.

According to a second aspect of the present invention, in the system reliability design device according to the first aspect, the probability calculation means determines a reference reference event from among sub-events of which the occurrence probability is unknown, and the reference The occurrence probability of an event is represented by a variable, and the first equation representing the relationship between the occurrence probability of an upper event and the occurrence probability of each lower event given in advance as a goal is generated, and the occurrence probability of a lower event other than the reference event is calculated. , And is configured to generate a second equation represented using the importance of the reference event and the variable. The invention of claim 5 is obtained by considering the invention of claim 2 as a method. In the method for designing reliability of a system according to claim 5, the probability calculation step is a sub-event whose occurrence probability is unknown. A reference event as a reference is determined, the occurrence probability of the reference event is represented by a variable, and a first equation representing the relationship between the occurrence probability of the upper event and the occurrence probability of each lower event given in advance as a target is generated. However, a second equation expressing the occurrence probability of a subordinate event other than the reference event by using the importance of the reference event and the variable is generated.
In the inventions of claims 2 and 5 , not only an equation is created for the occurrence probability of the lower event from the relationship with the occurrence probability of the upper event, but also an equation is created for the degree of importance that affects the upper event, It is possible to allocate the probability of occurrence between events according to their importance. For example, even when there are various possible combinations of occurrence probabilities of lower events corresponding to the same occurrence probabilities of lower events, for example, by assigning a lower probability of occurrence to a lower event with higher importance such as structural importance, It is possible to easily perform rational reliability design, such as focusing on enhancing the reliability of equipment. Even if the probability of occurrence for each sub-event has already been obtained, the probability of occurrence that has already been obtained is calculated by recalculating the probability of occurrence based on such importance as unknown. It is easy to evaluate from a viewpoint. The order in which the first equation and the second equation are generated is arbitrary, and for example, it is desirable to use the second equation when generating the first equation.

The invention of claim 3 is claim 1 or claim
2. The reliability design device for a system according to 2 is configured to calculate and output an occurrence probability of an upper event when the occurrence probabilities of all lower events included in the fault tree are known. And The invention of claim 6 is obtained by considering the invention of claim 3 as a method, and in the system reliability design method according to claim 4 or 5 , all the sub-events included in the fault tree are included. When the occurrence probability is known, the occurrence probability of the upper event is calculated and output. In the inventions of claims 3 and 6, when the occurrence probabilities of all the lower events in the fault tree are known, the occurrence probabilities of the upper events are calculated and output as in the conventional case.
Various reliability designs, including bottom-up calculations, are implemented.

[0018]

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention (hereinafter referred to as "embodiments") will be described with reference to the drawings. Note that the present invention is generally considered to be realized by controlling a computer having peripheral devices with software. In this case, the software is made by combining the instructions according to the description of this specification, and the method described in the prior art is also used for the common part with the above-mentioned prior art. The software includes not only the program code but also data prepared in advance for use when executing the program code.

The software utilizes physical resources such as a CPU, a coprocessor, a processing device such as various chipsets, an input device such as a keyboard and a mouse, a storage device such as a memory and a hard disk device, an output device such as a display and a printer. By doing so, the effects of the present invention are realized.

However, the specific software and hardware configurations for implementing the present invention can be changed in various ways. For example, the software format is a compiler,
There are various kinds of interpreters, assemblers, etc. For exchanging information with the outside, various kinds of removable recording media such as floppy disks, network connecting devices, etc. are also conceivable. Further, a recording medium such as a CD-ROM that records software or a program for realizing the present invention,
Independently, it is one embodiment of the present invention. Further, some of the functions of the present invention can be realized by a physical electronic circuit such as an LSI.

As described above, various modes of implementing the present invention using a computer are conceivable. Therefore, in the following, a virtual circuit block that implements each function included in the present invention or the embodiment is used to implement the present invention. The invention and embodiments will be described.

[1. First Embodiment] A first embodiment is a system reliability design device (hereinafter, referred to as “this device”) for designing the system reliability, and is one of the bottom events forming a fault tree. , Shows an example of estimating the occurrence probabilities of the bottom event when the occurrence probabilities of all the bottom events are unknown.

[1-1. Configuration of First Embodiment] First, FIG. 1 is a functional block diagram showing the configuration of the first embodiment. That is, in FIG. 1, reference numeral 101 represents input information input to the present apparatus, and specifically, it is determined from among the tree structure of the fault tree and the occurrence probability of the top event and the occurrence probability of the bottom event. There is something. Further, the fault tree mentioned here is data that represents the relationship between upper events and lower events relating to the reliability of the system being designed in a hierarchical tree structure.

Reference numeral 102 is an input device for inputting the input information 101 including the tree structure of the fault tree. Reference numeral 103 is an importance determining unit that calculates the importance of at least each sub-event whose occurrence probability is unknown according to a predetermined criterion by analyzing the tree structure of the input fault tree. It corresponds to the calculation means.

Reference numeral 104 denotes a peak event probability calculation unit, which calculates the value of the peak event occurrence probability when the occurrence probabilities of all bottom events in the fault tree are known, and otherwise, the fault tree This is a part that creates a multidimensional equation using variables corresponding to unknown occurrence probabilities for the bottom event from the tree structure of tree and the importance of each bottom event.

More specifically, the peak event probability calculator 104 determines a reference reference event as a reference from among lower order events whose occurrence probability is unknown, represents the occurrence probability of the reference event as a variable, and sets it as a target. A first equation representing the relationship between the occurrence probability of the upper event and the occurrence probability of each lower event given in advance is generated, and the occurrence probability of the lower events other than the reference event is defined as the importance of the reference event and the variables. It is configured to generate a second equation represented by.

Reference numeral 105 denotes an equation analysis unit that analytically solves the multidimensional equation to calculate a solution of 0 or more and 1 or less for each of the variables. Reference numeral 106 denotes an event probability calculator that calculates the occurrence probability of each bottom event from the solution of the multidimensional equation.

The peak event probability calculator 10
4, the equation analysis unit 105 and the event probability calculation unit 106,
Using the importance of each bottom event and the occurrence probabilities given for the top events, by generating a multidimensional equation and finding the solution,
It constitutes a probability calculation means for calculating the occurrence probability of a subordinate event.

Further, 107 is an occurrence probability calculated by other means such as associating previously stored device information and device reliability parameters with each bottom event of the fault tree, and an event probability calculation unit 106. It is a comparison operation unit that compares the occurrence probability of each bottom event.

The equipment information is information representing what kind of constituent element, that is, equipment is likely to be used for system design, and reliability data regarding reliability of each equipment. The storage device stores various device information in advance. An output device 109 displays the output result such as the evaluation result on the display or the like from the present device. Further, 110 is an output result output from this apparatus, and includes the occurrence probability of each bottom event calculated by the event probability calculation unit 106 and the comparison result by the comparison calculation unit 107.

[1-2. Operation of First Embodiment] Next, the operation of the first embodiment configured as described above will be described with reference to FIGS. 2 to 6. [1-2-1. Overall Processing Procedure] First, FIG. 2 is a flowchart showing the overall processing procedure in the first embodiment. That is, in this procedure, first, by processing the tree structure of the fault tree input to the input device 102 of FIG. 1, the importance degree determination unit 103 determines the importance degree of each bottom event in the given fault tree. Calculate (step 201 in FIG. 2).

Here, the importance is determined for each bottom event unit according to a predetermined standard, and a specific standard can be freely determined, but for example, it is related to each bottom event. It is the cost for the device, the structural importance of each bottom event in a given fault tree, or the quotient of the structural importance and cost of each bottom event. Then, more generally, when n standards C1 to Cn are prepared, the importance I of each bottom event is represented by I = f (C1, ..., Cn).

Next, at step 202, the peak event probability calculation unit 104 determines whether or not the occurrence probabilities of all the bottommost events of the given fault tree are known. Is calculated (step 203)
Go to step 204. In other cases, the process directly proceeds to step 204, and in this case, the peak event probability calculation unit 1
04 is a peak event and each bottom event by using the occurrence probability of the base bottom event as an unknown variable and using the given tree structure of the fault tree and the importance of each bottom event calculated in step 201. Calculate the multidimensional equation that holds between.

If the equation generation fails (step 205), the processing failure is output as the processing result of this procedure (step 206), and the process ends, but if the equation generation succeeds (step 205), the equation Analysis unit 1
05 solves the multidimensional equation using an analytical method to obtain an approximate solution of 0 or more and 1 or less that satisfies the equation (step 207). As a result, when there is no solution, that is, when there is no solution (step 208),
The processing failure is output as the processing result of this procedure (step 206), and the process ends.

On the other hand, if a solution is obtained (step 20)
8), the event probability calculation unit 106 calculates the occurrence probability of each bottom event from the solution and the importance of each bottom event (step 2).
09). The occurrence probability calculated by the comparison calculation unit 107 by another means such as reliability data in the storage device 108,
The probability of occurrence of each bottom event calculated in step 209 is compared. Then, the output device 109 outputs the result (step 210). Hereinafter, the procedure shown in FIG. 2 will be described more specifically.

[1-2-2. Example of Fault Tree] First, FIG. 3 is a conceptual diagram showing the structure of a fault tree taken as an example in the description of the first embodiment. That is, in this example, the node A (301) that is the root of the tree structure
Is a node representing a peak event, each node X, Y, Z at the end of the tree structure is a bottom event, and these bottom events represent the most subdivided events that cause the peak event.

The bottom event node X (303) and the intermediate event node B (304) are connected to the OR gate (30
It is associated with node A by 2). Also, the bottom event node Y (306) and the bottom event node Z (3
07) is associated with node B by an AND gate (305).

Here, each lower event associated with the upper event by an AND gate corresponds to a parallel element, and the upper event occurs only when both events occur at the same time.
Further, each lower event associated with the upper event by the OR gate corresponds to the serial element, and when either one of them occurs, the upper event occurs.

Then, for example, when the occurrence probability of an event represented by a certain node is represented by P (node name), in the example of FIG. 3, for the nodes Y and Z associated with the node B by the AND gate, P (B) = P (Y) * P (Z) holds.

For the nodes X and B associated with the node A by the OR gate, P (A) = 1- (1-P (X)) * (1-P (B)) holds.

[1-2-3. Specific procedure for calculating the degree of importance]
Further, FIG. 4 shows the calculation of the degree of importance in FIG.
It is a flowchart showing a specific procedure of 1), and in the present embodiment, a procedure that employs the structural importance of each bottom event in the fault tree is used as the importance of each bottom event. Here, the structural importance of a certain event means that, when considering whether the whole system is normal or faulty for each combination of whether each event is normal or faulty, the case where a certain event is normal is compared with the case where it is faulty. It is how much the ratio of combinations that become totally defective is reduced, and is usually expressed by the difference in failure ratio.

For example, in the example of FIG. 3, the event or the failure related to the node Y or Z causes the entire failure only when the other also fails, whereas the node X
A failure related to will always cause an overall failure,
It is more important than the nodes Y and Z.

[1-2-3-1. Classification into Levels] That is, in the procedure of FIG. 4, first, all the events of a given fault tree are classified so that the events having the same hierarchical depth from the summit event have the same Level, and the depth Level1, Level2, ... (Step 40)
1).

Here, it is assumed that one classification consists of a list of sets including the following items. (Node, List of Nodes Related to One Step Above, Gate, Related Node Below One Step) For example, in the example of FIG. 3, {(node A, None, OR, node X, node B)} is Level1, {( Node X, node A, None, None), (node B, node A, AND, node Y, node Z)} is Level2, {(node Y, node B, None, None), (node Z, node B, None, None)} becomes Level3.

Here, None means that the corresponding item does not exist. At this time, Le of the deepest bottom event
If vel is 1 (step 402), {(A = top event), (1)} is output as the processing result of this procedure as a set of structural importance (step 40).
3), end.

[1-2-3-2. Acquisition of Combination Set of Events] On the other hand, when the level of the deepest bottom event is other than 1 in step 402, the combination set L of the events of Level 2 that makes the event of Level 1 1
2 is calculated (step 404). It should be noted that "1" indicates that the event has occurred, and in particular, the state of failure.

Here, the combination set has a set consisting of the following items as its constituent elements. (List of related nodes, list of combinations that make the node one level higher than 1) For example, in the example of FIG.
The combination set L2 of Level2 events that makes the event of l1 into 1 is {((X, B), (0, 1), (1, 0), (1,
1))}.

Next, a variable i is prepared, 2 is substituted (step 405), and Level (i + 1) that satisfies the combination L (i) of each event of Level (i).
Then, the combination L (i + 1) of the respective events is obtained (step 406).

For example, in the example of FIG. 3, a combination set L3 of Level3 events satisfying each element of L2 is obtained. Specifically, first, the set of (X, Y, Z) that satisfies (X, B) = (0, 1) is {(0, 1,
1)}. Next, a set of (X, Y, Z) that satisfies (X, B) = (1,0) {(1,0,0), (1,0,1), (1,1,0) )} Is obtained. Then, a set of (X, Y, Z) that satisfies (X, B) = (1, 1) is {(1, 1,
1)}.

Therefore, Le that satisfies each element of L2
The combination set L3 of events of vel3 is {((X, Y, Z), (0, 1, 1), (1, 0,
0), (1,0,1), (1,1,0), (1,1,
1))}.

Thereafter, i + 1 is assigned to i and incremented (step 407), and i is the deepest bottom event Le.
If it is less than the number of vel (step 408), L (i +
Returning to the process of obtaining 1) (step 406), if i reaches the level number of the deepest bottom event in step 408, the combination of each event of the bottom event is set to L again (step 409).

For example, in the example of FIG. 3, after obtaining a combination set L3 of Level3 events satisfying each element of L2 (step 406), when i is incremented (step 407), i is the deepest and deepest. Level of the lower event
Since it is equal to the number of l (3) (step 408), the process proceeds to step 409.

[1-2-3-3. Calculation of Structural Importance Based on Set] Then, after the combination of each event of the bottom event is set again as L (step 409), the number of each event being 1 in each element of L (each combination) is calculated. Check for each event (step 410). Here, the results of the examination will be represented by the following sets. (List of node names, list of the number of times that the event corresponding to each node in L becomes 1) For example, in the example of FIG. 3, L = {((X, Y, Z), (0,1,1), (1, 0,
0), (1,0,1), (1,1,0), (1,1,
1))} and the number of each event being 1 is represented by {(X, Y, Z), (4, 3, 3)}.

Then, the structural importance of each bottom event is calculated (step 411). That is, the number of bottom events is N, L
The structural importance K is expressed by the following equation, where n is the number of elements of A and a is the number of each lowest event in L. K = (2 * a- (n-1)) / (2 ^ (N-1)) Further, the calculation result of the structural importance is represented by the following set. (List of node names, list of structural importance of events corresponding to each node) For example, in the example of FIG. 3, the structural importance KX of X is (2 * 4- (6-1)) / (2 ^ (3-1)) = 3/4, structural importance KY of Y is (2 * 3- (6-1)) / (2 ^ (3-1)) = 1/4, structural importance of Z The KZ is (2 * 3- (6-1)) / (2 ^ (3-1)) = 1/4. Finally, the structural importance of each bottom event is output as the processing result of this procedure (step 412). Figure 3
In the example, {(X, Y, Z), (3/4, 1/4, 1/4)} is output.

[1-2-4. Specific Procedure of Top Event Calculation] Next, FIG. 5 is a flowchart showing a specific processing procedure of the generation of the multidimensional equation (step 203) shown in FIG. That is, the top event probability calculation unit 104
Is a reference event that is used as a reference among subevents whose occurrence probability is unknown, and the occurrence probability of the reference event is represented by a variable. A first equation expressing the relationship with is generated, and a second equation expressing the probability of occurrence of a subordinate event other than the reference event using the importance of the reference event and the variable is generated.

[1-2-4-1. Data Input and Event Level Classification] More specifically, in this procedure, first, the tree structure of the fault tree, the occurrence probability of the top event, and the structural importance of each bottom event obtained in step 201 are determined. Input (step 501). For example, in the fault tree of FIG. 3, it is assumed that the occurrence probability of the top event is set to 0.1. Next, all the events of a given fault tree are classified so that the events having the same hierarchical depth from the summit event have the same Level, and the events are sorted in the depth order.
1, Level2, ... (Step 502).

[1-2-4-2. Exceptional Case] At this time, if the level of the deepest bottom event is 1 (step 503), it is determined whether the occurrence probability of the bottom event (= top event) is known (step 504). If the occurrence probability of the bottom event (= top event) is known in step 504, the value of the occurrence probability of the top event is output as the processing result of this procedure (step 513), and the process ends. On the other hand, if the occurrence probability of the bottom event (= top event) is not known in step 504, the equation generation failure is output as the processing result of this procedure (step 50
5) Finish.

If the level of the deepest bottom event is greater than 1 in step 503, it is determined whether the occurrence probabilities of all bottom events are known (step 5).
06). In this step 506, if the occurrence probabilities of all bottom events are known, the process proceeds to step 509.

[1-2-4-3. Occurrence probability weighting]
On the other hand, in step 506, if the occurrence probabilities of all the bottom events are not known, then among the bottom events whose occurrence probabilities are unknown,
A reference event is determined, its occurrence probability is set as a variable x (step 507), and the probability of occurrence of each bottom event is unknown and expressed as a ratio with x using structural importance ( Step 508).

At this time, if the structural importance is high, the probability of occurrence is set to be small according to the ratio. Specifically, the occurrence probability of the bottom event corresponding to a certain node D is represented by the variable x by the following formula. Occurrence probability of the bottom event corresponding to node D = (structural importance of the node corresponding to the reference bottom event) / (node D
(Structural importance of) * x This means that an event with a high structural importance is weighted so that it has a low probability of occurrence.

For example, in the example of FIG. 3, the occurrence probability of the bottom event corresponding to the node X is set as the variable x. At this time, Nod
The occurrence probability of the bottom event corresponding to eY is (3/4) / (1/4) * x = 3 * x, and the occurrence probability of the bottom event corresponding to NodeZ is also (3/4) / ( Set 1/4) * x = 3 * x.

If the occurrence probabilities of all bottom events are known in step 506, and after the occurrence probabilities of all bottom events have been set by the variable x (steps 507, 5).
08), the level number of the bottom event is substituted for the variable i (step 509). Then, based on the fault tree classification obtained in step 502 and the occurrence probability of each bottom event obtained in step 508, Level (i-
The occurrence probability of each event of 1) is expressed by using the occurrence probability of each event of Level (i) with a variable (step 51).
0).

Here, the expression differs depending on whether the type of the node, that is, the gate, which associates the respective events is AND and OR. That is, N events are related by AND, and the occurrence probability of each event is P.
In the case of (i) and (1 ≦ i ≦ N), the occurrence probability P of the event one step above is expressed by the following equation.

P = P (1) * P (2) * ... * P (N) On the other hand, N events are associated by OR, and the occurrence probabilities of the events are P (i) and (1 ≦ When i ≦ N), the occurrence probability P of the event one step higher is expressed by the following equation.

P = 1- (1-P (1)) * (1-P
(2)) * ... * (1-P (N)) For example, in the example of FIG. 3, first, 3 is substituted for i,
The occurrence probability of each event of Level 2 is represented by the occurrence probability of each event of Level 3. Here, the expression of the occurrence probability is
It shall be represented by a list of sets consisting of the following items: (Probability of occurrence, node one step higher corresponding to the event for which the probability of occurrence is calculated) In this case, the probability of occurrence of each event of Level 3 is {(3 * x, node Y), (3 * x, node Z)} The probability of occurrence of each Level2 event is {(x, node A), (9 * x ^ 2, node B)}.

[1-2-4-4. Generation of Equation Using Expression of Occurrence Probability] Subsequently, i−1 is substituted for i and decremented (step 511), and if i = 1 (step 512), the process proceeds to step 513, and a peak event occurs. Probability or probability of the first given top event and L
An equation is generated from the occurrence probability of evel1 and the equation is output as the processing result of this procedure (step 513), and the process ends. Further, in the determination of step 512, i
If = 1 is not satisfied, the process returns to step 510.

For example, in the example of FIG. 3, when i = 3-1 = 2, the process proceeds to step 510 and the process is repeated. That is, the occurrence probability of the Level 1 event is L
It is represented by the probability of occurrence of each event of level2. as a result,
The occurrence probability of the Level1 event is {(-9 * x ^ 3 + 9 * x ^ 2 + x, None)}. Here, None means that there is no node one level higher. At this stage, again step 511
In, i = 2-1 = 1, so that the process proceeds to step 513.

That is, since the occurrence probability of the top event given first is 0.1, the following relational expression holds. -9 * x ^ 3 + 9 * x ^ 2 + x = 0.1 Therefore, the equation 9 * x ^ 3-9 * x ^ 2-x + 0.1 = 0 is output and the processing ends.

[1-2-5. Specific procedure for equation analysis]
6 and 7 are flowcharts showing the specific procedure of the equation analysis (step 207) shown in FIG. 2, which are connected together by the connectors 1 and 2. In addition, here, a processing procedure when the Newton method is used will be described.

[1-2-5-1. When the Order is Not 1 or More] That is, in this procedure, first, the multidimensional equation f (x) = 0 obtained in step 204 is input (step 601). At this time, if the order of f (x) is not 1 or more (step 602), no solution of the equation is output as the processing result of this procedure and the process ends (step 61).
6) In step 602, if the order of f (x) is 1 or more, the following procedure is executed.

[1-2-5-2. Initialization] That is, first, the first derivative f ′ (x) of f (x) is obtained (step 6
03) and the allowable error δ of the approximate solution in advance (step 6
04), the trial number limit α and (step 605), and the step size γ and (step 606) are determined. Also, 0 is assigned to the variable i (step 607), and 1 is assigned to the variable c (step 608).

[1-2-5-3. Repeated Processing] Here, if i <1, the processing is ended (step 609), but otherwise, the initial value a = i is set (step 610),
Then, b = a−f (a) / f ′ (a) is obtained (step 611), and if | b−a | <δ (step 612), it is regarded as the range of the allowable error, and b is initialized. It is output as an approximate solution when the value is a (step 613), and the process proceeds to step 618.

On the other hand, if it is determined in step 612 that │b-a│ <δ is not satisfied, b is substituted for a (step 614), and c + 1 is substituted for c (step 615). Here, if f ′ (a) ≠ 0 or c <α is not satisfied (step 616), no solution of the equation is output as the processing result of this procedure (step 61).
7) The process proceeds to step 618, but if f ′ (a) ≠ 0 or c <α is not determined in step 616, the process returns to step 611.

For example, in the example of FIG. 3, the equation f (x) = 9 * x ^ 3-9 * x ^ 2-x + 0.1 = 0 is given, and at step 604, δ = 0.00000001 and at step 606. By setting γ = 0.05, the following output will be obtained.

[0075]

[Table 1]

[1-2-6. Processing after Calculation of Occurrence Probability of Bottom Event] Then, based on the solution of the equation obtained as described above, the occurrence probability of each bottom event is calculated in the event probability calculation unit (106) in FIG. Yes (Step 20)
9). At this time, only when the occurrence probabilities of all bottom events are 0 or more and 1 or less (steps 207, 20).
8) and outputs the result (step 209).

In the example of FIG. 3, from the assumption set in step 508, the occurrence probability P of the bottom event corresponding to the node X is generated.
(X) is a variable x. Further, the occurrence probabilities P (Y) and P (Z) of the bottom event corresponding to NodeY and Z are 3 * x. Therefore, the relationship between the solution of the equation and the probability of occurrence of each bottom event is

[Table 2] become that way.

In the combination of the occurrence probabilities of each bottom event, when the occurrence probabilities of all bottom events are 0 or more and 1 or less, {P (X), P (Y), P (Z)} = {0.06473
058304, 0.19419174912, 0.19
419174912}. This combination is output as the output result (110) from the output device (109) in FIG. 1 (step 21).
0).

[1-2-7. Simplified Example] The above specific example is simplified and shown below. That is, in the example of FIG. 3, when the occurrence probability P (A) = 0.1 and the importance S () is S (X) = 3/4 S (Y) = S (Z) = 1/4, The occurrence probability of the summit event is P (X), P (Y), P
When expressed using (Z), 0.1 = 1- (1-P (X)) * (1-P (Y) * P
(Z)), and weighting such that an event having a high structural importance has a low probability of occurrence, P (X): P (Y): P (Z) = (1-S (X) ) :( 1-S (Y)) :( 1-S (Z)) = 1: 3: 3. From these two equations, P (X), P (Y),
When P (Z) is calculated, P (X) = 0.06473058304, P (Y) = P (Z) = 0.19419174912.

[1-3. Effect of First Embodiment] As described above, in the first embodiment, even if there is a lower event whose occurrence probability is unknown in a given fault tree, the occurrence probability designated for the upper event and the structure of the fault tree. By generating and solving a multidimensional equation using the importance of each sub-event calculated from, the unknown occurrence probability of the sub-event can be calculated, that is, estimated and output. That is, it is possible to calculate the occurrence probability of the lower event corresponding to the target occurrence probability of the upper event in a top-down manner,
The design related to the reliability of the system such as the equipment corresponding to the subordinate events is effectively supported.

In particular, such top-down calculation is performed upstream of the system design, that is, at a stage when the constituent devices have not yet been specifically determined in the initial stage, so that the reliability required for each constituent device is calculated in advance. It can be easily decided, and great effects such as rational resource allocation and prevention of stage reversion can be expected.

Further, in the first embodiment, not only an equation is created for the occurrence probability of the lower event from the relationship with the occurrence probability of the upper event, but also an equation is created for the importance of affecting the upper event. It is possible to assign the probability of occurrence among the subordinate events according to the degree of importance. For example, even when there are various possible combinations of occurrence probabilities of lower events corresponding to the same occurrence probabilities of lower events, for example, by assigning a lower probability of occurrence to a lower event with higher importance such as structural importance, It is possible to easily perform rational reliability design, such as focusing on enhancing the reliability of equipment. Further, in the first embodiment, reliability data such as criteria such as expected occurrence probability and expected occurrence probability obtained by another method are prepared in advance in a database or the like for each component of the system and calculated. By comparing the occurrence probabilities with those reliability data and outputting the comparison results, it is possible to judge whether the occurrence probabilities for each component are excessive or insufficient, and which component has a problem in terms of reliability. Will be easier.

Further, in the first embodiment, when the occurrence probabilities of all the lower events in the fault tree are known, the occurrence probability of the upper event is calculated and output as in the conventional case. Various reliability designs, including calculations, are realized.

[2. Second Embodiment] In the second embodiment, in the configuration as shown in FIG. 1, occurrence of some of the bottom events among the bottom events constituting the fault tree as shown in FIG. It shows an example of estimating the occurrence probabilities of these bottom events when the probabilities are unknown.

[2-1. Specific Example in Second Embodiment]
That is, in the fault tree shown in FIG.
It is assumed that the occurrence probability of the node Z is known and its value is 0.02. At this time, the occurrence probability of the peak event is 0.0
It is assumed that the occurrence probability of the bottom event nodes X and Y for making 5 is estimated.

In this case, first, in the procedure shown in FIG. 2, the tree structure of the fault tree input to the input device 102 of FIG. 1 is processed in step 201 of FIG. Calculate the structural importance of each bottom event.

For example, as the structural importance based on the example of FIG. 3, {(X, Y, Z), (3/4, 1/4, 1/4)} is as in the first embodiment. can get. Here, since the occurrence probabilities of the bottom event nodes X and Y are unknown, the process proceeds from step 202 to step 204. Then, using the given tree structure of the fault tree and the structural importance of each bottom event calculated in step 201 as the unknown occurrence probability of the bottom event, which is the basis, and the top event and each bottom event. Calculate multidimensional equations that hold between events.

That is, in the example of FIG. 3, when the occurrence probability of the bottom event X node is x, the occurrence probability of each event of Level3 is {(3 * x, node Y), (0.02, node Z)} and the occurrence probability of each Level2 event is {(x, node A), (0.06 * x, node B)}. Then, the occurrence probability of the Level1 event is {(-0.06 * x ^ 2 + 1.06 * x, None)}.

By solving the multidimensional equation using an analytical method (step 207), an approximate solution of 0 or more and 1 or less satisfying this equation is obtained. Specifically, FIG.
In the example, x = 0.2293941 is obtained. When the probability of occurrence of each bottom event is estimated from this solution and the structural importance of each bottom event (step 2
09), the occurrence probability of the node X in consideration of the structural importance can be estimated to be 0.2293941. Further, the occurrence probability considering the structural importance of the node Y is 0.688.
It can be estimated as 1823. The occurrence probability of each of these bottom events is output as an output result 110 from the output device 109 of FIG.

[2-2. Simplified Example] The above specific example is simplified and shown below. That is, in the example of FIG.
When the occurrence probability P (A) = 0.05 P (Y) = 0.02 and the importance S () is S (X) = 3/4 S (Y) = S (Z) = 1/4, If the occurrence probability of the peak event is expressed using P (X), P (Y) = 0.02 and P (Z), then 0.1 = 1- (1-P (X)) * (1-0.02 * P
(Z)), and weighting such that an event having a high structural importance has a low probability of occurrence, P (X): P (Z) = (1-S (X)) :( 1- S (Z)) = 1: 3. When P (X) and P (Z) are calculated from these two equations, P (X) = 0.2293941 P (Z) = 0.6881823.

As described above, in the second embodiment, the occurrence probabilities of other bottom events are calculated based on the occurrence probabilities known for some bottom events and the given occurrence probabilities for top events. Therefore, it becomes easy to smoothly proceed the design regarding reliability for each bottom event.

[3. Third Embodiment] In the third embodiment, in the configuration shown in FIG. 1, occurrence of some of the bottom events among the bottom events forming the fault tree as shown in FIG. When the probability is unknown or all values are known, the occurrence probability of each bottom event calculated by the reliability design device of the system of the present invention and the occurrence probability of the known bottom event are compared. This is an example in which the suitability of the known occurrence probability can be determined.

In the following description, the case where all the values are known among the bottom events forming the fault tree is shown. However, among all bottom events, the occurrence probability of some bottom events is It is possible to perform the same processing even when unknown.

[3-1. Specific Example in Third Embodiment]
First, in the fault tree shown in FIG. 3, the occurrence probabilities of all bottom event nodes X, Y, Z are known,
It is assumed that the values are 0.3, 0.4 and 0.2, respectively. At this time, first, the occurrence probability of the top event is calculated from the occurrence probabilities of the bottom events. Then, based on the occurrence probability of the summit event, the value of each bottom event in the case of considering the structural importance according to the present embodiment is calculated, and the initially known value and each value newly calculated. Should be compared.

That is, first, in the procedure shown in FIG. 2, by processing the tree structure of the fault tree input to the input device 102 of FIG. 1 in step 201 of FIG. 2, each maximum in the given fault tree is processed. Calculate the structural importance of the lower event. For example, in the example of FIG. 3, similar to the first embodiment, {(X, Y, Z), (3/4, 1 /
4, 1/4)} is obtained. In this case, since the occurrence probabilities of all bottom event nodes X, Y, Z are known, step 202
To step 203, the probability of the occurrence of the summit event is calculated. For example, in the example of FIG. 3, the occurrence probability of the top event node A is 1- (1-0.3) * (1-0.4 * 0.2) = 0.3
56 is calculated.

Next, in step 204, the tree structure of the given fault tree and the structural importance of each bottom event calculated in step 201 are used with the occurrence probability of the base bottom event as an unknown variable. , Calculate a multidimensional equation that holds between the top event and each bottom event. For example, in the example of FIG. 3, when the occurrence probability of the bottom event node X is x,
The occurrence probability of each event of Level3 is represented by {(3 * x, node Y), (3 * x, node Z)}, and the occurrence probability of each event of Level2 is {(x, node A), ( 9 * x ^ 2, node B)}. Then, the occurrence probability of the Level1 event is {(-9 * x ^ 3 + 9 * x ^ 2 + x, None)}.

By solving the multidimensional equation using an analytical method (step 207), an approximate solution of 0 or more and 1 or less satisfying the equation is obtained. For example, in the example of FIG. 3, x = 0.1607718315 is obtained. When the probability of occurrence of each bottom event is estimated from this solution and the structural importance of each bottom event (step 2
09), it is possible to estimate the occurrence probability of the node X in consideration of the structural importance as 0.1607718315. Further, the occurrence probability in consideration of the structural importance of the node Y is 0.
It can be estimated as 4823154.

The probability of occurrence of each of these bottom events is compared with the comparison operation unit (107) of FIG. 1, and the output result (110) as illustrated below is output from the output device (109).

[0099]

[Table 3]

[3-2. Simplified Example] The above specific example is simplified and shown below. That is, in the example of FIG.
Occurrence probability P (X) = 0.3 P (Y) = 0.4 P (Z) = 0.2 P (A) = 1- (1-0.3) * (1-0.4 * 0. 2) = 0.356 and the importance S () is S (X) = 3/4 S (Y) = S (Z) = 1/4, the occurrence probability of the peak event is P (X), P (Y), P
When expressed using (Z), 0.356 = 1- (1-P (X)) * (1-P (Y) *
P (Z)), and weighting such that an event with a high structural importance has a low occurrence probability, P (X): P (Y): P (Z) = (1-S (X )) :( 1-S (Y)) :( 1-S (Z)) = 1: 3: 3. From these two equations, P (X), P (Y),
When P (Z) is obtained, P (X) = 0.16077183315 P (Y) = P (Z) = 0.482153

As described above, in the third embodiment, even if the occurrence probabilities have already been obtained for each subordinate event, the occurrence probabilities based on such importance are newly calculated as unknown ones. , It becomes easy to evaluate the occurrence probability already obtained from the viewpoint of importance.

[4. Other Embodiments] The present invention is not limited to the above-described embodiments, and includes other embodiments as illustrated below. For example, any type of system may be used as a target for reliability design according to the present invention. For example, not only the probability of occurrence of constituent devices but also the probability of occurrence of human error can be calculated. Further, the configuration, the fault tree and the calculation procedure shown in each of the above embodiments are merely examples,
It can be appropriately changed according to a specific mounting mode or an application target. Further, as a method for obtaining the solution of the equation, a conventionally known method can be freely selected.

The specific standard for determining the standard event from among a plurality of sub-events is free,
For example, if the event with the highest number of appearances is selected as the reference event among the importance values of the lowest event of which the occurrence probability is unknown, the coefficient of each order of the resulting equation will have a certain value. It is suppressed and the calculation becomes efficient. Also, in the fault tree, the mode in which each of the plurality of constituent elements included in the system is associated with each subordinate event is arbitrary, and nodes corresponding to the constituent elements and the like may be provided to explicitly associate them, or implicitly. May be associated with.

[0104]

As described above, according to the present invention,
A system reliability design device that effectively supports system reliability design by calculating the occurrence probability of a lower event based on the fault tree of the target system and the occurrence probability given for an upper event Since it is possible to provide a recording medium in which software for reliability design of a system, method, and system is recorded, accuracy and efficiency relating to reliability design of the system are improved.

[Brief description of drawings]

FIG. 1 is a functional block diagram showing a configuration of a first embodiment of the present invention.

FIG. 2 is a flowchart showing an overall processing procedure according to the embodiment of the present invention.

FIG. 3 is a diagram showing an example of a fault tree according to the embodiment of the present invention.

FIG. 4 is a flowchart showing a specific processing procedure for calculating structural importance in the embodiment of the present invention.

FIG. 5 is a flowchart showing a specific processing procedure for generating a multidimensional equation in the embodiment of the present invention.

FIG. 6 is a flowchart (first half) showing a specific processing procedure for obtaining a solution of a multidimensional equation in the embodiment of the present invention.

FIG. 7 is a flowchart (second half) showing a specific processing procedure for obtaining a solution of a multidimensional equation in the embodiment of the present invention.

[Explanation of symbols]

101 ... Input information 102 ... Input device 103 ... Importance calculation section 104 ... Top event probability calculation unit 105 ... Equation analysis unit 106 ... Event probability calculator 107 ... Comparison operation unit 108 ... Storage device 109 ... Output device 110 ... Output result

─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP-A-5-143570 (JP, A) JP-A-9-237102 (JP, A) Yoshimasa Kameyama, another person, mechanical system by quantification of sensory information Reliability / Safety Analysis, Management Science Operations Research, Japan, Japan Operation Research Society, January 1, 1999, Volume 44, No. 1, p. 18-24 Yoshimasa Kameyama, 5 others, Subjective comprehensive criticality analysis considering multiple fault trees, Proceedings of the Society of Instrument and Control Engineers, Japan, Japan Society for Instrument and Control Engineers, May 31, 1998. 34, No. 5, p. 422-429 (58) Fields surveyed (Int.Cl. ⁷ , DB name) G06F 11 / 22-11 / 26 JST file (JOIS)

Claims (7)

(57) [Claims] 1. A reliability design of the system for performing the design for system reliability having a plurality of components, a plurality of components included in the system, the system
High-level events and low-level events based on the impact on reliability
And the relationship is represented by a hierarchical tree structure.
Input means for inputting the structure of the vault tree and reliability data regarding the reliability of each of the above-mentioned constituent elements are pre- registered.
Means for storing and solving the fault tree input from the input means.
By analyzing the
Importance calculation means for calculating importance for ranking events
And the probability of occurrence given to the upper events and the importance
Generate a multi-dimensional equation and solve for
Probability calculation means for calculating the occurrence probability of a rank event, the occurrence probability calculated for each subordinate event, and the subordinate event
Compare with the reliability data of the component corresponding to the elephant
Reliability design of the system, characterized in that it comprises means, the for. 2. The probability calculating means determines a reference reference event as a reference from among lower order events whose occurrence probability is unknown, represents the occurrence probability of the reference event by a variable, and determines a higher order event given in advance as a target. A second equation that generates a first equation representing the relationship between the occurrence probability and the occurrence probability of each sub-event, and expresses the occurrence probability of the sub-events other than the reference event using the importance of the reference event and the variable. The system reliability design apparatus according to claim 1 , wherein the reliability design apparatus is configured to generate If wherein occurrence probability for all sub events included in the fault tree is known, to calculate the probability of order event is characterized by being configured to output claim 1, wherein Item 2. A system reliability design device according to item 2 . 4. A computer is used to make a plurality of configuration requirements.
For designing the reliability of disparate systems
In a system reliability design method, a plurality of systems included in the system, which are input by a user, are input.
Based on the effect of components on system reliability
It is divided into upper events and lower events, and these relationships are hierarchically
It is possible to analyze the structure of a fault tree expressed as a tree structure.
And at least for each sub-event whose occurrence probability is unknown
The importance calculation step for calculating the importance , the occurrence probability of the upper event input by the user, and
Generate a multidimensional equation using the calculated importance
Calculate the probability of occurrence of the lower event by finding the solution
Probability calculation step, occurrence probability calculated for each sub event, and from the user
Reliability of each component corresponding to the given sub-event
Comparing the reliability data with respect to the reliability data of the system. 5. The probability calculating step determines a reference event serving as a reference from among subordinate events whose occurrence probability is unknown,
The occurrence probability of the reference event is represented by a variable, and a first equation representing the relationship between the occurrence probability of an upper event given in advance as a goal and the occurrence probability of each lower event is generated, and the occurrence of a lower event other than the reference event is generated. The system reliability design method according to claim 4, wherein a second equation expressing a probability using the importance of the reference event and the variable is generated. When 6. probability for all sub events included in the fault tree is known, claims and outputs to calculate the occurrence probabilities of the order event 4
Alternatively, the system reliability design method according to claim 5 . 7. A recording medium in which software for reliability design of a system for designing the reliability of the system is recorded using a computer, the software being input to the computer by a user,
The components of the system are connected to the system.
Upper and lower events based on the impact on reliability
A tree that divides these relationships and represents them in a hierarchical tree structure.
At least by analyzing the structure of the Rult tree
The importance is calculated for each sub-event whose occurrence probability is unknown.
The occurrence probability of the upper event input by the user and
Generate a multidimensional equation using the calculated importance
By calculating the solution, the probability of occurrence of the lower event is calculated.
Then, the calculated probability of occurrence for each sub-events, from the user
Reliability of each component corresponding to the given sub-event
A recording medium on which software for reliability design of a system is recorded, which is characterized by comparing with reliability data regarding .