CN116258223A - Nuclear power plant spare part demand prediction method based on gamma distribution - Google Patents

Nuclear power plant spare part demand prediction method based on gamma distribution Download PDF

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CN116258223A
CN116258223A CN202111463782.9A CN202111463782A CN116258223A CN 116258223 A CN116258223 A CN 116258223A CN 202111463782 A CN202111463782 A CN 202111463782A CN 116258223 A CN116258223 A CN 116258223A
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spare part
gamma distribution
distribution
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姚昊
胡文勇
杜君尧
蔡胜武
熊伟
刘忠良
李志鹏
肖薇
皮敏
潘炼
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CNNC Nuclear Power Operation Management Co Ltd
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Abstract

The invention belongs to the technical field of spare part management, and particularly relates to a nuclear power plant spare part demand prediction method based on gamma distribution. The method comprises the following steps: step 1: acquiring a rate parameter lambda of gamma distribution according to the spare part life data; step 2: acquiring failure times of spare parts in a given time interval according to gamma distribution; step 3: inventory quota for the spare parts is determined based on the service level of the spare parts. The invention has the beneficial effects that: at present, the nuclear power plant determines the inventory quota of spare parts according to experience manually, the subjectivity is strong, the quota is conservative, and the quantitative calculation of the demand and the probability of the spare parts with the life distribution obeying the gamma distribution in a given time interval in the future can be realized by the method, so that the manual subjective judgment is reduced, and the inventory of the spare parts is reduced.

Description

Nuclear power plant spare part demand prediction method based on gamma distribution
Technical Field
The invention belongs to the technical field of spare part management, and particularly relates to a nuclear power plant spare part demand prediction method based on gamma distribution.
Background
In general, due to technical deficiency, economic limitations, etc., it is impossible to design a product to fully fulfill its intended function throughout its life cycle, which may lead to downtime for commercial equipment (e.g., nuclear power plants, airplanes, high-speed rails, etc.), at which point the assurance of spare parts is important. When the components are expensive, the inventory of spare parts must be properly managed, as a low inventory means an increased likelihood of waiting for spare parts, and a high inventory means too much money is spent. To ensure a certain safety stock to meet the demand for unplanned replacement of spare parts in field service work, nuclear power plants implement spare part quota management.
Spare part demand is an important input to spare part quota management, and its prediction accuracy is of great importance to reduce inventory and ensure on-site operation. The spare part demand prediction methods generally adopted mainly have two types: the first is a reliability-based method, and the second is a black box method based on spare part consumption history data. In some cases, spare part requirements present a pattern that is not well predicted by conventional methods.
Disclosure of Invention
The invention aims to provide a nuclear power plant spare part demand prediction method based on gamma distribution, which can ensure spare part consumption requirements of a nuclear power plant in a certain time, rationalize spare part inventory and provide support for better development of the rated management work of the spare parts of the nuclear power plant.
The technical scheme of the invention is as follows: a nuclear power plant spare part demand prediction method based on gamma distribution comprises the following steps:
step 1: acquiring a rate parameter lambda of gamma distribution according to the spare part life data;
step 2: acquiring failure times of spare parts in a given time interval according to gamma distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
The step 1 includes the steps of,
fitting life data of spare parts with life obeying the gamma distribution to the gamma distribution according to the reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003390445840000021
Calculate, recorded as LK i The method comprises the steps of carrying out a first treatment on the surface of the For the truncated data t j Use +.>
Figure BDA0003390445840000022
Calculate, recorded as LK j ；
Step 12: all LK is taken i And LK (sum of LK) j Summing up, the likelihood values LK are obtained,
step 13: (solving the rate parameter estimated value lambda when LK is the maximum value by using an Excel programming solving function, a Matlab fsolve function and other tools, wherein lambda is the parameter to be fitted.
The step 2 of the method comprises the steps of,
calculating expected values of failure times in a given interval (0, t) according to the gamma distribution obtained in the step 1, wherein the calculated general formula is as follows:
Figure BDA0003390445840000023
the design numerical value calculation method in the step 2 calculates M (t), and comprises the following steps:
step 21: dividing the interval (0, t) into N equal parts, wherein each part has an interval length deltat, and the calculation accuracy of M (t) is higher as each part has an interval length deltat, namely t=N multiplied by deltat, N is larger;
step 22: calculating an expected value of the average number of failures
Figure BDA0003390445840000024
Wherein F (t) is the cumulative probability density function of the gamma distribution; t is t i For the position of the ith part Deltat in the interval (0, t), t i ＝i×Δt；
Step 23: calculating variance
Figure BDA0003390445840000031
The step 3 includes the steps of,
step 31: assuming that there are S positions requiring the use of a spare part, the life of each spare part is L at the time of prediction i Then the average demand for all the positional spare parts after the lapse of time L is
Figure BDA0003390445840000032
Variance is
Figure BDA0003390445840000033
Step 32: calculating inventory quota D using poisson distribution p ＝P -1 (k％,M s ) Wherein P is -1 () An inverse function representing the Poisson's distribution cumulative density function, k being the service level to be achieved by the spare part, M s Calculating inventory quota D for parameters of poisson distribution using normal distribution N ＝N -1 (k％,M s ,var[N s (t)]) Wherein N is -1 () An inverse function representing a normal distribution cumulative density function, k being the service level to be achieved by the spare part, M s Is the mean value of normal distribution, var [ N ] s (t)]Is the variance of the normal distribution.
The invention has the beneficial effects that: at present, the nuclear power plant determines the inventory quota of spare parts according to experience manually, the subjectivity is strong, the quota is conservative, and the quantitative calculation of the demand and the probability of the spare parts with the life distribution obeying the gamma distribution in a given time interval in the future can be realized by the method, so that the manual subjective judgment is reduced, and the inventory of the spare parts is reduced.
Detailed Description
The present invention will be described in further detail with reference to specific examples.
The method is suitable for demand prediction of nuclear power plant spare parts with service lives obeying gamma distribution, such as parts with constant failure rate of the nuclear power plant, products for timing maintenance before wear, parts with failures caused by random high stress, parts with weak wear caused by failures in the service life, and the like.
A nuclear power plant spare part demand prediction method based on gamma distribution comprises the following steps:
step 1: acquiring a rate parameter lambda of gamma distribution according to the spare part life data;
fitting life data of spare parts with life obeying the gamma distribution to the gamma distribution according to the reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003390445840000041
Calculate, recorded as LK i The method comprises the steps of carrying out a first treatment on the surface of the For the truncated data t j Use +.>
Figure BDA0003390445840000042
Calculate, recorded as LK j ；
Step 12: all LK is taken i And LK (sum of LK) j Summing up, the likelihood values LK are obtained,
step 13: (solving the rate parameter estimated value lambda when LK is the maximum value by using an Excel programming solving function, a Matlab fsolve function and other tools, wherein lambda is the parameter to be fitted.
Step 2: obtaining failure times of spare parts in given time interval according to gamma distribution
Calculating expected values of failure times in a given interval (0, t) according to the gamma distribution obtained in the step 1, wherein the calculated general formula is as follows:
Figure BDA0003390445840000043
in this embodiment, the design numerical calculation method calculates M (t) as follows:
step 21: the interval (0, t) is divided into N equal parts, each part has an interval length Δt, and the greater the interval length Δt, i.e., t=n×Δt, N, the higher the calculation accuracy of M (t).
Step 22: calculating an expected value of the average number of failures
Figure BDA0003390445840000044
Wherein F (t) is the cumulative probability density function of the gamma distribution; t is t i For the position of the ith part Deltat in the interval (0, t), t i ＝i×Δt。
Step 23: calculating variance
Figure BDA0003390445840000045
Wherein: var [ N [ t ] ] is the variance of the number of failures that occur in the spare part during the time interval (0, t).
Step 3: determining inventory quota for spare parts based on service level of spare parts
Step 31: assuming that there are S positions requiring the use of a spare part, the life of each spare part is L at the time of prediction i Then the average demand for all the positional spare parts after the lapse of time L is
Figure BDA0003390445840000051
Variance is
Figure BDA0003390445840000052
Step 32: calculating inventory quota D using poisson distribution p ＝P -1 (k％,M s ) Wherein P is -1 () An inverse function representing the Poisson's distribution cumulative density function, k being the service level to be achieved by the spare part, M s Calculating inventory quota D for parameters of poisson distribution using normal distribution N ＝N -1 (k％,M s ,var[N s (t)]) Wherein N is -1 () An inverse function representing a normal distribution cumulative density function, k being the service level to be achieved by the spare part, M s Is the mean value of normal distribution, var [ N ] s (t)]Is the variance of the normal distribution.

Claims (10)

1. The nuclear power plant spare part demand prediction method based on gamma distribution is characterized by comprising the following steps of:
step 1: acquiring a rate parameter lambda of gamma distribution according to the spare part life data;
step 2: acquiring failure times of spare parts in a given time interval according to gamma distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
2. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 1, wherein: the step 1 includes the steps of,
fitting life data of spare parts with life obeying the gamma distribution to the gamma distribution according to the reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
Figure FDA0003390445830000011
Calculate, recorded as LK i The method comprises the steps of carrying out a first treatment on the surface of the For the truncated data t j Using
Figure FDA0003390445830000012
Calculate, recorded as LK j 。
3. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 2, wherein: the step 1 includes the steps of,
step 12: all LK is taken i And LK (sum of LK) j Summing to obtain likelihood value LK.
4. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 3, wherein: the step 1 includes the steps of,
step 13: (solving the rate parameter estimated value lambda when LK is the maximum value by using an Excel programming solving function, a Matlab fsolve function and other tools, wherein lambda is the parameter to be fitted.
5. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 1, wherein: the step 2 of the method comprises the steps of,
calculating expected values of failure times in a given interval (0, t) according to the gamma distribution obtained in the step 1, wherein the calculated general formula is as follows:
Figure FDA0003390445830000013
6. the nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 5, wherein: the design numerical value calculation method in the step 2 calculates M (t), and comprises the following steps:
step 21: the interval (0, t) is divided into N equal parts, each part has an interval length Δt, and the greater the interval length Δt, i.e., t=n×Δt, N, the higher the calculation accuracy of M (t).
7. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 6, wherein: the design numerical value calculation method in the step 2 calculates M (t), and comprises the following steps:
step 22: calculating an expected value of the average number of failures
Figure FDA0003390445830000021
Wherein F (t) is the cumulative probability density function of the gamma distribution; t is t i For the position of the ith part Deltat in the interval (0, t), t i ＝i×Δt。
8. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 7, wherein: the design numerical value calculation method in the step 2 calculates M (t), and comprises the following steps:
step 23: calculating variance
Figure FDA0003390445830000022
9. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 1, wherein: the step 3 includes the steps of,
step 31: assuming that there are S positions requiring the use of a spare part, the life of each spare part is L at the time of prediction i Then the average demand for all the positional spare parts after the lapse of time L is
Figure FDA0003390445830000023
Variance is
Figure FDA0003390445830000024
10. The nuclear power plant spare part demand prediction method based on gamma distribution as set forth in claim 9, wherein: the step 3 includes the steps of,
step 32: calculating inventory quota D using poisson distribution p ＝P -1 (k％,M s ) Wherein P is -1 () Watch (watch)An inverse function of the Poisson's distribution cumulative density function, k being the service level to be achieved by the spare part, M s Calculating inventory quota D for parameters of poisson distribution using normal distribution N ＝N -1 (k％,M s ,var[N s (t)]) Wherein N is -1 () An inverse function representing a normal distribution cumulative density function, k being the service level to be achieved by the spare part, M s Is the mean value of normal distribution, var [ N ] s (t)]Is the variance of the normal distribution.
CN202111463782.9A 2021-12-03 2021-12-03 Nuclear power plant spare part demand prediction method based on gamma distribution Pending CN116258223A (en)

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