JP5601468B2 - Method and system for efficiently evaluating the minimum cut set of fault trees - Google Patents

Description

  The present invention relates to failure tree reliability analysis, and more particularly to failure tree reliability analysis that includes a majority gate (k, k / n out of n).

であるため空間計算量は依然として階乗問題として残る。それ故、nが大きく、kがn/2に近いと、MCSsを算出するには困難を伴う。入力が基本事象ではなく、他の事象に依存する中間事象の場合、問題は更に複雑となる。 Traditionally, k / n gate minimum cut sets (MCSs) have been calculated by counting all possible k / n gate input event combinations. An extended algorithm is presented in Non-Patent Document 1, where the time complexity is reduced to k × n, but the total number of possible combinations is

Therefore, the space complexity still remains a factorial problem. Therefore, when n is large and k is close to n / 2, it is difficult to calculate MCSs. The problem is further complicated when the input is not a basic event but an intermediate event that depends on other events.

  In addition, other problems with expansion and counting are difficult to decipher the resulting MCSs because a large number of MCSs are generated from k / n gates.

Antoine Rauzy, Toward an efficient implementation of the MOCUS algorithm, IEEE Transactions on Reliability, Vol. 52, No. 2, June 2003, pp. 175-180.

  The first problem is that extending a k / n gate directly to a set of combinations is a factorial problem. This is because the total number of k / n gate combinations is n! / (N-k)! K !.

  The second problem is that since a large number of MCSs are generated by k / n gates, the resulting MCSs are long and cannot be deciphered.

  Therefore, the present invention has been invented in view of the above problems, and its purpose is to provide a more efficient method for evaluating k / n gates, a more concise and decipherable method for representing MCSs of fault trees. Is to provide.

  The present invention is a system for evaluating a minimum cut set (MCS) of a fault tree, which reduces a composite k / n gate to a basic k / n gate based on a set of simplification rules. And an evaluation system having basic k / n gate minimization means for reducing the basic k / n gate to the minimum k / n gate based on a set of minimization rules.

  The present invention is a method for evaluating a minimum cut set (MCS) of a fault tree, wherein a composite k / n gate is reduced to a basic k / n gate based on a set of simplification rules and a set of minimization rules. Is an evaluation method for reducing the basic k / n gate to the minimum k / n gate.

  The first effect is that the amount of calculation for evaluating the k / n gate can be reduced. The reason is that a part of the composite k / n gate can be finally reduced to the minimum k / n gate without expanding, and the overall calculation cost can be reduced.

  The second effect is that the reliability of the resulting MCSs can be increased. The reason is that the resulting total number of MCSs can be reduced with the concept of minimum k / n gates.

It is a block diagram which shows the structure of embodiment of this invention. It is a flowchart which shows the operation | movement of this Embodiment. It is description of the symbol of this Embodiment. Related MCS evaluation rules. Related k / n gate extension algorithm The simplified rule for the composite k / n gate of this embodiment is shown. The minimization rule for the basic k / n gate of this embodiment is shown. It is the figure which showed an example of the failure tree used in a present Example. FIG. 9 is a diagram showing MCSs of a failure tree when a related method is applied to the failure tree shown in FIG. 8. It is the figure which showed MCSs of the failure tree at the time of applying this invention to the failure tree shown in FIG.

  Embodiments of the present invention will be described in detail with reference to the drawings.

  In summary, the evaluation system of the present invention includes a composite k / n gate simplification means for reducing a composite k / n gate to a basic k / n gate, and a basic k / n gate to a minimum k / n gate. Basic k / n gate minimizing means to be reduced. The minimum k / n gate does not need to be extended and can be considered as a concise form of the set of MCSs. The k / n gate need only be expanded when it cannot be simplified or minimized by the composite k / n gate simplification means or the basic k / n gate minimization means.

  A basic k / n gate is to be understood as a k / n gate into which all the basic events are input and whose output itself is the top event of the fault tree as a result. A composite k / n gate is not a basic k / n gate. For example, k / n gates that need to accompany other events so that the input includes intermediate events and results in a top event.

  A minimum k / n gate means a basic k / n gate that does not contain any redundant cut sets or fault tree cut sets for other basic k / n gates. The minimum k / n gate does not need to be extended further and can be considered as a concise form of the set of MCSs denoted by k / n gate.

  Hereinafter, embodiments will be described with reference to the drawings.

  Referring to FIG. 1, the first embodiment of the present invention includes a general MCS evaluation unit 110, a composite k / n gate simplification unit 120, and a basic k / n gate minimization unit 130. Each of these means generally operates as follows.

  The general MCS evaluation means 110 evaluates MCSs with respect to the conventional reduction rule for conversion of disjunctive normal form and deletion of redundant events and cut sets, as shown in FIG.

  The composite k / n gate simplification means 120 reduces the composite k / n gate to the basic k / n gate with respect to the set of simplification rules, as shown in FIG.

  The basic k / n gate minimizing means 130 reduces the basic k / n gate to the minimum k / n gate with respect to the set of minimization rules, as shown in FIG.

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

  First, a fault tree is input to the system (step A1).

  The general MCS evaluation means 110 applies normal MCS evaluation to the fault tree (step A2). Note that in this step the k / n gate is not extended, if any.

  If the fault tree does not contain k / n gates, then the result of step A2, ie the set of MCSs, can be output directly (step A6). On the other hand, if the fault tree includes k / n gates, the k / n gates are first simplified by the composite k / n gate simplification means 120 (step A3) and then the basic k / n gate minimization means 130. (Step A4).

  After simplification and minimization of the k / n gate, the general MSC evaluation is applied again (step A5). This is because simplification and minimization may result in redundant events and / or non-disjunctive normal forms (eg, simplification rule 6-2e of the simplification rule shown in FIG. 6). in the case of).

  If all k / n gates are the minimum k / n gates as a result of step A5, these minimum k / n gates are output together with the other MCSs in step A5. On the other hand, if not all k / n gates are minimum k / n gates, the system returns to step A3 until all k / n gates are reduced to minimum k / n gates. Note that a new composite k / n gate may be generated in the simplification process of step A4 (for example, in the case of rule 7-2b of the simplification rule shown in FIG. 6). .

  Next, the effect of this embodiment will be described.

  Since the present embodiment includes a k / n gate simplification and minimization step, the minimum k / n gate is not expanded. Therefore, the calculation cost can be reduced and the reliability of the result can be improved.

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

  An example of a fault tree used in this embodiment is shown in FIG. The fault tree is composed of a composite k / n gate, and its input is an OR gate.

個の基本事象の論理積が生成され、冗長カットセットを除去後のMCSsの合計数は２１である。 FIG. 9 shows the resulting MCSs by applying the conventional extended algorithm shown in FIG. In the worst case, the expansion process

The logical product of the basic events is generated, and the total number of MCSs after removing the redundant cut set is 21.

  On the other hand, in the present invention, the result can be derived from three simple steps. First, the failure tree is evaluated by the general MCS evaluation rule (step 2), and the result is a composite k / n gate and b7 · b8 + 3/6 (b1 + b7, b2 + b7, b3 + b7, b4 + b7, b5 + b7, b6 + b7) foam cut sets are included. Second, the composite k / n gate is simplified by rule 6-3a shown in FIG. 6 (step A3), and the result is the basic k / n gate and b7 · b8 + b7 + 3/6 ( b1, b2, b3, b4, b5, b6) and consists of the other two cut sets.

  Since the basic k / n gate cannot be further minimized, it is the minimum k / n gate. Finally, the general MCS evaluation rule 4-2c of FIG. 4 can be applied to remove the redundant cut sets b7 and b8. As a result, as shown in FIG. / 6 (b1, b2, b3, b4, b5, b6) can be output.

  As is clear from the above description, the general MCS evaluation unit 110, the composite k / n gate simplification unit 120, and the basic k / n gate minimization unit 130 can be configured by hardware. It 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 applied to improve the efficiency of MCS evaluation of a fault tree including a k / n gate by being executed by a composite k / n gate simplification means and a basic k / n gate minimization means. . Furthermore, using the concept of minimum k / n gates, the present invention can be used to improve the reliability of MCSs resulting from fault trees.

110 General MCS evaluation means 120 Compound k / n gate simplification means 130 Basic k / n gate minimization means

Claims (6)

A system for evaluating a minimum cut set (MCS) of a fault tree,
A compound k / n gate simplification means for reducing a compound k / n gate to a basic k / n gate based on a set of simplification rules;
An evaluation system comprising basic k / n gate minimizing means for reducing the basic k / n gate to the minimum k / n gate based on a set of minimization rules.   The evaluation system according to claim 1, wherein the minimum k / n gate is included in an output of an MCS evaluation of a fault tree. The evaluation system according to claim 1 or 2, wherein the minimization rule of the basic k / n gate minimizing means is also applied to the composite k / n gate by replacing a basic event variable with an event variable. . An evaluation system using an information processing device is a method for evaluating a minimum cut set (MCS) of a fault tree,
The information processing apparatus reduces a composite k / n gate to a basic k / n gate based on a set of simplified rules stored in a storage unit of the information processing apparatus ,
The information processing apparatus is an evaluation method in which the basic k / n gate is reduced to a minimum k / n gate based on a set of minimization rules stored in a storage unit of the information processing apparatus . The information processing apparatus evaluating method of claim 4, wherein the minimum k / n gate, and outputs included in the output of the MCS Evaluation wood failure. 5. The information processing apparatus applies the minimization rule of the basic k / n gate minimizing unit to the composite k / n gate by replacing a basic event variable with an event variable. 5. The evaluation method according to 5.

Images