JP3415583B2 - System reliability analysis apparatus and method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a reliability evaluation method for a system having a complicated redundant configuration. In particular, even if it stops like the air conditioning system in the communication machine room, it does not immediately lead to the function stop of the communication system to be air-conditioned, so by considering it as a system down only after a certain period of stop The present invention relates to a system reliability analysis device and method for evaluating reliability of a system.

[0002]

2. Description of the Related Art Prior to describing the present invention, a conventional reliability evaluation method for an air conditioning system will be described. An example of the configuration of the air conditioning system is shown in FIG. The air conditioning system includes a plurality of air conditioners for air conditioning a communication machine room that houses a commercial power source, a standby power generator, and a communication system. In this example, power is normally supplied to the air conditioner from a commercial power source. The number of air conditioners is, for example, three. When the commercial power supply is stopped, a backup generator is activated to supply power to the air conditioner. Here, if both the commercial power supply and the standby generator fail, the power supply to the air conditioner is stopped and the air conditioner is stopped. In addition, the air conditioner also failed,
The air conditioning capacity decreases according to the number of failed units. By the way, when the air conditioning capacity is stopped or lowered due to the reasons described above, the room temperature of the communication machine room does not rise instantaneously, but after a certain time determined according to the lowered air conditioning capacity, the cooling target Reaches a room temperature that interferes with the operation of the existing communication system. For example, 30 minutes when all air conditioners are stopped, 1 hour when only one is operating,
It takes about two hours when two units are movable. Incidentally, when all three units are operating, this time is naturally infinite (that is, the room temperature does not rise no matter how much time elapses).

In the reliability evaluation of such a system, the behavior of the system is analyzed by a Markov model to analyze the state probability for each number of air conditioners, and only the part exceeding the above time is shut down. The method of analyzing as time is taken. The specific procedure is shown below. First,
Draw a Markov transition diagram for the air conditioning system. Failure rate of commercial power supply (reciprocal 1 / X when failure occurs once every X hours)
Let λ _{CS be} the repair rate (reciprocal of the repair time) be μ _CS , the standby generator failure rate be λ _DEG , the repair rate be μ _DEG , the air conditioner failure rate be λ _AC , and the repair rate be μ _AC . The transition diagram is shown in FIG. In addition, here, the occurrence of failures is random, and the repair time distribution is an exponential distribution. Further, it is assumed that the commercial power supply, the standby power generator, and each air conditioner malfunction independently. In the figure (x, y, z), x = 0 commercial power up, x = 0
= 1 for commercial power down, y = 0 for standby generator up, y = 1
Means that the standby generator is down, and z = 0,1,2,3 represents the number of air conditioners that are down. Then, in the figure, the arrow indicates the frequency (transition rate) at which a transition from one state to another occurs. This point is the same as the usual Markov analysis method.

In the Markov process shown in FIG. 2, for example, a state change (transition) occurs repeatedly as shown in FIG. In FIG. 3, the state (1,0,0) is started first, and then (1,1,
0), (1,1,1), (1,0,1), (1,1,1) are shown in this order. Here, focusing on the number of operating air conditioners, in the case of (1,0,0), room temperature does not rise because all three are operating. When it is (1,1,0), the power supply to the air conditioner is cut off, so all three units are stopped. Therefore, if this state is not removed within 30 minutes (allowable time), the room temperature will reach the allowable value. Break through. The same applies to the case of (1,1,1). When (1,0,1), only one air conditioner is stopped, so the system is down unless this state is removed within 2 hours.

In the system reliability analysis method according to the prior art, the occurrence frequency of each state and the probability that the state will continue even after the allowable time has elapsed are calculated and added to obtain the system down occurrence frequency. The system unavailability is determined by adding the lengths of the parts considered to be system down and taking the ratio with the total time. (In this method, when a transition from (1,1,0) to (1,1,1) occurs as shown in FIG. 3 (that is, when the power supply is cut off, the three air conditioners are (If one of them goes down), it is considered that the system has recovered in the analysis, so it is not strictly correct, but it is known that this method can perform an analysis with no problem in practical use.) Find the frequency of transition to each state. It does as follows.

First, the equilibrium equation corresponding to FIG. 2 is established and solved, and the stationary probability P (x, y, z) of each state is obtained. Since this method is a well-known general technique of Markov analysis, its details are omitted. Based on this, the state of interest, for example, another state where transition to state (1,1,1,) may occur
To the stationary probability (P ()) of (0,1,1,), (1,0,1), (1,1,0), (1,1,2), go to (1,1,1) Transition rate (fault rate λ, repair rate μ)
Multiply by and add. That is, the frequency of transition to (1,1,1) = λ _CS P (0,1,1) ＋ λ _DEG P (1,0,1) ＋ 3λ _AC P (1,1,0) ＋ 2μ _AC P ( It is 1,1,2) (1).

In this way, after the frequency of the transition to the state (1,1,1) is obtained, thereafter, for the event that remains in that state for a certain period of time (until the transition to another state). )
If the frequency of occurrence is calculated, it will be the frequency of occurrence of system down. Further, the system downtime can be obtained by obtaining the ratio of the time remaining in that state over a certain time to the total time. If the state (x, y, z) is generalized to the state i,

[0008]

[Equation 1] Here, λ _i : the frequency of transition to the state i (from all transition source states) (for example, the frequency of transition to the state (1,1,1) of FIG. 2: Expression (1)) g _i (t): Probability density at which transition from state i to another state occurs at time t T _i : Allowable time Σ until room temperature exceeds the limit in state i SUM for all states (i) Means

[0009]

[Equation 2] Is. Here, (t−T _i ) represents the system down time, and g _i (t) is from the state of interest (for example, (1,1,1)) to another state (for example, (1,1,0). ), (0,1,1), ...) It is the probability density of the time until the transition occurs, but in the case of Markov process, it is calculated by the sum of the transition rates from the state of interest.

That is, the integral part of the above equation is specifically as follows. For the integral in equation (2),

[0011]

[Equation 3] Here, μ _i is the sum of transition rates from state i to other states (for example, the sum of transition rates from state (1,1,1) in FIG. 2 to other states: μ _AC + μ _CS + μ _DEG + 2μ _AC ) Represents. For the integral in equation (3),

[0012]

[Equation 4] Is.

[0013]

The above is the outline of the reliability evaluation method for the air conditioning system according to the conventional technique. However, since the recent air conditioning system has a complicated structure,
There are the following problems in performing reliability evaluation by the conventional technology. In the system examination scene, the optimum system configuration (for example, the configuration of the air conditioner group) is sought by analyzing the systems of various configurations and comparing the results. In order to do this efficiently, A method for mechanically performing the above analysis is essential. When the system configuration becomes complicated, the number of states of the Markov process, which is the basis of the analysis, explosively increases, which makes it impractical in terms of calculation time and accuracy.

[0014]

In order to solve the above-mentioned problems, in the present invention, the air conditioning system to be analyzed is divided into subsystems having independent behaviors, and the Markov process of those subsystems (hereinafter "Sub-Markov process") is created (this is given individually), these are combined, and the method of mechanical analysis is presented below. In order to solve the above problems, the present invention assumes that some of the subsystems do not fail and evaluates the reliability of the evaluation target system as the upper limit approximation value of the reliability, Some of the above are replaced by a system in which the deterioration of the air conditioning capacity is replaced by a system in which the deterioration becomes zero at a stroke rather than in a stepwise manner, and the lower limit approximation value of the reliability is set as an approximation method, and an approximation method for narrowing these is presented.

[0015]

BEST MODE FOR CARRYING OUT THE INVENTION The present invention will be described below based on Examples. (Example 1 for solving the problem) The behavior of the system shown in FIG. 1 is as follows:
The behavior of each of the three parts) is independent.
Therefore, these are the subsystems that make up the entire system.
Consider it as 1,2,3 (Fig. 4 (a)). Each subsystem forms a Markov process. We call these sub-Markov processes 1,2,3 (i ₁ , i ₂ , i ₃ ). There are three Markov transition diagrams for each sub-Markov process, as shown in FIG. 4 (b). Note that the number of divisions into independent sub-processes is not always one. That is, it is considered to be a subsystem in which a commercial power source and a standby generator are set, and two subsystems of a group of three air conditioners. At this time, the sub-Markov process becomes as shown in Fig. 5 (b).

The procedure of the first embodiment will be described with reference to FIG. (1) Here, it is assumed that the state transition diagram of the sub-Markov process is given aside. As a parameter expression that defines the Sub-Markov process, for example, there is a method of writing the transition rate between states in a matrix format. That is, in a square matrix A having the degree of the number of states (its (i, j) element is a _ij ), if the transition rate a _ij from the state j to the state i is used, an arbitrary form can be obtained. The Sub-Markov process is represented. Further, using this, when realizing the reliability analysis device, the transition rate matrix A _k of each sub-Markov process may be input. (2) Next, enter the number of shutdown air conditioners for each state.

In this way, the transition of each sub-Markov process
Given the transfer matrix, the above submarco
System reliability created by the combination of
The evaluation is as follows. First of all, all the Sub-Markov processes
Suppose there are m. Sub-Markov process k (1 ≤ k ≤ m)
State is n_kAnd the transition rate matrix is A_k(That
(i, j) element as a_ij ^(k)And). At this time, the system
The state of the Markov process that describes the entire system is
Set of statuses (i₁, i₂, ・ ・ ・, I_k,
..., i_m) (Three in the example of FIG. 4), and the number is
n₁× n₂× ・ ・ ・ × n_k× ・ ・ ・ × n _mThere are some (in the example of FIG. 4,
2x2x4 pieces). For all these states, the state
Transition frequency, the average duration in that state,
If you can obtain the allowable time for the room temperature to rise in
System down frequency and downtime rate
Can be

The procedure of the present invention will be described. In the steady state probability calculating] (3) First, attention state occurrence frequency of transition _{(i 1, i 2, ···} , i k, ···, i m) to is determined as follows. At first,
Obtain the steady state probability of each state in each sub-Markov process. This can be obtained by a well-known Markov analysis method if the transition rate matrix of each sub-Markov process is given.

Specifically, it is the solution of the following equation for the column vector x _k . 0 = A _k x _k (k = 1,2, ..., m) The sum of the elements of x _k is 1, and 0, x _k (for example, x ₁ = P (j ₁ in FIG. 4B). ), X ₂ = P (j ₂ ), x ₃ = P (j ₃ )) are column vectors. (For example, in FIG. 4 (b), the information described by the sub-Markov process 1 is the number of dimensions: 2

[0020]

[Equation 5] It is represented by. ) (4) If the steady state probability of the state j _k in the sub-Markov process k obtained in this way is P (j _k ), the state (j ₁ ,
j ₂ , ・ ・ ・, j _k , ・ ・ ・, j _m ), the steady state probability is P (j ₁ ) × P (j ₂ ) × ・ ・ ・ × P (j _k ) × ・ ・ ・ × P (j _m ). In this way, the steady state probability of each state is obtained when the entire system is considered as one Markov process. [Calculation of the transition frequency to the state of interest] (5) Next, the frequency of transition to the state of interest is calculated as the sum of the state probabilities of all possible states multiplied by the transition rate to the state of interest. To be

That is, the state of interest is (i ₁ , i ₂ , ..., I _k ,
,, i _m ), the transitionable state is m
Focus on one of the sub-Markov processes (for example, the k-th sub-Markov process), and enumerate the states that can transit to the state i _k in the sub-Markov process.

[Equation 6] Then, in the above (i ₁ , i ₂ , ..., i _k , ..., i _m ), the i _k location is replaced by these, and these replacements are made k 1 It is a state obtained by performing all of to m. Then, the occurrence frequency of the transition from the “state capable of transitioning to the state of interest” thus obtained to the state of interest is

[0022]

[Equation 7] Is the sum of (α). Therefore, pay attention
State (i₁, i₂, ・ ・ ・, I _k, ・ ・ ・, I_m) To the transition
Is the sum of

[0023]

[Equation 8] Becomes [Calculation of transition rate from state of interest to other states] (6) Next, the time distribution from the state of interest to the transition to any of the other states. This is from the state of interest to all other states. Is a simple sum of the transition rates of. Therefore, among the elements of the transition rate matrix that describe each sub-Markov process, those that correspond to those that leave the state of interest may be summed. That is,

[0024]

[Equation 9] β represents another state transitioning from the state i _k . [Calculation of system down frequency and system non-operation rate according to the state of interest] [System down frequency and system non-operation rate accumulation] (7) Thus, in the prior art, three types of system down occurrence frequency and system non-operation rate required The former two of the elements (frequency of transition to the state of interest, transition rate from the state of interest to another state, and permissible time in the state of interest) are obtained. The last allowable time in the state of interest may be stored in the storage means in association with the state of the entire system and referred to when the system down frequency is calculated. For example, when dividing the air conditioning system of FIG. 1 into subsystems as shown in FIG. 4A, the system state is (i ₁ ,
i ₂ , i ₃ ), but these are associated and stored with the allowable time (for example, the allowable time T _i when there is one operation-stop air conditioner _).
Is 2 hours). An example of the association table is shown in FIG. (8) The system down occurrence frequency and the system down non-operation rate are calculated based on the prior art equations (2) and (3).

Frequency of occurrence of the transition to the state of interest,
The transition rate calculation from the state of interest to another state and the system reliability calculation are repeated until the state of interest runs out of all states. (9) Next, the sum of the system down occurrence frequency and the system down unavailability for each focused state is calculated. FIG. 8 shows a block diagram of the system reliability analysis device (Example 1). This system reliability analysis device (Embodiment 1) uses a transition rate matrix (A _k , k = 1, ..., M) of a plurality of (m) subsystems that constitute a system and have independent behaviors. Transition rate matrix to remember
A _k storage means, a table TAB _k storage means for storing a table (TAB _k , k = 1, ..., m) in which states of each subsystem are associated with allowable times, and a transition rate matrix storage means. Based on the stored transition rate matrix, steady state probability calculating means for calculating the steady state probability of each subsystem, and each subsystem for storing the steady state probability of each subsystem calculated by the steady state probability calculating means Based on the steady state probability storage means and the transition rate matrix stored in the transition rate matrix storage means, the state of interest in determining the system down frequency and the system downtime is changed and designated as the attention storage means. Calculation routine control means for instructing the state and also for accumulating the system down frequency and the system downtime to the means for accumulating the system down frequency and the system downtime, Attention state storage means for storing the attention state instructed by the routine control means, and the steady state probability of the attention state stored in the attention state storage means are stored in the steady state probability storage means of each subsystem. The steady state probability calculating means for the state of interest, which is calculated based on the steady state probability of the system, and the transition frequency to the state of interest stored in the state of interest storing means are stored in the steady state probability storing means of the state of interest. Transition frequency calculation means to the state of interest calculated based on the steady state probability and the transition rate matrix stored in the transition rate matrix storage means, and transition from the state of interest stored in the state of interest storage means to another state The rate is calculated based on the transition rate matrix stored in the transition rate matrix storage means, the transition rate calculation means from the state of interest to another state, and the steady state probability calculation means of the state of interest. The steady state probability of the eye state, the transition frequency to the state of interest calculated by the transition frequency calculation unit to the state of interest, and the state of interest to another state calculated by the transition rate calculation unit from the state of interest to another state Based on the transition rate and a table in which the state of each subsystem stored in the table storage means and the allowable time are associated with each other, the system down frequency and the system downtime related to the state of interest are calculated. The system down frequency and system unavailability calculation means, and the system down frequency and system unavailability calculated by the system down frequency and system unavailability calculation means are accumulated based on the instruction of the calculation routine control means. It is composed of means for accumulating the frequency of system down and the system downtime. (Embodiment 2 for solving the problem) Next, an embodiment for reducing the amount of calculation will be described.

According to the method of the embodiment, if the information describing the sub-Markov process is given in the form of a transition rate matrix and the relation between the state of the system and the allowable time is stored, the reliability can be evaluated mechanically. Can be done, but this still increases the amount of calculation. For example, in FIG.
Even if the system is as shown in, the sub-process m is 6
The number of states n constituting each sub-process is 4, 4, 4, 10, 4, and 6 in order from the sub-process 1, and the number of states of the entire system is 15360. For these, the amount of calculation is large to perform the calculation by the method shown in. Therefore, a method of reducing this calculation amount while evaluating the calculation error will be described.

In order to implement the feature of the present invention, the division into subsystems only needs to satisfy the condition that the behaviors of the subsystems are independent of each other. The conditions described below are also required. Condition: Assuming that there are no failures in the elements that make up other subsystems, and when focusing on the number of movable air conditioners that are stopped due to the failure of the elements that make up one subsystem, some of these are This includes cases where there is no stopped air conditioner and cases where the number of previous air conditioners has stopped operating. In addition, the number of air conditioner outages caused as a result of element failure of each subsystem is (s ₁ , s ₂ , ...
・, S _k ), the air conditioning capacity stop of the entire system is represented by max (s ₁ , s ₂ , ..., s _k ) in terms of the number of operating air conditioners.

This condition cannot be satisfied by division into subsystems as shown in FIG. 4 (a). This is because the subsystem 1 has two states corresponding to whether the commercial power source is up or down, but the number of air conditioners that have stopped operating cannot be determined only from the information that the state is one of these states.
On the other hand, the division into subsystems as shown in FIG. 5A satisfies this condition. In the subsystem 1, the number of operation-stop air-conditioners is 3 only when both the commercial power supply and the standby power generator are down, and is 0 in other states. Further, in the subsystem 2, the number of air conditioners that have gone down is the same as the number of air conditioners that have stopped operating. Furthermore, the larger one of the number of operation-stop air conditioners caused by the subsystem 1 and the number of operation-stop air conditioners caused by the subsystem 2 is the number of operation stop air-conditioners in the system as a whole (that is, , The number of air conditioners that are shut down when subsystem 1 goes down).

When the division into subsystems satisfies this condition, if the subsystem status and the number of shutdown air conditioners are stored in combination, the number of shutdown air conditioners in all states of the system can be obtained. FIG. 10 shows an example of a correspondence table between the subsystem status and the number of operation-stopped air conditioners. The basic idea of implementing the features of the invention is to note two facts: (1) Assuming that one of the subsystems does not fail, the reliability of the entire system will be better than if it did. Generally speaking, we call this subsystem S ₁ , S
₂ , ... S _m , some of them (S _i1 , S _i2 ,
When comparing the analysis result (result 1) assuming that (...) does not fail and the analysis result (result 2) assuming that (S _j1 , S _j2 , ...) _Does not fail, If (S _i1 , S _i2 , ・
..) ⊃ (S _j1 , S _j2 , ...) (included as a set), the result 1 gives better reliability than the result 2.
In other words, result 2 is closer to the true value.

(2) Generally, the number of stages of deterioration of the air conditioning capacity of the subsystem is not limited to two (ie, the stage where the air conditioning capacity is not deteriorated and the stage where the air conditioning capacity is completely lost). Like, there is only two. This will be referred to as one unit of subsystem. This means that a subsystem consisting of multiple elements is treated as if it had only one unit.
When we analyze a system in which the original subsystem is replaced with the subsystem thus simulated, the reliability (result of occurrence of system down and unavailability) of the result is worse than the true value. (Procedure for One Unit) The procedure for one unit will be described with reference to FIG.

The states forming the sub-Markov process of interest are the set of states in which the air conditioning capacity is not deteriorated (group 1) and the set of states in which the capacity is completely lost (group 2).
2 minutes. The state of the former group is i ₁ ,, i ₂ , ..., i
_k , ..., i _u, and the state of the latter group is j ₁ , j ₂ , ...
,, j _k , ..., j _v (u + v = number of states of submarkov process of interest). First, the steady-state probability of the original Sub-Markov process is obtained. P (i ₁ ), P (i ₂ ), ...
, P (i _u ), P (j ₁ ), P (j ₂ ), ..., P (j _v ). The sum of these values for each group is designated as Q ₀ and Q ₁ .

Next, from these steady state probabilities and the transition rate matrix, the frequency of occurrence of transitions between two groups is obtained. This is specifically as follows. First, the frequency at which the transition from the former group to the latter group occurs (hereinafter referred to as γ) is as follows.

[0033]

[Equation 10] In short, the transitions over the groups are weighted with the steady state probability of the transition source and the sum is calculated. Similarly, the occurrence frequency δ of the transition from the latter group to the former group is obtained. The γ and δ thus obtained are not the transition rates in the Markov process in which one unit is formed as shown in FIG. 11, but are the transition occurrence frequencies. Therefore, this is adjusted as follows.
That is, λ ′, μ ′ in FIG. 11 is determined so that the steady state probabilities in the state (0,1) are Q ₀ , Q ₁ and the transition frequencies between the states are γ, δ. . Specifically, the following equation Q ₀ = μ ′ / (λ ′ + μ ′) Q ₁ = λ ′ / (λ ′ + μ ′) γ = λ′Q ₀ δ = μ′Q ₁ is satisfied. It should be noted that only the latter two equations have practical meaning among them.

The procedure of the second embodiment will be described with reference to FIG. The following is a method of improving the sequential calculation accuracy by the principle of pinching and shooting by utilizing the above two properties. (1) Regarding each subsystem that constitutes the system, the system reliability analysis results are obtained assuming that all subsystems other than the specified subsystem do not fail. This analysis may be performed on the assumption that the system is a system including only the specific subsystem. In this way, as many analysis results as subsystems can be obtained. (2) Next, these results are ordered from the one with the lowest reliability (for example, the one with the highest unavailability), and each subsystem is ranked. (3) Of the above rankings, only the most unreliable "bad" subsystem is the original Sub-Markov process,
The other subsystem analyzes the system replaced with one unit. This result is referred to as a result 11. (4) In the above, the system in which one subsystem is assumed to have no failure is analyzed, and the result is set to result 10. (5) The results thus obtained are as follows: result 10 (good reliability) <true value <result 11 (poor reliability). The result 10 and the result 11 are compared, and if the difference between the two is within the predetermined range, the calculation is terminated assuming that the result with the desired calculation accuracy is obtained. (6) When the calculation accuracy does not reach the prescribed level, the original Markov process is used for the subsystem that brought the second worst reliability in the ordering of (2), and the others are unitized. Is analyzed and the result is designated as result 21. Further, here, a system in which it is assumed that a failure does not occur in the subsystem made into one unit, and the result is set as the result 20. As a result, result 10
<Result 20 <True value <Result 21 <Result 11 This operation may be continued until the desired accuracy is achieved.

It should be noted that this procedure always ends (because if all subsystems are analyzed as fully described Sub-Markov processes, it is nothing but an approximation). FIG. 13 shows a block diagram of a system reliability analysis device (Example 2). This system reliability analysis device (embodiment 2) is a transition rate matrix (A _k , k = 1, ...) Of a plurality of (m) subsystems that constitute a system and have independent behaviors.
., M), a transition rate matrix A _k storage means and a table (TAB _k , which associates the states of each subsystem with the allowable time
table TAB _k storage means for storing k = 1, ..., m),
One unit is referred to by referring to the target subsystem storage means for storing the subsystem to be made into one unit (which should be assumed not to fail) instructed by the calculation routine control means and the subsystem stored in the target subsystem storage means. Requesting a table (TAB _k , k = 1, ..., m) in which the transition rate matrix in which only the subsystem of interest is integrated into one unit and the state of each subsystem and the allowable time are associated with each other An input transition rate matrix and table selecting means (1) to be input to the system reliability analyzing apparatus according to claim 1, and a result 10 storing means for storing a result 10 generated by the system reliability analyzing apparatus according to claim 1. And a transition rate matrix and table relating to subsystems other than the subsystem of interest by referring to the subsystems stored in the subsystem of interest storage means. 2. An input transition rate matrix and table selecting means (2) to be input to the system reliability analyzing apparatus of claim 1, a result 11 storing means for storing a result 11 generated by the system reliability analyzing apparatus according to claim 1, and a result 10. The result of comparing the result of the storage means with the result of the result 11 storage means is notified to the calculation routine control means, and the result is output if the result of the determination by the judgment means is within a predetermined error range. If it is instructed and the result is out of the range, it is composed of a calculation routine storage means for newly instructing the subsystem of interest as a subsystem of interest.

[0036]

Since the present invention is configured as described above, when analyzing a complex system configuration, the number of states of the Markov process, which is the basis of the analysis, does not increase explosively and the calculation time is reduced. Analysis can be performed efficiently in terms of accuracy and accuracy.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an air conditioning system that is an example of a system to which the present invention is applied.

FIG. 2 is a Markov transition diagram of the air conditioning system.

FIG. 3 is a diagram illustrating an image of repeated states.

FIG. 4 is a diagram for explaining the first embodiment of the present invention.

FIG. 5 is a diagram illustrating a second embodiment of the present invention.

FIG. 6 is a correspondence table (part 1) between the state and the number of operation-stop air conditioners.

FIG. 7 is a flowchart of the first embodiment of the present invention.

FIG. 8 is a system reliability analysis device of the present invention (Example 1).
Block diagram of.

FIG. 9 is a configuration example of a slightly complicated system to which the present invention is applied.

FIG. 10 is a correspondence table (part 2) between the state and the number of operation-stop air conditioners.

FIG. 11 is a diagram for explaining one unitization of a subsystem.

FIG. 12 is a flowchart of the second embodiment of the present invention.

FIG. 13 is a block diagram of a system reliability analyzer (second embodiment) of the present invention.

Claims (4)

(57) [Claims] 1. A system reliability analysis apparatus comprising a plurality of elements, which calculates the reliability of a system which is considered as a system down for the first time after a lapse of an allowable time determined for each failure pattern of these elements, Multiple, independent behaviors (m) that make up the system
Transition rate matrix storage means for storing the transition rate matrix (A _k , k = 1, ..., m) of the subsystems, and a table (TAB _k , which associates the states of the subsystems with the allowable times). k = 1, ..., M) table storage means, and steady state probability calculation means for calculating the steady state probability of each subsystem based on the transition rate matrix stored in the transition rate matrix storage means. Based on the transition rate matrix stored in the transition rate matrix storage means, the steady state probability storage means of each subsystem that stores the steady state probability of each subsystem calculated by the steady state probability calculation means, While changing the state of interest when determining the system down frequency and the system downtime and instructing the state of interest specified in the state of interest storage means, the system downtime and the system downtime are accumulated. Calculation routine control means for instructing accumulation of the shutdown frequency and system downtime, attention state storage means for storing the attention state instructed by the calculation routine control means, and the attention state stored in the attention state storage means Steady-state probability is calculated based on the steady-state probability of each subsystem stored in the steady-state probability storage means of each subsystem; The transition frequency to the focused state is calculated based on the steady state probability of the focused state stored in the steady state probability storage means of the focused state and the transition rate matrix stored in the transition rate matrix storage means. A transition frequency calculation means for transitioning to the state of interest, and a transition rate from the state of interest to another state stored in the state of interest storage means are stored in the transition rate matrix storage means. Transition rate calculation means from a focused state to another state calculated based on a transition rate matrix, steady state probability of the focused state calculated by the steady state probability calculation means of the focused state, and transition frequency calculation to the focused state The transition frequency to the focused state calculated by the means, the transition rate from the focused state to another state calculated by the transition rate from the focused state to another state, and each sub stored in the table storage means Based on a table in which the system state and the allowable time are associated with each other, the system down frequency and the system downtime related to the focused state are calculated, the system down frequency related to the focused state and the system downtime calculating means, Accumulates the system down frequency and system downtime calculated by the system downtime and system downtime related to the state of interest based on the instruction of the calculation routine control means. That the system reliability analysis apparatus characterized by having a means for accumulating the system down frequency and system unavailability. 2. A system reliability analysis apparatus comprising a plurality of elements, which calculates the reliability of a system which is considered as a system down for the first time after a lapse of a permissible time determined for each failure pattern of these elements. Multiple, independent behaviors (m) that make up the system
Transition rate matrix storage means for storing the transition rate matrix (A _k , k = 1, ..., m) of the subsystems, and a table (TAB _k , which associates the states of the subsystems with the allowable times). table storage means for storing k = 1, ..., M), and a target subsystem storage means for storing the subsystem to be made into one unit (which should be assumed not to fail) instructed by the calculation routine control means, By referring to the subsystems stored in the subsystem of interest storage means, by using the unitization means, the transition rate matrix in which only the subsystem of interest is integrated into one unit, the state of each subsystem and the allowable time are associated with each other. An input transition rate matrix and table selecting means (1) for inputting the table to the system reliability analysis apparatus according to claim 1, and a result 10 generated by the system reliability analysis apparatus according to claim 1. The system reliability according to claim 1, wherein the result 10 storage means for storing and a transition rate matrix and a table relating to subsystems other than the subsystem of interest are referred to by referring to the subsystems stored in the subsystem of interest storage means. An input transition rate matrix and table selection means (2) to be inputted to the analysis device, a result 11 storage means for storing the result 11 generated by the system reliability analysis device according to claim 1, and a result 10 result storage means. And the result 11 comparing the result of the storage means with the result, the determination means for notifying the result to the calculation routine control means, and instructing to output the result if the determination result of the determination means is within a predetermined error range If the result is out of the range, another system is set as a target subsystem, and a calculation routine storage unit for newly instructing the target subsystem storage unit is provided. System reliability analyzer. 3. A system reliability analysis method comprising a plurality of elements, which calculates the reliability of a system which is considered to be system down for the first time after a lapse of a permissible time determined for each failure pattern of these elements. Multiple, independent behaviors (m) that make up the system
Table (TAB _k , k = 1, ...) that stores the transition rate matrix (A _k , k = 1, ..., M) of each subsystem and associates the state of each subsystem with the allowable time. , M) is stored, the steady state probability of each subsystem is calculated based on the stored transition rate matrix, the calculated steady state probability of each subsystem is stored, and the stored transition rate is stored. Based on the matrix, change the state of interest when determining the system down frequency and system downtime and indicate the specified state of interest, accumulate the system down frequency and system downtime, and store the instructed state of interest. Then, the stored steady-state probability of the focused state is calculated based on the steady-state probability of each subsystem, and the transition frequency to the stored focused state is calculated as the stored steady-state probability of the focused state and the stored The transition rate matrix Based on the transition rate matrix, the transition rate from the stored designated state of interest to another state is calculated based on the calculated steady state probability of the focused state, and the calculated transition frequency to the focused state, Based on the calculated transition rate from the state of interest to another state and a table in which the state of each subsystem and the allowable time that are stored are associated with each other, the system down frequency and the system downtime related to the state of interest are calculated. A system reliability analysis method characterized by calculating and accumulating the calculated system down frequency and system non-operation rate. 4. A system reliability analysis method, comprising a plurality of elements, for calculating the reliability of a system which is considered as a system down for the first time after a lapse of an allowable time determined for each failure pattern of these elements, Multiple, independent behaviors (m) that make up the system
Table (TAB _k , k = 1, ...) that stores the transition rate matrix (A _k , k = 1, ..., M) of each subsystem and associates the state of each subsystem with the allowable time. , M) is stored, subsystems that should be unitized (things that should be assumed not to fail) are stored, the stored subsystems are referenced, and only the subsystem of interest is converted into a unit and the transition rate matrix and each A table (TAB _k , k =) in which subsystem states and allowable times are associated with each other.
, ..., m) and the transition rate matrix and table of the system reliability analysis method according to claim 3 are selected as input, and the result generated by the system reliability analysis method according to claim 3 10. The system stores 10 and refers to the stored subsystems, selects a transition rate matrix and a table relating to subsystems other than the subsystem of interest, and selects the table as the input of the system reliability analysis method according to claim 3. The result 11 generated by the system reliability analysis method according to Item 3 is stored, the result obtained by comparing the result 10 with the result 11 is determined and notified, and the determination result is within a predetermined error range. Then, if the result is out of the range, if the result is out of the range, another system is set as the target subsystem, a new target subsystem is specified, and the above procedure is repeated, and the system reliability analysis method is characterized. .