JP2012108699A - Method and system for simplifying minimum cut set of tree of failure - Google Patents

Abstract

PROBLEM TO BE SOLVED: To simplify a minimum cut set of a fault tree in a briefer and more readable form.SOLUTION: A system which simplifies a minimum cut set of a fault tree has: original MCSs storage means which stores a plurality of original minimum cut sets to be simplified; and reduction means to reduce a collection of a correlation minimum cut set which has size k of the original minimum cut set in k/(k+i) function (i≥1).

Description

  The present invention can be used to simplify the qualitative analysis results of a fault tree into a simpler and more readable form.

  In general, failure tree qualitative analysis results are generally expressed as minimum cut sets (MCSs), and each MCS in the qualitative analysis results is the smallest combination of basic events. As a result, a failure event occurs (for example, Non-Patent Document 1).

  In fact, a large number of MCSs are generated and generally difficult to read and understand even when analyzed, especially for large and complex systems that contain a large number of components. Furthermore, simply listing all MCSs does not capture their potential relationships. For example, the set of minimal cut sets with the same dimension k (composed of k elementary events) is all k-combinations (connections of elementary events with dimension k) that are possible in the set of n elementary events May represent. A standard k / n (majority) function with parameters n and k and the value of the k-combination set can be used as a simple representation of the set of correlated MCSs. The rationale behind the simplification is that if each MCS is treated as a connection of basic events, the set of correlated MCSs can be expressed as an additive normal form (DNF), and the k / n function is also a DNF equivalent to the set of correlated MCSs. Can be extended as

W.E.Vesely, F.F.Goldberg, N.H.Roberts, and D.F.Haasl, Fault Tree Handbook, U.S. Nuclear Regulatory Commission, NUREG-0492, Jan. 1981, pp.VII-15.

  The problem of the present invention is that the result of qualitative analysis of a fault tree is complicated and difficult to understand by analysis. This is particularly difficult if the target system is complex and consists of many (excessive) components. This is because a large number of MCSs are generated in a large system.

  Thus, it is a primary object of the present invention to provide a method and system that simplifies and represents MCSs in a simpler and more readable form.

  The present invention is a system that simplifies a minimum cut set of a fault tree, the original MCSs storing means for storing a plurality of original minimum cut sets for simplification, and a correlation having a size k of the original minimum cut set It is a minimum cut set simplification system characterized by having a contraction means for contracting a set of minimum cut sets to a k / (k + i) function (i ≧ 1).

  The present invention is a method for simplifying a minimum cut set of a fault tree, storing a plurality of original minimum cut sets for simplification, and a set of correlated minimum cut sets having a size k of the original minimum cut set Is reduced to a k / (k + i) function (i ≧ 1).

  The present invention is a program for simplifying a minimum cut set of a fault tree, the original MCSs storing means for storing a plurality of original minimum cut sets for simplification, a process of reading the original minimum cut set, A program that causes a computer to execute a process of shrinking a set of correlated minimum cut sets having an original minimum cut set size k to a k / (k + i) function (i ≧ 1).

  The effect of the present invention is that many correlated MCSs can be reduced to some simple k / n functions to make them more readable. The reason is that a set of correlated MCSs having the same dimensions and satisfying specific mathematical characteristics can be expressed by a simple k / n function.

FIG. 1 is a block diagram showing the configuration of the first embodiment of the present invention. FIG. 2 is a flowchart showing the operation of the first embodiment. FIG. 3 is a block diagram showing the configuration of the second embodiment of the present invention. FIG. 4 is a flowchart showing the operation of the second embodiment. FIG. 5 is a diagram showing a processor cluster as a specific example of the operation according to the embodiment of the present invention. FIG. 6 is a diagram showing a specific example of the original MCSs. FIG. 7 illustrates the simplification (shrinkage) from the original MCSs to the k / k + i function (i = 1). FIG. 8 illustrates the simplification (shrinkage) from the k / (k + i) function and the remaining original MCSs to the k / (k + (i + 1)) function (i ≧ 1). FIG. 9 is a diagram showing a standard k / n function expansion algorithm. FIG. 10 is a diagram showing simplified MCSs.

  A first embodiment of the present invention will be described in detail with reference to the drawings.

  Referring to FIG. 1, the first embodiment of the present invention includes an original MCSs storage unit 110 and a contraction unit 120.

  Each of these means generally operates as follows.

  The original MCSs storage means 110 stores original MCSs for simplification, for example, MCSs generated from some current FTA tools (not included in the present invention).

  The contracting means 120 contracts the set of correlated MCSs of the original MCSs to a set of k / n functions (n ≧ k + 1).

  Next, the overall operation of the present embodiment will be described in detail with reference to the flowcharts of FIGS.

  First, the original MCSs is transmitted from the original MCSs storage means 110 to the contraction means 120 (step A1).

  The MCS is positioned as a basic MCS in one dimension until transmission of all MCSs is completed, and the parameter i is initially set to 0 due to contraction (step A2).

  When the transmission is completed, the system moves to the last step, that is, outputs a simplified result of MCSs (step A10).

If the basic MCS is of the form B ₁ &… & B _k-1 & B _{k + 1} , the system has only one basic event B _{k + 1} and is different from the basic MCS, B ₁ &… & B _k Find MCS candidates in the form _-1 & B _{k + 1} (step A3). In other words, the difference between the candidate MCSs and the basic MCSs is that B _{k + 1} singleton sets, that is, {B ₁ &… & B _k−1 & B _{k + 1} }-{B ₁ &… & B _k } = {B _{k + 1} }. When such a candidate MCS exists, all MCSs included in the k / (k + 1) function, expressed as Vote ({B ₁ ,…, B _k , B _{k + 1} }, k) are calculated. (Step A4). These MCSs are called extended MCSs of the k / (k + 1) function.

  On the other hand, if there is no candidate MCS, the system moves to step A2 and positions another basic MCS.

  Differences between the extended MCSs in step A4 and the combination of the basic MCSs and candidate MCSs in steps A2 and A3 are searched in the remaining original MCSs (step A5).

If there is a difference MCSs, add 1 to the parameter i and derive the k / (k + 1) function, ie, Vote ({B ₁ ,…, B _k , B _{k + 1} }, k) to obtain the original MCSs The basic MCSs, candidate MCSs, and difference MCSs are replaced (step A6).

The generated k / (k + 1) function is processed as a basic majority function, and the system further has only one basic event B _{k + (i + 1)} , which is different from the basic majority function k + i basic event, B Try to find an MCS candidate in the form of ₁ &... & B _{k + (i-1)} & B _{k + (i + 1)} (step A7). When such a candidate MCS is found, an extended MCSs of Vote ({B ₁ ,..., B _{k + i} , B _{k + (i + 1)} }, k) is calculated (step A8). On the other hand, if not found, the system moves to step A2 to locate another basic MCS.

Differences between the extended MCSs of step A8 and the combination of the basic k / (k + 1) function and the candidate MCS of step A7 are searched in the remaining original MCSs (step A9). If there is such a difference MCSs, the system moves to step A6 where 1 is added to the parameter i, and then a new k / (k + i) function, namely Vote ({B ₁ ,…, B _{k + i} , B _{k + (i + 1)} }, k) to replace the original basic majority function, the candidate MCS, and the difference MCSs. Note that the process from step A6 to step A9 is repeated until the basic majority function and the remaining original MCSs can no longer shrink.

  Finally, the contraction means 120 outputs the simplified MCSs (which cannot be contracted any more, composed of the k / n function and the remaining original MCSs) (step A10).

  Next, the effect of this embodiment will be described.

  Since the present embodiment includes a step of repeatedly shrinking the correlated MCSs of dimension k into k / (k + i) (i ≧ 1) functions, the original MCSs can be simplified to the simplest form that cannot be shrunk any more. .

  Next, a second embodiment of the present invention will be described in detail with reference to the drawings.

  Referring to FIG. 3, the second embodiment of the present invention is an extension of the first embodiment, and the second embodiment includes a type classification means 115, and classifies original MCSs before contraction. .

  The reason why the type classifying means 115 is introduced is that the k / n function is different if the dimension of the position of the basic MCS is different (step 2 in the first embodiment). In other words, the original MCSs can be shrunk into several different forms depending on the positioning dimension of the basic MCSs. In fact, the meaning of the k / n function is easier to read if the k / n function is a majority function within a set of basic events that are related to the same type of component. For this reason, the main function of the type classification means 115 is to classify MCSs with respect to the component types. As a result, MCSs having the same type of components are positioned and contracted prior to MCS having different types of components.

  Next, the overall operation of the present embodiment will be described in detail with reference to the flowcharts of FIGS.

  The difference between the flowchart of the first embodiment and the flowchart of the second embodiment is that the step of classifying input original MCSs (step B1) between step A1 and step A2 is the second embodiment. It was added in. As a result, MCSs associated with components of the same type are positioned and contracted prior to MCS associated with components of different types.

  Next, the operation of the embodiment will be described using specific examples.

An exemplary fault tolerant parallel processor (FTPP) system is shown in FIG. The configuration of the FTPP system is as follows.
The system is composed of 12 processors, and 3 processors are connected to each of 4 buses, that is, b01, b02, b03, and b04.
• Twelve processors are logically connected to form four clusters: pc1, pc2, pc3 and pc4.
Set the redundancy of each cluster to 1, that is, the cluster is fault tolerant even if one or less components fail. In other words, a cluster fails when more than one component fails.

  It is assumed that the functionality of the processor depends on the bus unit connected to the processor. That is, it is assumed that when a bus unit fails, all processors connected to the bus are disabled. Further assume that if any of the four clusters fails, the system will fail.

The original MCSs of an exemplary FTPP system are shown in FIG. Some notations are as follows.
The possible fault trees of the FTPP system are omitted here for clarity. Different fault trees with the same MCSs exist according to different concepts / deployment strategies.
• For clarity, the original MCSs are shown in the logical setting form rather than the standard setting form, and the symbols “&” and “+” represent the logical connection operator and the disjunction operator, respectively. Each connection corresponds to an MCS, and all connections joined by the “+” operator constitute an additive standard form (DNF) representing the entire MCSs. There are a total of 42 MCSs for this exemplary system.
・ For the sake of clarity, the basic failure event is indicated directly by the name of the component. For example, b1 & b2 interprets that both b1 and b2 fail.

  Based on the original MCSs, the system first positions the first MCS, that is, b01 & b02 as the basic MCS (step A2 in FIG. 2). Then, candidate MCSs, ie b01 & b03, are found in the original MCSs (step A3). The extended MCSs of the majority function can be derived based on the set of basic events of the basic MCSs and candidate MCSs and the size of the basic MCS, that is, the standard extended algorithm of the majority gate shown in FIG. 9, Vote ({b01, b02, b03 }, 2) = b01 & b02 + b02 & b03 + b01 & b02 (Step A4). The extended MCSs are combined in the base MCSs and the candidate MCSs, that is, the difference MCS from b02 & b03 is found in the original MCSs (step A5). Therefore, the basic MCSs, the candidate MCSs, and the difference MCS are contracted and replaced with a 2/3 function, that is, Vote ({b01, b02, b03}, 2) (step A6). The process is depicted in FIG.

  Based on the basic 2/3 function obtained, namely Vote ({b01, b02, b03}, 2), the system will further shrink the original MCSs and derive if there is a 2 / (3 + 1) function Try. Candidate MCS, ie b01 & b04, is found in the original MCSs (step A7), 2/4 function, ie Vote ({b01, b02, b03, b04}, 2) = Vote ({b01, b02, b03}, 2) The extended MCSs of + b01 & b04 + b02 & b04 + b03 & b04 are calculated (step A8).

  Difference MCSs, ie b02 & b04 and b03 & b04, can also be found in the original MCSs (step A9). Therefore, the basic 2/3 function, the candidate MCSs, and the difference MCS are contracted and replaced with the 2/4 function, that is, Vote ({b01, b02, b03, b04}, 2) (redo step A6). This process is shown in FIG.

  The above two processes are repeated until all the original MCSs are located and the original MCSs can no longer shrink, and the final simplified MCSs are shown in FIG. If the k / n function is regarded as one (special) MCS, the simplified MCSs is composed of only 13 MCSs, and the simplified MCSs is composed of the original MCSs (42 MCSs in FIG. 6). .) Is more concise and easier to read.

  As is clear from the above description, the type classification unit 115 and the contraction unit 120 can be configured by hardware, but can also be realized by a computer program. In this case, functions and operations similar to those of the above-described embodiment are realized by a processor that operates according to a program stored in the program memory.

  Although the present invention has been described with reference to the preferred embodiments and examples, the present invention is not necessarily limited to the above-described embodiments and examples, and various modifications can be made within the scope of the technical idea. I can do it.

  The present invention can be used to simplify the MCSs of a fault tree into a simpler, more readable form by performing the contraction means that simplify the set of correlated MCSs to a standard k / n function.

110 MCSs storage means 115 type classification means 120 contraction means

Claims (6)

A system that simplifies the minimum cut set of a fault tree,
Original MCSs storage means for storing multiple original minimum cut sets for simplicity;
A minimum cut set simplification system comprising a contraction means for contracting a set of correlated minimum cut sets having a size k of the original minimum cut set to a k / (k + i) function (i ≧ 1) . Further comprising type classification means for classifying the input original minimum cut set with respect to the type of component associated with the basic event of the minimum cut set;
2. The minimum cut set simplification system of claim 1, wherein an original minimum cut set having the same type of elements is contracted prior to an original minimum cut set having different types of components. A method of simplifying the minimum cut set of a fault tree,
Memorize multiple original minimum cut sets for simplicity,
A method of simplifying a minimum cut set, comprising shrinking a set of correlated minimum cut sets having the size k of the original minimum cut set to a k / (k + i) function (i ≧ 1). Classifying the input original minimum cut set with respect to the type of component associated with the basic event of the minimum cut set;
4. The minimum cut set simplification system of claim 3, wherein an original minimum cut set having the same type of elements is contracted prior to an original minimum cut set having different types of components. A program that simplifies the minimum cut set of a fault tree,
Processing to read the original minimum cut set from the original MCSs storage means for storing a plurality of original minimum cut sets for simplification,
A program causing a computer to execute a process of shrinking a set of correlated minimum cut sets having a size k of the original minimum cut set to a k / (k + i) function (i ≧ 1). Categorizing the input original minimum cut set with respect to the type of component associated with the basic event of the minimum cut set;
6. The program according to claim 5, further comprising a process of shrinking an original minimum cut set having the same type of element prior to an original minimum cut set having a different type of component.

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