JP2002182735A - Device and method for analyzing system reliability - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a system reliability analyzing method capable of efficiently evaluating and analyzing the reliability of a system. SOLUTION: An air conditioning system being the object of analysis is divided into sub-systems 1, 2 and 3 where behaviors can be made independent. The Markov processes (sub-Malkov processes 1, 2 and 3) of the sub-systems are generated and they are combined. Then, they are mechanically analyzed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method for evaluating the reliability of a system having a complicated redundant configuration. In particular, since the shutdown of the air conditioning system in a communication machine room does not immediately lead to the stoppage of the function of the communication system to be air-conditioned, the system is considered to be down for the first time after stopping for a certain period of time. The present invention relates to a system reliability analysis device and method for evaluating the reliability of a system.

[0002]

Prior to the description of the present invention, a conventional method for evaluating the reliability of an air conditioning system will be described. FIG. 1 shows a configuration example of an air conditioning system. The air conditioning system includes a plurality of air conditioners for air conditioning a communication machine room containing a commercial power supply, a backup generator, and a communication system. In this example, electric power is normally supplied to the air conditioner from a commercial power supply. The number of air conditioners is, for example, three. When the commercial power supply is stopped, a spare 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 conditioning is stopped. Also, failures occur in air conditioners,
The air-conditioning capacity is reduced according to the number of failed units. By the way, when the air-conditioning capacity is stopped or decreased due to the above-mentioned cause, the room temperature of the communication machine room does not rise instantaneously, but after a certain time determined according to the reduced air-conditioning capacity, Reaches a room temperature that would hinder the operation of the communication system. For example, 30 minutes when all air conditioners are stopped, 1 hour when only one air conditioner is operating,
In the case of two movable units, it is like two hours. When all three units are operating, the time is of course infinite (that is, the room temperature does not rise no matter how much time passes).

In such a system reliability evaluation, the behavior of the system is analyzed using a Markov model, and the state probabilities and the like for each number of air conditioners are analyzed. A method of analyzing time is used. 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)
Λ _CS , repair rate (reciprocal of repair time) μ _CS , failure rate of backup generator λ _DEG , repair rate μ _DEG , air conditioner failure rate λ _AC , repair rate μ _AC , Markov The transition diagram is shown in FIG. Here, the occurrence of a failure is random, and the distribution of repair time is an exponential distribution. Further, it is assumed that failures of the commercial power supply, the backup generator, and each air conditioner occur independently. In the state (x, y, z) in the figure, x = 0 means that the commercial power is up, x
= 1 is commercial power down, y = 0 is standby generator up, y = 1
Means that the spare generator is down, and z = 0, 1, 2, 3 represents the number of air conditioners that are down. In the drawing, arrows indicate the frequency (transition rate) at which a transition from one state to another state occurs. This point is the same as the ordinary Markov analysis method.

In the Markov process shown in FIG. 2, for example, a state change (transition) repeatedly occurs as shown in FIG. In FIG. 3, first, the state (1,0,0) is started, and then (1,1,0).
0), (1,1,1), (1,0,1), and (1,1,1) in this order. Here, paying attention to the number of operating air conditioners, in the case of (1,0,0), since all three are operating, the room temperature does not rise. In the case of (1,1,0), the power supply to the air conditioner is cut off, so all three units are stopped. Break through. The same applies to the case of (1,1,1). Also, in the case of (1,0,1), only one air conditioner is stopped, so if this state is not removed within two hours, the system will be down.

In the system reliability analysis method according to the prior art, the frequency of occurrence of each state and the probability that the state continues even after the permissible time has elapsed are obtained and added to determine the frequency of occurrence of system down. The sum of the lengths of the parts considered to be system down and the ratio to the total time is used as the system non-operation rate. (In this method, when a transition occurs from (1,1,0) to (1,1,1) as shown in FIG. 3 (that is, when three power supply units are disconnected while the power supply is cut off). If one of them goes down), it is assumed that the system is recovered in the analysis, so it is not strictly correct, but it has been found that this method can perform analysis with accuracy that is practically acceptable.) The frequency of transition to each state occurs. It does the following:

First, an equilibrium equation corresponding to FIG. 2 is set up and solved, and a steady 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, other states that may transition to state (1,1,1,)
To (0,1,1,), (1,0,1), (1,1,0), and (1,1,2) stationary probabilities (P ()), to (1,1,1) Transition rate (failure rate λ, repair rate μ)
What is necessary is just to add what is multiplied by. In other words, it occurs frequent transition to the _{(1,1,1) = λ CS P (} 0,1,1) + λ DEG P (1,0,1) + 3λ AC P (1,1,0) + 2μ AC P ( 1,1,2) (1).

After the frequency at which the transition to the state (1,1,1) occurs is obtained in this way, after that, for an event that stays in that state for a certain period of time (until the state transitions to another state) )
If the occurrence frequency is determined, it becomes the occurrence frequency of the system down. In addition, if the ratio of the time remaining in the state beyond the predetermined time to the total time is obtained, the system non-operation rate can be obtained. Generalizing the state (x, y, z) to state i,

[0008]

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

[0009]

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

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

[0011]

(Equation 3) Here, μ _i is the total transition rate from state i to another state (for example, the total transition rate from state (1,1,1) in FIG. 2 to another state: μ _AC + μ _CS + μ _DEG +2 μ _AC). ). For the integral in equation (3),

[0012]

(Equation 4) It is.

[0013]

The above is an outline of the reliability evaluation method of the air conditioning system according to the prior art. However, recent air conditioning systems have become more and more complicated.
There are the following problems in performing reliability evaluation by the conventional technology. In the context of system review, the optimal system configuration (for example, the configuration of a group of air conditioners, etc.) is searched for by analyzing systems of various configurations and comparing the results. To do so efficiently, A method of performing the above analysis mechanically 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 the calculation time and accuracy impractical.

[0014]

In order to solve the above-mentioned problems, in the present invention, an air conditioning system to be analyzed is divided into subsystems having independent behaviors, and first, the Markov processes (hereinafter referred to as "markov processes") of those subsystems. A "sub-Markov process") is created (each of which is given), and a method of mechanically analyzing the combination is presented below. In order to solve the above-described problem, the present invention assumes that some of the subsystems do not fail, and evaluates the reliability of the evaluation target system as an approximate upper limit of the reliability. The analysis results of a system that can replace some of them with the system in which the deterioration of the air-conditioning capacity becomes zero at once instead of in steps are set as lower limit approximations of reliability, and an approximation method for appropriately narrowing these is presented.

[0015]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below with reference to embodiments. (Embodiment 1 for Solving the Problems) The behavior of the system shown in FIG. 1 is described as a system in which a commercial power supply, a backup generator, and three units are considered as a set.
) Are independent of each other.
Therefore, these are the subsystems that make up the entire system.
Consider them as 1, 2, and 3 (Fig. 4 (a)). Each subsystem forms a Markov process. These are called sub-Markov processes ₁ , ₂ , 3 (i ₁ , i ₂ , i ₃ ). As shown in FIG. 4B, there are three Markov transition diagrams of each sub-Markov process. The division into independent sub-processes is not always one. That is, it is considered as a subsystem in which a commercial power supply and a backup generator are set, and two subsystems of a group of three air conditioners. In this case, the sub-Markov process is as shown in FIG.

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 has been given in advance. As an expression of a parameter defining the sub-Markov process, for example, there is a method of expressing a transition rate between states in a matrix format. That is, in a square matrix A having the degree of the number of states (the (i, j) element is a _ij ), and expressed by the transition rate a _ij from the state j to the state i, an arbitrary shape A sub-Markov process is represented. In addition, in realizing the reliability analysis device by using this, the transition rate matrix A _k of each sub-Markov process may be configured to be input. (2) Next, the number of operation-stop air conditioners for each state is input.

As described above, the transition of each sub-Markov process
Given that the transfer matrix is given,
System reliability created by the combination of
The evaluation is as follows. First, the sub-Markov process is all
And 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 is a_ij ^(k)). At this time, the system
The state of the Markov process describing the entire program is
Set of statuses (i₁, i_Two, ・ ・ ・, I_k,
..., i_m) (Three in the example of FIG. 4), and the number is
n₁× n_Two× ・ ・ ・ × n_k× ・ ・ ・ × n _m(In the example of FIG. 4,
2 × 2 × 4). For all these states, the state
Frequency, the average duration in that state, and
If the time allowed for the room temperature to rise in the condition
Required system down frequency and non-operation rate by conventional technology
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,
The steady state probability of each state in each sub-Markov process is obtained. This can be obtained by a well-known Markov analysis method, given the transition rate matrix of each sub-Markov process.

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 ), 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) was thus determined, the steady state probability of state j _k in the sub-Markov process k and P (j _k), state (j _1,
j ₂ , ..., j _k , ..., j _m ) is P (j ₁ ) × P (j ₂ ) × ・ ・ ・ × P (j _k ) × ・ ・ ・ × P (j _m ). In this way, when the whole system is considered as one Markov process, the steady state probability of each state is obtained. [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 and the transition rate to the state of interest. Can be

That is, the state of interest is represented by (i ₁ , i ₂ ,..., I _k ,
..., i _m ), the state that can transition to it is m
Focused on one of the sub-Markov process (e.g., k-th sub-Markov process), in its sub-Markov process in, enumerate transition possible state to state i _k

(Equation 6) And, the _{(i 1, i 2, ···} , i k, ···, i m) of the location of the i _k, there are replaced by these, 1 to the replacement of k This is a state obtained by performing all of the steps from to m. Then, the frequency of occurrence of the transition from the “state that can transition to the state of interest” thus obtained to the state of interest is

[0022]

(Equation 7)Is the sum of (α). Therefore, attention
State (i₁, i_Two, ・ ・ ・, I _k, ・ ・ ・, I_mFrequency of transition to)
Is the sum of

[0023]

(Equation 8) Becomes [Calculation of transition rate from state of interest to other state] (6) Next, the time distribution from the state of interest to any other state is the same as the time distribution from the state of interest to any other state. Is the simple sum of the transition rates. Therefore, among the elements of the transition rate matrix describing each sub-Markov process, those corresponding to those that go out of the state of interest may be summed. That is,

[0024]

(Equation 9) β represents the other state transition from the state i _k. [Calculation of system down frequency and system unavailability related to the state of interest] [System down frequency and system unavailability accumulation] (7) Thus, in the related art, the three systems required to obtain the system down frequency and the system unavailability Of the elements (frequency of occurrence of transition to the state of interest, transition rate from the state of interest to another state, and allowable time in the state of interest), the former two are determined. The last allowable time in the state of interest may be stored in the storage unit in association with the state of the entire system, and may be referred to when calculating the system down frequency. For example, when the air conditioning system of FIG. 1 is divided into subsystems as shown in FIG. 4A and described, the system state is (i ₁ ,
i ₂ , i ₃ ), which are stored in association with the permissible time (for example, the permissible time T _{i in} the case of one operation-stop air conditioner _).
Is 2 hours). FIG. 6 shows an example of the association table. (8) The system down occurrence frequency and the system down unavailability are obtained based on the conventional formulas (2) and (3).

The frequency of occurrence of the transition to the state of interest,
The calculation of the transition rate from the state of interest to another state and the calculation of system reliability are repeated until the state of interest exhausts all states. (9) Next, the sum of the system down occurrence frequency and the system down unavailability for each state of interest is obtained. FIG. 8 shows a block diagram of a system reliability analysis device (first embodiment). This system reliability analysis apparatus (Embodiment 1) calculates transition rate matrices (A _k , k = 1,..., M) of a plurality (m) of subsystems having independent behavior in a system. Transition rate matrix to store
A _k storage means, a table TAB _k storage means for storing a table (TAB _k , k = 1,..., M) in which the state of each subsystem is associated with the permissible time, and a transition rate matrix storage means Steady state probability calculating means for calculating the steady state probability of each subsystem based on the stored transition rate matrix, and each subsystem 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, changing the state of interest when obtaining the system down frequency and the system unavailability, and specifying the attention to the attention storage means Calculating routine control means for instructing the state and accumulating the system down frequency and the system unavailability for the means for accumulating the system down frequency and the system unavailability; The state-of-interest storage means for storing the state-of-interest indicated by the routine control means, and the steady-state probability of the state-of-interest stored in the state-of-interest 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 storage means are stored in the steady state probability storing means for 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 transition rate from the state of interest to another state is calculated based on the transition rate matrix stored in the transition rate matrix storage means, and the steady state probability calculation means for the state of interest is calculated. The steady state probability of the eye state, the transition frequency to the state of interest calculated by the transition frequency calculation means to the state of interest, and the transition rate from the state of interest to another state calculated by the transition rate calculation means from the state of interest to another state Based on the transition rate and a table in which the state of each subsystem and the permissible time stored in the table storage unit are associated with each other, a system down frequency and a system inoperability rate related to the state of interest are calculated. The system down frequency and the system unavailability ratio calculating means, and the system down frequency and the system unavailability ratio calculated by the system of interest and the system unavailability ratio calculated by the system unavailability ratio calculating means are accumulated based on the instructions of the calculation routine control means. And means for accumulating the system down frequency and the system non-operation rate. (Second Embodiment for Solving the Problem) Next, an embodiment for reducing the amount of calculation will be described.

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 permissible time is stored by the method shown in the embodiment, the reliability can be evaluated mechanically. Can be performed, but the calculation amount still increases. For example, FIG.
Sub-process m is 6
The number n of states 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 calculation amount is large to perform the calculation by the method shown in. Therefore, a method of reducing the amount of calculation while evaluating the calculation error will be described.

In order to implement the features of the present invention, the division into subsystems only needs to satisfy the condition that the behavior of each subsystem is independent of each other. The following conditions are further required. Condition: When it is assumed that there is no failure in the elements constituting another subsystem, when focusing on the number of air-conditioning units that have been stopped due to the failure of an element constituting a certain subsystem, some of these may be in operation. This includes the case where there is no stopped air conditioner and the case where the number of previous air conditioners has stopped operating. Furthermore, the number of air conditioner outages caused as a result of the element failure of each subsystem is calculated as (s ₁ , s ₂ ,
·, S _k ), the halt of the air conditioning capacity 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 is not satisfied by the division into subsystems as shown in FIG. This is because the subsystem 1 has two states corresponding to whether the commercial power supply is up or down, but the number of air conditioners whose operation has been stopped cannot be determined only from information that the state is either of these states.
On the other hand, division into subsystems as shown in FIG. 5A satisfies this condition. In the subsystem 1, only when both the commercial power supply and the standby generator are down, the number of air conditioners whose operation is stopped is 3, and in other states, it is 0. In the subsystem 2, the number of air conditioners that have gone down is the number of air conditioners that have stopped operating. Furthermore, the larger 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 larger number of operation-stop air-conditioners as a whole system (that is, the number of operation-stop air-conditioners). , The number of air conditioners that are stopped when the subsystem 1 goes down).

When the division into subsystems satisfies this condition, if the state of the subsystems and the number of air conditioners that are stopped are set and stored, the number of air conditioners that are stopped 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-stop air conditioners. The basic idea of implementing the features of the present invention is to note the following two facts. (1) Assuming that any one of the subsystems does not fail, the reliability of the entire system is higher than if it failed. Generally speaking, we call this subsystem S ₁ , S
_2, when a · · · S _m, some of them (S _i1, S _i2,
…) Does not fail (Result 1) and the result of analysis (Result 2) assumes that (S _j1 , S _j2 ,...) _Does not fail, If (S _i1 , S _i2 ,
..) ⊃ (S _j1 , S _j2 ,...) (Included as a set), result 1 gives better reliability than result 2.
In other words, result 2 is closer to the true value.

(2) There are generally two stages of deterioration of the air-conditioning capacity of the subsystem (that is, two stages, ie, a stage where the air-conditioning capability does not deteriorate and a stage where the air-conditioning capability is completely lost). I pretend that there are only two. This is referred to as a unitization of the subsystem. This means that a subsystem composed of a plurality of elements is treated as if it had only one unit.
When analyzing a system in which the original subsystem is replaced with the subsystem simulated in this way, the resulting reliability (frequency of system down occurrence and non-operation rate) is lower than the true value. (Procedure for One Unit) The procedure for one unit will be described with reference to FIG.

The states constituting the sub-Markov process of interest are classified into a set of states in which the air conditioning capacity is not deteriorated (group 1) and a set of states in which the capacity is completely lost (group 2).
2 minutes. The state of the former group is represented by i ₁ , i ₂ , ..., i
_k, ···, and i _u, j ₁ the state of the latter group, j _2, ··
, J _k ,... J _v (u + v = the number of states of the sub-Markov process of interest). First, the steady state probability of the original sub-Markov process is determined. P (i ₁ ), P (i ₂ ), ...
, P (i _u ), P (j ₁ ), P (j ₂ ),..., P (j _v ). The sum of these for each group is defined as Q ₀ and Q ₁ .

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

[0033]

(Equation 10) In short, the transitions between groups are weighted by the steady state probability of the transition source and the sum is calculated. In the same manner, the occurrence frequency δ of the transition from the latter group to the former group is obtained. Γ and δ obtained in this way are not transition rates in the Markov process unitized as shown in FIG. 11, but are transition occurrence frequencies. Therefore, this is adjusted as follows.
That is, λ ′ and μ ′ in FIG. 11 are determined such that the steady state probabilities in the state (0, 1) are Q ₀ and Q ₁ and the occurrence frequency of transition between the states is γ and δ. . Specifically, the following equation is satisfied: Q ₀ = μ ′ / (λ ′ + μ ′) Q ₁ = λ ′ / (λ ′ + μ ′) γ = λ′Q ₀ δ = μ′Q ₁ It should be noted that only the following two equations are substantially significant.

The procedure of the second embodiment will be described with reference to FIG. A method of improving the sequential calculation accuracy by using the above two properties and by the principle of pinching and shooting is as follows. (1) As for each subsystem constituting the system, a result of analyzing system reliability is obtained assuming that no failure occurs except for a specific subsystem. This analysis may be performed assuming that the system is a system including only the specific subsystem. In this way, analysis results are obtained for the number of subsystems. (2) Next, these results are ordered from those with low reliability (for example, the one with the highest unavailability), and each subsystem is ranked. (3) Among the above rankings, only the worst "worst" subsystem is the original Sub-Markov process,
The other subsystems analyze the system that has been replaced with a single unit. This result is referred to as a result 11. (4) In the above description, a system in which a single-unit subsystem is assumed not to fail is analyzed, and the result is set as result 10. (5) The result obtained in this way is as follows: result 10 (good reliability) <true value <result 11 (poor reliability). The results 10 and 11 are compared, and if the difference between the two falls within a predetermined range, the calculation ends as a result having a desired calculation accuracy is obtained. (6) If the calculation accuracy does not reach the predetermined level, the system that adopted the original Markov process for the subsystem that brought the second lowest reliability in the ordering of (2) and unitized the other units Is analyzed, and the result is set as a result 21. Further, a system in which it is assumed that no failure occurs in the one-unit subsystem is analyzed, and the result is set as a result 20. As a result, the result 10
<Result 20 <True Value> Result 21 <Result 11 This operation may be continued until the desired accuracy is obtained.

Note that this procedure always ends (because if all the subsystems are analyzed as a sub-Markov process fully described), this is nothing but an analysis that does not approximate. FIG. 13 shows a block diagram of a system reliability analysis device (second embodiment). This system reliability analysis apparatus (Embodiment 2) includes a transition rate matrix (A _k , k = 1,...) Of a plurality (m) of subsystems having independent behavior which constitute a system.
· Transition rate matrix storing m) A _k storage means and, table associating (TAB _k and allowed time the state of each subsystem,
k = 1, the table TAB _k storage means for storing · · ·, m) and,
Referring to the subsystem of interest storage unit that stores the subsystems to be made into one unit (assuming that there is no failure) designated by the calculation routine control unit, and the subsystems stored in the subsystem of interest storage unit, Using the conversion means, a table (TAB _k , k = 1,..., M) in which the transition rate matrix in which only the subsystem of interest is made 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 selection means (1) to be input to the system reliability analysis device according to claim 1, and a result 10 storage means for storing a result 10 generated by the system reliability analysis device according to claim 1. And a transition rate matrix and a table relating to subsystems other than the subsystem of interest with reference to the subsystems stored in the subsystem of interest storage means. 2. An input transition rate matrix and table selection means (2) to be input to the system reliability analysis device of (1), a result 11 storage means for storing a result 11 generated by the system reliability analysis device of claim 1, and a result (10). A determination unit for notifying the calculation routine control unit of the result of comparing the result of the storage unit with the result of the result 11 storage unit; and outputting the result if the determination result of the determination unit is within a predetermined error range. If the result is out of the range, the system is constituted by a calculation routine storing means for newly instructing the focused subsystem storing means with another system as a focused subsystem.

[0036]

Since the present invention is configured as described above, when analyzing a complex system configuration, the number of states of the Markov process that 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 the drawings]

FIG. 1 is a configuration diagram of an air conditioning system as 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 repetition of a state.

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

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

FIG. 6 is a table (No. 1) showing a correspondence between a state and the number of operation-stop air conditioners.

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

FIG. 8 is a system reliability analysis device according to the present invention (first embodiment);
FIG.

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

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

FIG. 11 is a diagram illustrating the integration of a subsystem into one unit.

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

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

Claims (4)

[Claims] 1. A system reliability analysis device comprising a plurality of elements, and calculates the reliability of a system which is considered to be system down for the first time after an allowable time determined for each failure pattern of these elements has elapsed. Multiple (m pieces) with independent behavior that make up the system
A transition rate matrix storing means for storing a transition rate matrix (A _k , k = 1,..., M) of the subsystems; and a table (TAB _k , k = 1,..., m) and a steady state probability calculating means for calculating a steady state probability of each subsystem based on the transition rate matrix stored in the transition rate matrix storing means. A steady state probability storage means for each subsystem that stores the steady state probability of each subsystem calculated by the steady state probability calculation means, and a transition rate matrix stored in the transition rate matrix storage means. The state of interest at the time of obtaining the system down frequency and the system unavailability is changed to indicate the specified state of interest in the state of interest storage means, and the system that accumulates the system down frequency and the system unavailability is given a system Calculation routine control means for instructing the accumulation of the system downtime and the system downtime rate; attention state storage means for storing the attention state indicated by the calculation routine control means; and the attention state stored in the attention state storage means. The steady state probability is stored in the steady state probability storage means of each subsystem, and is calculated based on the steady state probability of each subsystem.The steady state probability calculation means of the state of interest, and stored in the state of interest storage means The calculated transition frequency to the state of interest is calculated based on the steady state probability of the state of interest stored in the steady state probability storage means of the state of interest and the transition rate matrix stored in the transition rate matrix storage means. A transition frequency calculation unit for transitioning to the state of interest, and a transition rate from the state of interest stored in the state of interest storage unit to another state is stored in the transition rate matrix storage unit. Means for calculating a transition rate from the state of interest to another state calculated based on the transition rate matrix; calculating a steady state probability of the state of interest calculated by the means for calculating a steady state probability of the state of interest; calculating a transition frequency to the state of interest The transition frequency from the noted state to another state calculated by the means, the transition rate from the noted state to another state calculated by the transition rate from the noted state to another state, and each sub-table stored in the table storage means. Based on a table that associates the state of the system and the permissible time, a system down frequency and a system inoperability rate according to the state of interest are calculated, a system down frequency and a system inoperability rate calculation unit according to the state of interest, The system down frequency and the system unavailability calculated by the system down frequency and the system unavailability ratio calculation means for the state of interest are accumulated based on the instruction of the calculation routine control unit. 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, and calculating a reliability of a system which is regarded as a system down for the first time after an allowable time determined for each failure pattern of these elements, Multiple (m pieces) with independent behavior that make up the system
A transition rate matrix storing means for storing a transition rate matrix (A _k , k = 1,..., M) of the subsystems; and a table (TAB _k , table storage means for storing (k = 1,..., m); subsystem-of-interest storage means for storing subsystems designated by the calculation routine control means to be unitized (assuming no failure); Referring to the subsystems stored in the subsystem of interest storage unit, using a unitization unit, associating a transition rate matrix in which only the subsystem of interest is unitized with the state of each subsystem and the allowable time An input transition rate matrix and table selecting means (1) for inputting the table and the table to the system reliability analysis device according to claim 1, and a result 10 generated by the system reliability analysis device according to claim 1. 2. The system reliability according to claim 1, wherein the storage unit stores a result 10 storage unit, and a transition rate matrix and a table related to subsystems other than the subsystem of interest by referring to the subsystems stored in the subsystem of interest storage. 3. An input transition rate matrix and table selection means (2) to be input to the analyzer, a result 11 storage means for storing a result 11 generated by the system reliability analysis apparatus according to claim 1, and a result of a result 10 storage means. Determining means for comparing the result of the comparison with the result of the result 11 storage means to the calculation routine control means; and instructing to output the result if the determination result of the determining means is within a predetermined error range; If the result is out of the range, a calculation routine storage unit that newly instructs another storage unit as a target subsystem storage unit as a target subsystem storage unit is provided. System reliability analyzer. 3. A system reliability analysis method comprising a plurality of elements, and calculating a reliability of a system which is regarded as a system down for the first time after an allowable time determined for each failure pattern of these elements, Multiple (m pieces) with independent behavior that make up the system
Table (TAB _k , k = 1,...) Storing the transition rate matrix (A _k , k = 1,..., M) of the subsystem , M), calculate the steady state probability of each subsystem based on the stored transition rate matrix, store the calculated steady state probability of each subsystem, and store the stored transition rate The designated state of interest is indicated by changing the state of interest when calculating the system down frequency and system inoperability based on the matrix, and the system down frequency and system inoperability are accumulated, and the instructed state of interest is stored. Then, the stored steady state probability of the state of interest is calculated based on the steady state probability of each subsystem, and the transition frequency to the stored state of interest is calculated based on the stored steady state probability of the state of interest and stored. The transition rate matrix Based on the transition rate matrix, the transition rate from the stored indicated state of interest to another state is calculated based on the transition rate matrix, and the calculated steady state probability of the state of interest, the calculated transition frequency to the state of interest, Based on the calculated transition rate from the state of interest to another state, and a table in which the stored states of each subsystem and the permissible time are associated with each other, the system down frequency and the system inoperability rate related to the state of interest are calculated. A system reliability analysis method comprising calculating and accumulating the calculated system down frequency and system non-operation rate. 4. A system reliability analysis method comprising a plurality of elements, and calculating a reliability of a system which is considered to be a system down for the first time after an allowable time determined for each failure pattern of these elements, Multiple (m pieces) with independent behavior that make up the system
Table (TAB _k , k = 1,...) Storing the transition rate matrix (A _k , k = 1,..., M) of the subsystem ., M), the subsystems to be unitized (assuming no failures) are stored, and the stored subsystems are referred to, and the transition rate matrix in which only the subsystem of interest is unitized to one unit and A table (TAB _k , k =
1,..., M) are selected as a transition rate matrix and a table of the system reliability analysis method according to claim 3 and input, and the result generated by the system reliability analysis method according to claim 3 10, and refers to the stored subsystem, selects a transition rate matrix and a table relating to a subsystem other than the subsystem of interest, and selects them as inputs to the system reliability analysis method according to claim 3. A result 11 generated by the system reliability analysis method according to item 3 is stored, a result obtained by comparing the result 10 with the result 11 is determined and notified, and the determined result is within a predetermined error range. If the result is out of the range, another system is set as a target subsystem, a new target subsystem is specified, and the above procedure is repeated. .