JP6845126B2 - Failure probability calculation device, failure probability calculation method and program - Google Patents

Description

The present invention relates to a failure probability calculation device, a failure probability calculation method, and a program.

As a probability distribution model that expresses the probability of failure, a method of deriving a functional expression of a failure rate curve that follows the Weibull distribution by Weibull analysis and predicting the failure rate of each facility using this functional expression has been conventionally known. There is. In the Weibull distribution, the relational expression of the bathtub curve is defined by the following equation 1.

ここで、ｍは形状パラメータ、ηは尺度パラメータと呼ばれる。

Here, m is called a shape parameter and η is called a scale parameter.

By determining the shape parameter m and the scale parameter η, the failure rate λ according to the usage time t is calculated.

In addition, based on Weibull analysis, there is known a technique for calculating the probability of failure that takes into account the deterioration state from the accumulated data of the inspection results of each equipment that is divided into three or more deterioration states in stages. (See, for example, Patent Document 1). In the technique disclosed in Patent Document 1, even if the equipment has the same usage time, different failure probabilities are calculated depending on the deterioration state. Therefore, even if maintenance resources are limited and all equipment cannot be inspected at once, maintenance and inspection can be prioritized.

Japanese Unexamined Patent Publication No. 2016-115008

Here, when the equipment is installed outdoors, it is considered that the parameters (shape parameter m and scale parameter η) of the failure probability model differ depending on the environment of the installation location of the equipment. For example, it is considered that the value of the shape parameter m and the value of the scale parameter η are different between the equipment installed outdoors in an area with a lot of rain and wind and the equipment installed outdoors in an area with relatively little rain and wind. ..

However, for example, when the parameters of the failure probability model are determined for each equipment, the actual data for determining these parameters is also for each equipment, so that the actual data is insufficient and the estimation accuracy of the failure probability is lowered. There is.

The present invention has been made in view of the above points, and an object of the present invention is to estimate the failure probability with high accuracy while considering the difference in the failure probability depending on the installation location.

Therefore, in the embodiment of the present invention, the failure probability calculation device that calculates the failure probabilities of a plurality of facilities, and the probability distribution of the model parameters of the failure probability model for calculating the failure probability is determined by the probability distribution. A first formulation means that is formulated using an average variable that indicates the average and a location-dependent eigenvariable that indicates a probability variable that depends on the installation location of the equipment, and a correlation parameter that indicates the strength of the correlation between the equipment. Using the second formulation means for formulating the probability distribution of the location-dependent eigenvariable variable, the usage time of the equipment, and the state of the equipment, the predetermined likelihood is maximized. It is characterized by having an estimation means for estimating the probability distribution of the model parameters and a calculation means for calculating the failure probability of the equipment by the failure probability model using the estimated probability distribution of the model parameters. ..

The failure probability can be estimated with high accuracy while considering the difference in failure probability depending on the installation location.

It is a figure which shows an example of the structure of the failure probability calculation apparatus in embodiment of this invention. It is a figure which shows an example of the inspection information DB. It is a flowchart which shows an example of the pre-processing in embodiment of this invention. It is a flowchart which shows an example of the failure probability calculation process in embodiment of this invention. It is a figure which shows an example of the hardware configuration of the failure probability calculation apparatus in embodiment of this invention.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. Hereinafter, the failure probability calculation device 10 for calculating the failure probability of each of these facilities will be described using a failure probability model considering the difference in the failure probability according to the installation location of each facility. The equipment is a device or structure in which maintenance and inspection are carried out regularly or irregularly and the inspection result is managed. In addition, the installation location of the equipment may be either outdoors or indoors.

<Configuration of failure probability calculation device 10>
First, the configuration of the failure probability calculation device 10 according to the embodiment of the present invention will be described with reference to FIG. FIG. 1 is a diagram showing an example of the configuration of the failure probability calculation device 10 according to the embodiment of the present invention.

As shown in FIG. 1, the failure probability calculation device 10 according to the embodiment of the present invention has a failure probability model creation unit 110 and a failure probability calculation unit 120. Further, the failure probability calculation device 10 according to the embodiment of the present invention has an inspection information DB (database) 130.

The failure probability model creation unit 110 creates a failure probability model. The failure probability model creation unit 110 includes a model parameter formulation unit 111, a eigenvariable formulation unit 112, a prior probability setting unit 113, and a posterior probability setting unit 114.

Here, in the embodiment of the present invention, the index indicating the equipment is i, the usage time of the equipment is t, and the functional expression representing the failure probability model is defined by the following equation 2.

ここで、Ｐ_ｍ［ｉ］は設備ｉにおける形状パラメータｍの確率分布、Ｐ_η［ｉ］は設備ｉにおける尺度パラメータηの確率分布である。以降では、形状パラメータｍ及び尺度パラメータηを「モデルパラメータ」とも表す。すなわち、上記の式２で定義した故障確率モデルを表す関係式は、上記の式１に示す関係式の形状パラメータｍ及び尺度パラメータηを確率分布として扱ったものである。

Here, P _m [i] is the probability distribution of the shape parameter m in the equipment i, and P _η [i] is the probability distribution of the scale parameter η in the equipment i. Hereinafter, the shape parameter m and the scale parameter η are also referred to as “model parameters”. That is, the relational expression representing the failure probability model defined in the above equation 2 treats the shape parameter m and the scale parameter η of the relational expression shown in the above equation 1 as a probability distribution.

Model parameter formulation unit 111, a probability distribution P _{m [i]} of the shape parameter m, formulate a probability distribution P _{η [i]} of the scale parameter eta.

For the probability distribution P _m [i] of the shape parameter m, for example, a variable (mean variable) P _m ⁻ _{representing the average of P m} [i] with respect to i and a place-dependent eigenvariable p _m [i] described later are used. Therefore, it is formulated by the following equation 3.

同様に、尺度パラメータηの確率分布Ｐ_η［ｉ］は、例えば、ｉに関する平均を表す変数（平均変数）Ｐ_η ⁻と、後述する場所依存固有変数ｐ_η［ｉ］とを用いて、以下の式４で定式化される。

Similarly, the probability distribution P _η [i] of the scale parameter η is described below by using, for example, the variable (mean variable) P _η ⁻ representing the average with respect to i and the location-dependent eigenvariable p _η [i] described later. It is formulated by Equation 4 of.

ただし、形状パラメータｍの確率分布Ｐ_ｍ［ｉ］及び尺度パラメータηの確率分布Ｐ_η［ｉ］は、上記の式３及び式４に代えて、以下の式５及び式６で定式化されても良い。

However, the probability distribution of the shape parameter m P _{m [i]} and the probability distribution P of the scale parameter η η _[i], instead of the equation 3 and equation 4 above, is formulated in Equations 5 and 6 below Is also good.

固有変数定式化部１１２は、場所依存固有変数ｐ_ｍ［ｉ］と、場所依存固有変数ｐ_η［ｉ］とを定式化する。場所依存固有変数ｐ_ｍ［ｉ］及びｐ_η［ｉ］とは、設備ｉの設置場所に依存する確率変数である。

Local Variable formulation 112, the location-dependent and specific variables _p m [i], to formulate a location-dependent specific variables p η _[i]. Location-dependent specific variables p _{m [i]} and p _eta and [i], it is a random variable that depends on the installation location of the equipment i.

Local Variable formulation unit 112, assuming the distance between the installation site and the equipment together is within a predetermined range there is a predetermined correlation, location-dependent and specific variables p _{m [i],} where dependent specific variables p _{Formulate η} [i].

An index indicating a certain correlation with the equipment i facilities as j, when the strength of the correlation between the installation site and equipment j amenities i and a _ij, where dependent specific variables p _{m [i],} for example, Under the condition that all the model parameters in the equipment j (that is, the shape parameter m and the scale parameter η in the equipment j) are determined, it can be formulated as a random variable that follows a normal distribution as shown in Equation 7 below. it can.

ここで、〜Ｎ（μ，σ^２）は平均μ、分散σ^２の正規分布に従うことを表す。

Here, ~ N (μ, σ ² ) indicates that it follows a normal distribution with mean μ and variance σ ^2.

Similarly, the location-dependent eigenvariable p _η [i] is formulated as a random variable that follows a normal distribution as shown in 8 below, under the condition that all the model parameters in the equipment j are determined. Can be done.

ここで、相関の強さを決めるパラメータａ_ｉｊは、例えば、設備ｉの設置場所と、設備ｊの設置場所との距離が所定の範囲内である場合に「１」、そうでない場合に「０」とすれば良い。又は、相関の強さを決めるパラメータａ_ｉｊは、例えば、設備ｉの設置場所と、設備ｊの設置場所との距離に反比例するように決定される値であっても良い。

_{Here, the parameter aij} that determines the strength of the correlation is, for example, "1" when the distance between the installation location of the equipment i and the installation location of the equipment j is within a predetermined range, and "0" when the distance is not. ". _{Alternatively, the parameter aij} that determines the strength of the correlation may be, for example, a value that is determined to be inversely proportional to the distance between the installation location of the equipment i and the installation location of the equipment j.

Formulation of model parameter probability distribution P _m of the shape parameter m by formulation unit 111 _[i] and the probability distribution P of the scale parameter η η _[i] and the location-dependent due to the inherent variable formulation unit 112 specific variables p _{m [i} ] And p _η [i] are formulated in advance before the actual operation (that is, the step of actually calculating the failure probability of the equipment using the inspection information data stored in the inspection information DB 130). ..

The prior probability setting unit 113 sets the prior probability distribution of the model parameters of the failure probability model defined in Equation 2. It may be assumed that the prior probability distribution of the model parameters follows a normal distribution, for example, before the posterior probability distribution is estimated by the posterior probability setting unit 114. After the posterior probability distribution is estimated by the posterior probability setting unit 114, the estimated posterior probability distribution may be followed.

The posterior probability setting unit 114 estimates the posterior probability distribution of the model parameters of the failure probability model defined in Equation 2 using the inspection information data stored in the inspection information DB 130.

Here, the inspection information DB 130 will be described with reference to FIG. FIG. 2 is a diagram showing an example of the inspection information DB 130.

As shown in FIG. 2, the inspection information data stored in the inspection information DB 130 includes an "equipment ID" that identifies the equipment, an "installation location" that indicates the latitude and longitude of the installation location of the equipment, and the use of the equipment. Indicates the "use start date" indicating the date when the equipment was started, the "inspection date" indicating the date when the equipment was inspected, and the condition of the equipment obtained as an inspection result in the inspection. "Equipment status" is included.

The inspection information DB 130 is added with inspection information data every time the equipment is inspected. Therefore, the inspection information data including the same equipment ID is stored in the inspection information DB 130 as many times as the number of inspections performed on the equipment identified by the equipment ID. The distance between the equipment can be calculated from, for example, the latitude and longitude indicating the installation location.

The inspection information data is added by, for example, a maintenance inspector or the like who inspects the equipment using a PC (personal computer) or the like capable of communicating with the failure probability calculation device 10 via a network.

When the number of inspection information data stored in the inspection information DB 130 is K, "0" is defined if the equipment status included in the inspection information data k is "normal", and "1" is defined if it is "failure". The posterior probability setting unit 114 has the likelihood shown in the following equation 9 as the _{usage time T k} obtained by subtracting the usage start date from the inspection date included in the inspection information data k, _{where f k} is the variable to be used. Set the degree L.

ここで、ｉは点検情報データｋに含まれる設備ＩＤにより識別される設備を示すインデックスである。

Here, i is an index indicating the equipment identified by the equipment ID included in the inspection information data k.

At this time, the posterior probability setting unit 114 estimates the model parameter whose inspection data is plausible by searching for the model parameter such that the likelihood L shown in the equation 9 is maximized. In the embodiment of the present invention, as shown in Equation 2, the model parameters of the failure probability model are treated as a probability distribution and the model is complicated. Therefore, based on Bayesian estimation, Markov Chain Monte Carlo (MCMC) Use the method. In Bayesian estimation, the posterior probability distribution of model parameters is obtained from the prior probability distribution of model parameters and the likelihood L obtained from the inspection information DB 130. In the MCMC method, the values of each model parameter can be sampled by trial and error, and the mean value and variance of the posterior probability distribution can be estimated from the set of sampled values.

The failure probability calculation unit 120 uses the posterior probability distribution estimated by the posterior probability setting unit 114 (that is, P _m [i] and P _η [i]), and uses the failure probability model defined in Equation 2 to perform the equipment i. Calculate the failure probability λ [i] ( _Ti ) at the usage time _{Ti of.} The calculated failure probability λ [i] ( _Ti ) may be output to, for example, a display, transmitted to another device capable of communicating via a network, a storage device, or the like. It may be saved in.

<Pre-processing>
In the following, prior to actual operation, the formulation of the probability distribution P _{m [i]} and the probability distribution P _eta scale parameter eta [i] of the shape parameter m, the location-dependent specific variables p _{m [i]} and p _eta [ The pre-processing for formulating i] will be described with reference to FIG. FIG. 3 is a flowchart showing an example of preprocessing according to the embodiment of the present invention.

Step S101: The model parameter formulation unit 111 of the failure probability model creation unit 110 uses the above equations 3 and 4 (or equations 5 and 6) to determine the probability distributions P _η [i] and P _η [i] of the model parameters. ] Is formulated.

Step S102: Local Variable Formulation 112 of the failure probability modeling unit 110 formulates location dependent specific variables _p m [i] and p _eta a [i] by Equations 7 and 8 above.

<Failure probability calculation process>
Hereinafter, the process of calculating the failure probability using the failure probability model during actual operation will be described with reference to FIG. FIG. 4 is a flowchart showing an example of the failure probability calculation process according to the embodiment of the present invention. The processes of steps S201 to S203 of FIG. 4 are repeatedly executed during actual operation. At this time, the processes of steps S201 to S203 of FIG. 4 may be repeatedly executed, for example, at predetermined time intervals, or every time the inspection information DB 130 is updated (inspection information data is added to the inspection information DB 130). It may be executed repeatedly every time. Alternatively, for example, it may be repeatedly executed according to a user's operation or the like.

Step S201: The prior probability setting unit 113 of the failure probability model creation unit 110 sets the prior probability distribution of the model parameters of the failure probability model defined in Equation 2.

The prior probability distribution of the model parameters may follow a normal distribution when r = 0 (that is, at the time of the first execution), for example, when the number of repetitions is r. On the other hand, when r ≧ 1, the prior probability distribution of the model parameter follows the posterior probability distribution estimated by the posterior probability setting unit 114 in the previous number of repetitions (r-1st time). good.

In this way, by updating the prior probability distribution of the model parameter based on the posterior probability distribution estimated by the number of repetitions immediately before, for example, when inspection information data is added to the inspection information DB 130 at any time. In addition, the posterior probability distribution estimated using the past inspection information data can be used as the prior probability, and the posterior probability distribution can be estimated by the likelihood L obtained from the latest inspection information data. As a result, for example, even if the environment of the installation location changes due to the influence of climate change or the like, the model parameters can be corrected with the latest inspection information data.

Step S202: The posterior probability setting unit 114 of the failure probability model creation unit 110 uses the inspection information data stored in the inspection information DB 130 so that the likelihood L shown in the above equation 9 is maximized. _{The posterior probability distributions P m} [i] and P _η [i] of the model parameters of the failure probability model defined in Equation 2 are estimated.

Step S203: The failure probability calculation unit 120 uses the posterior probability distributions P _m [i] and P _η [i] estimated by the posterior probability setting unit 114, and uses the failure probability model defined by the above equation 2 to install the equipment. The failure probability λ [i] ( _Ti ) at the usage time Ti of _i is calculated. As a result, the failure probability of each equipment is estimated.

As described above, the failure probability calculation device 10 according to the embodiment of the present invention can calculate the failure probability in the usage time of the equipment for each equipment. Moreover, the failure probability calculation device 10 according to the embodiment of the present invention assumes that there is a correlation between equipment whose installation location is within a predetermined range (in other words, the failure probabilities of these equipment are similar. By assuming that there is), the failure probability can be estimated with high accuracy while considering the difference in the failure probability depending on the installation location. The reason why it can be assumed that there is such a correlation is that when the installation locations are close, the installation environment at these installation locations is similar (for example, the installation environment such as climate is similar within the same prefecture). is there.

In the embodiment of the present invention, the case where the equipment state included in the inspection information data is either "normal" or "failure" has been described, but the present invention is not limited to this. For example, even when there are three or more states as the equipment state, the embodiment of the present invention can be applied in the same manner.

<Hardware configuration>
Finally, the hardware configuration of the failure probability calculation device 10 according to the embodiment of the present invention will be described with reference to FIG. FIG. 5 is a diagram showing an example of the hardware configuration of the failure probability calculation device 10 according to the embodiment of the present invention.

As shown in FIG. 5, the failure probability calculation device 10 according to the embodiment of the present invention includes an input device 11, a display device 12, an external I / F 13, a RAM (Random Access Memory) 14, and a ROM (Read Only). It has a Memory) 15, a CPU (Central Processing Unit) 16, a communication I / F 17, and an auxiliary storage device 18. Each of these hardware is connected so as to be able to communicate with each other via the bus 19.

The input device 11 is, for example, a keyboard, a mouse, a touch panel, or the like, and is used for a user to input various operations. The display device 12 is, for example, a display or the like, and displays the processing result of the failure probability calculation device 10. The failure probability calculation device 10 does not have to have at least one of the input device 11 and the display device 12.

The external I / F 13 is an interface with an external device. The external device includes a recording medium 13a and the like. The failure probability calculation device 10 can read or write the recording medium 13a or the like via the external I / F 13. The recording medium 13a may store, for example, a program for realizing each functional unit of the failure probability calculation device 10 according to the embodiment of the present invention.

The recording medium 13a includes, for example, a flexible disk, a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, and the like.

The RAM 14 is a volatile semiconductor memory that temporarily holds programs and data. The ROM 15 is a non-volatile semiconductor memory capable of holding programs and data even when the power is turned off. The ROM 15 stores, for example, OS (Operating System) settings, network settings, and the like. The CPU 16 is an arithmetic unit that reads a program or data from the ROM 15 or the auxiliary storage device 18 or the like onto the RAM 14 and executes processing.

The communication I / F 17 is an interface for connecting the failure probability calculation device 10 to the communication network. The program for realizing each functional unit of the failure probability calculation device 10 according to the embodiment of the present invention may be acquired (downloaded) from a predetermined server or the like via, for example, communication I / F17. Further, the failure probability calculation device 10 according to the embodiment of the present invention may provide another device with a program for realizing each of these functional units via, for example, communication I / F17.

The auxiliary storage device 18 is, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), or the like, and is a non-volatile storage device that stores programs and data. The programs and data stored in the auxiliary storage device 18 include, for example, an OS, an application program that realizes various functions on the OS, and each functional unit of the failure probability calculation device 10 according to the embodiment of the present invention. There is a program to do it.

In each functional unit (fault probability model creation unit 110 and failure probability calculation unit 120) of the failure probability calculation device 10 according to the embodiment of the present invention, one or more programs installed in the failure probability calculation device 10 are installed in the CPU 16. It is realized by the processing to be executed.

Further, the inspection information DB 130 included in the failure probability calculation device 10 according to the embodiment of the present invention is realized by using, for example, the auxiliary storage device 18. The inspection information DB 130 may be realized by using, for example, a storage device (for example, a database server) connected to the failure probability calculation device 10 via a communication network.

The present invention is not limited to the above-described embodiment disclosed specifically, and various modifications and modifications can be made without departing from the scope of claims.

10 Failure probability calculation device 110 Failure probability model creation unit 111 Model parameter formulation unit 112 Unique variable formulation unit 113 Prior probability setting unit 114 Posterior probability setting unit 120 Failure probability calculation unit 130 Inspection information DB

Claims (6)

It is a failure probability calculation device that calculates the failure probability of multiple equipment.
The probability distribution of the model parameters of the failure probability model for calculating the failure probability is determined by using an average variable indicating the average of the probability distributions and a location-dependent eigenvariable indicating a probability variable depending on the installation location of the equipment. The first formulation means to formulate,
A second formulation means for formulating the probability distribution of the location-dependent eigenvariables using a correlation parameter indicating the strength of the correlation between the facilities.
Using the usage time of the equipment and a variable indicating whether the equipment is normal or faulty, the probability of failure of the equipment and the likelihood defined by the variable at the usage time are maximized. In addition, an estimation means for estimating the probability distribution of the model parameters and
A calculation means for calculating the failure probability of the equipment by the failure probability model using the estimated probability distribution of the model parameters, and
A failure probability calculation device characterized by having. The first formulation means is
The probability distribution of the model parameters is formulated by the sum or product of the average variable and the place-dependent eigenvariable.
The failure probability calculation device according to claim 1. The second formulation means is
The probability distribution of the location-dependent eigenvariable is formulated using the correlation parameter, which is 1 for equipment whose installation location is within the predetermined range and 0 for equipment whose installation location is not within the predetermined range.
The failure probability calculation device according to claim 1 or 2. The second formulation means is
Formulate the probability distribution of the location-dependent eigenvariable using the correlation parameter, which takes a value inversely proportional to the distance between the equipment.
The failure probability calculation device according to claim 1 or 2. A failure probability calculation device that calculates the failure probability of multiple facilities
The probability distribution of the model parameters of the failure probability model for calculating the failure probability is determined by using an average variable indicating the average of the probability distributions and a location-dependent eigenvariable indicating a probability variable depending on the installation location of the equipment. The first formulation procedure to be formulated and
A second formulation procedure for formulating the probability distribution of the location-dependent eigenvariables using a correlation parameter indicating the strength of the correlation between the facilities.
Using the usage time of the equipment and a variable indicating whether the equipment is normal or faulty, the probability of failure of the equipment and the likelihood defined by the variable at the usage time are maximized. In addition, the estimation procedure for estimating the probability distribution of the model parameters and
A calculation procedure for calculating the failure probability of the equipment by the failure probability model using the estimated probability distribution of the model parameters, and
A failure probability calculation method characterized by executing. A program for causing a computer to function as each means in the failure probability calculation device according to any one of claims 1 to 4.

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