CN116258218A - Nuclear power plant spare part demand prediction method based on index distribution - Google Patents

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

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CN116258218A
CN116258218A CN202111461384.3A CN202111461384A CN116258218A CN 116258218 A CN116258218 A CN 116258218A CN 202111461384 A CN202111461384 A CN 202111461384A CN 116258218 A CN116258218 A CN 116258218A
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exponential distribution
distribution
spare
power plant
nuclear power
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姚昊
蔡胜武
胡文勇
黄海波
薛坤
诸海川
胡琛
张永兴
李志鹏
刘忠良
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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 index distribution. The method comprises the following steps: step 1: acquiring a rate parameter lambda of exponential distribution according to the spare part life data; step 2: acquiring failure times of spare parts in a given time interval according to the exponential 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 exponential 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 index 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 index 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 an exponential distribution-based nuclear power plant spare part demand prediction method, which can ensure the spare part consumption demand of a nuclear power plant in a certain time, rationalize the spare part inventory and provide support for better developing 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 index distribution comprises the following steps:
step 1: acquiring a rate parameter lambda of exponential distribution according to the spare part life data;
step 2: acquiring failure times of spare parts in a given time interval according to the exponential distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
Step 1 fits the life data of spare parts with life obeying the exponential distribution to the exponential distribution according to the reliability theory, and the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003389930930000021
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 BDA0003389930930000022
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: and solving a rate parameter estimated value lambda when LK is maximum by using an Excel programming solving function, a Matlab fsolve function and other tools, wherein lambda is a parameter to be fitted.
Step 2 calculates expected failure times in a given interval (0, t) according to the index distribution obtained in step 1, wherein the general formula is as follows:
Figure BDA0003389930930000023
/>
and the step 2 is used for calculating 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 BDA0003389930930000024
Wherein F (t) is an exponential distribution cumulative probability density function; 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 BDA0003389930930000025
Wherein: var [ N [ t ] ] is the variance of the number of failures that occur in the spare part during the time interval (0, t).
The step 3 comprises the following steps:
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 BDA0003389930930000031
Variance is
Figure BDA0003389930930000032
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)]Variance of 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 exponential 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 the spare parts of the nuclear power plant with the service life obeying the exponential 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 and tear caused by the failures in the service life, and the like.
A nuclear power plant spare part demand prediction method based on index distribution comprises the following steps:
step 1: acquiring a rate parameter lambda of exponential distribution according to the spare part life data;
fitting life data of spare parts with life obeying the exponential distribution to the exponential distribution according to the reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003389930930000041
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 BDA0003389930930000042
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: and solving a rate parameter estimated value lambda when LK is maximum by using an Excel programming solving function, a Matlab fsolve function and other tools, wherein lambda is a parameter to be fitted.
Step 2: obtaining failure times of spare parts in given time interval according to exponential distribution
Calculating expected values of failure times in a given interval (0, t) according to the index distribution obtained in the step 1, wherein the calculated general formula is as follows:
Figure BDA0003389930930000043
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 BDA0003389930930000044
Wherein F (t) is an exponential distribution cumulative probability density function; 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 BDA0003389930930000045
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 BDA0003389930930000051
Variance is
Figure BDA0003389930930000052
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 the exponential distribution is characterized by comprising the following steps of:
step 1: acquiring a rate parameter lambda of exponential distribution according to the spare part life data;
step 2: acquiring failure times of spare parts in a given time interval according to the exponential distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
2. The method for predicting the demand of a spare part of a nuclear power plant based on exponential distribution of claim 1, wherein: step 1 fits the life data of spare parts with life obeying the exponential distribution to the exponential distribution according to the reliability theory, and the specific process is as follows:
step 11: for all complete data t i Using functions
Figure FDA0003389930920000011
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 FDA0003389930920000012
Calculate, recorded as LK j 。
3. The method for predicting the demand of spare parts of a nuclear power plant based on exponential distribution of claim 2, wherein: step 1 fits the life data of spare parts with life obeying the exponential distribution to the exponential distribution according to the reliability theory, and the specific process is as follows:
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 exponential distribution according to claim 3, wherein: step 1 fits the life data of spare parts with life obeying the exponential distribution to the exponential distribution according to the reliability theory, and the specific process is as follows:
step 13: and solving a rate parameter estimated value lambda when LK is maximum by using an Excel programming solving function, a Matlab fsolve function and other tools, wherein lambda is a parameter to be fitted.
5. The method for predicting the demand of a spare part of a nuclear power plant based on exponential distribution of claim 1, wherein: step 2 calculates expected failure times in a given interval (0, t) according to the index distribution obtained in step 1, wherein the general formula is as follows:
Figure FDA0003389930920000013
6. the method for predicting the demand of a spare part of a nuclear power plant based on exponential distribution of claim 5, wherein: and the step 2 is used for calculating 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 method for predicting the demand of spare parts in a nuclear power plant based on exponential distribution of claim 6, wherein: and the step 2 is used for calculating M (t), and comprises the following steps:
step 22: calculating an expected value of the average number of failures
Figure FDA0003389930920000021
Wherein F (t) is an exponential distribution cumulative probability density function; t is t i For the position of the ith part Deltat in the interval (0, t), t i ＝i×Δt。
8. The method for predicting the demand of a spare part of a nuclear power plant based on exponential distribution of claim 7, wherein: and the step 2 is used for calculating M (t), and comprises the following steps:
step 23: calculating variance
Figure FDA0003389930920000022
Wherein: var [ N [ t ] ] is the variance of the number of failures that occur in the spare part during the time interval (0, t).
9. The method for predicting the demand of spare parts in a nuclear power plant based on exponential distribution according to claim 1, wherein said step 3 comprises:
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 FDA0003389930920000023
Variance is
Figure FDA0003389930920000024
10. The method for predicting the demand for spare parts in a nuclear power plant based on exponential distribution of claim 9, wherein said step 3 comprises:
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.
CN202111461384.3A 2021-12-03 2021-12-03 Nuclear power plant spare part demand prediction method based on index distribution Pending CN116258218A (en)

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