CN116258219A - Nuclear power plant spare part demand prediction method based on Weibull distribution - Google Patents

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

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CN116258219A
CN116258219A CN202111461386.2A CN202111461386A CN116258219A CN 116258219 A CN116258219 A CN 116258219A CN 202111461386 A CN202111461386 A CN 202111461386A CN 116258219 A CN116258219 A CN 116258219A
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weibull distribution
spare parts
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姚昊
杨沥铭
胡文勇
蔡胜武
尚鑫鑫
熊伟
李志鹏
郭强
皮敏
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 Weibull distribution. The method comprises the following steps: step 1: acquiring a shape parameter beta and a scale parameter eta of the Weibull distribution according to the spare part life data; step 2: acquiring failure times of spare parts in a given time interval according to Weibull 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 inventory quota of spare parts is determined by a nuclear power plant manually according to experience, the subjectivity is strong, the quota is conservative, and by the method provided by the invention, the quantitative calculation of the demand and the probability of the spare parts with the life distribution obeying Weibull distribution in a given time interval in the future can be realized, 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 Weibull 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 Weibull 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 Weibull distribution, 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 Weibull distribution comprises the following steps:
step 1: acquiring a shape parameter beta and a scale parameter eta of the Weibull distribution according to the spare part life data;
step 2: acquiring failure times of spare parts in a given time interval according to Weibull 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 Weibull distribution to the Weibull distribution according to the reliability theory, and the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003389933780000021
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 BDA0003389933780000022
Calculate, recorded as LK j ；
Step 12: all LK is taken i And LK (sum of LK) j Summing to obtain a likelihood value LK;
step 13: solving the shape parameter estimated value when the likelihood value LK takes the maximum value by using an Excel programming solving function or a Matlab fsolve function and other tools
Figure BDA0003389933780000023
And scale parameter estimation +.>
Figure BDA0003389933780000024
Step 2 calculates expected failure times in a given interval (0, t) according to the Weibull distribution obtained in step 1, wherein the calculation formula is as follows:
Figure BDA0003389933780000025
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 the greater the interval length deltat, namely t=N×deltat, the greater the N, the higher the calculation accuracy of M (t);
step 22: calculating an expected value of the average number of failures
Figure BDA0003389933780000026
Wherein F (t) is the cumulative probability density function of the Weibull 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 BDA0003389933780000031
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 BDA0003389933780000032
Variance is
Figure BDA0003389933780000033
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 Parameters that are poisson distribution; inventory quota D using normal distribution calculator 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 inventory quota of spare parts is determined by a nuclear power plant manually according to experience, the subjectivity is strong, the quota is conservative, and by the method provided by the invention, the quantitative calculation of the demand and the probability of the spare parts with the life distribution obeying Weibull distribution in a given time interval in the future can be realized, the manual subjective judgment is reduced, and the inventory of the spare parts is reduced.
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Fig. 1 is a schematic flow chart of a method for predicting the demand of spare parts of a nuclear power plant based on weibull distribution.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples.
The method is used for demand prediction of the nuclear power plant spare parts with the service lives obeying the Weibull distribution. The device is suitable for the technical fields of ball bearings, gyroscopes, motors, switches, circuit breakers, certain capacitors, electronic tubes, magnetrons, potentiometers, storage batteries, mechanical and hydraulic constant-speed transmission devices, hydraulic pumps, gears, valves, material fatigue and the like of nuclear power plants.
As shown in fig. 1, a method for predicting the demand of spare parts of a nuclear power plant based on weibull distribution includes the following steps:
step 1: acquiring a shape parameter beta and a scale parameter eta of the Weibull distribution according to the spare part life data;
fitting life data of spare parts with life obeying the Weibull distribution to the Weibull distribution according to the reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003389933780000041
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 BDA0003389933780000042
Calculate, recorded as LK j ；
Step 12: all LK is taken i And LK (sum of LK) j Summing to obtain a likelihood value LK;
step 13: solving the shape parameter estimated value when the likelihood value LK takes the maximum value by using an Excel programming solving function or a Matlab fsolve function and other tools
Figure BDA0003389933780000043
And scale parameter estimation +.>
Figure BDA0003389933780000044
Figure BDA0003389933780000045
And->
Figure BDA0003389933780000046
I.e. the parameters that need to be fitted.
Step 2: obtaining failure times of spare parts in a given time interval according to Weibull distribution
According to the Weibull distribution obtained in the step 1, calculating the expected value of failure times in a given interval (0, t), wherein the calculation formula is as follows:
Figure BDA0003389933780000047
in this embodiment, the numerical calculation method is used to calculate M (t), and the steps are as follows:
step 21: the interval (0, t) is divided into N equal parts, and the greater the interval length Δt, i.e., t=n×Δt, the greater the calculation accuracy of M (t).
Step 22: calculating an expected value of the average number of failures
Figure BDA0003389933780000051
Wherein F (t) is the cumulative probability density function of the Weibull 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 BDA0003389933780000052
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 BDA0003389933780000053
Variance is
Figure BDA0003389933780000054
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 Is a parameter of poisson distribution.
Inventory quota D using normal distribution calculator 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 Weibull distribution is characterized by comprising the following steps of:
step 1: acquiring a shape parameter beta and a scale parameter eta of the Weibull distribution according to the spare part life data;
step 2: acquiring failure times of spare parts in a given time interval according to Weibull 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 spare parts of a nuclear power plant based on Weibull distribution as claimed in claim 1, wherein said step 1 fits the life data of spare parts whose life follows Weibull distribution to Weibull distribution according to reliability theory, and the specific process is as follows:
step 11: for all complete data t i Using functions
Figure FDA0003389933770000011
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 FDA0003389933770000012
Calculate, recorded as LK j 。
3. The method for predicting the demand of spare parts of a nuclear power plant based on Weibull distribution as claimed in claim 2, wherein said step 1 fits the life data of the spare parts whose life follows Weibull distribution to Weibull distribution according to 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 method for predicting the demand of spare parts of a nuclear power plant based on Weibull distribution as claimed in claim 3, wherein said step 1 fits the life data of the spare parts with life obeying Weibull distribution to Weibull distribution according to reliability theory, and the specific process is as follows:
step 13: solving the shape parameter estimated value when the likelihood value LK takes the maximum value by using an Excel programming solving function or a Matlab fsolve function and other tools
Figure FDA0003389933770000013
And scale parameter estimation +.>
Figure FDA0003389933770000014
5. The method for predicting the demand of spare parts of a nuclear power plant based on Weibull distribution as claimed in claim 1, wherein the step 2 calculates expected values of failure times in a given interval (0, t) according to the Weibull distribution obtained in the step 1, and the calculation formula is as follows:
Figure FDA0003389933770000021
6. the method for predicting the demand of spare parts of a nuclear power plant based on Weibull distribution as claimed in claim 5, wherein said step 2 calculates M (t) as follows:
step 21: the interval (0, t) is divided into N equal parts, and the greater the interval length Δt, i.e., t=n×Δt, the greater the calculation accuracy of M (t).
7. The method for predicting the demand of spare parts in a nuclear power plant based on weibull distribution as set forth in claim 6, wherein said step 2 calculates M (t) as follows:
step 22: calculating an expected value of the average number of failures
Figure FDA0003389933770000022
Wherein F (t) is the cumulative probability density function of the Weibull distribution；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 spare parts in a nuclear power plant based on weibull distribution as set forth in claim 7, wherein said step 2 calculates M (t) as follows:
step 23: calculating variance
Figure FDA0003389933770000023
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 weibull distribution as set forth in claim 1, wherein said step 3 comprises 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 FDA0003389933770000024
Variance is
Figure FDA0003389933770000031
10. The method for predicting the demand of spare parts in a nuclear power plant based on weibull distribution as set forth in claim 9, wherein said step 3 comprises the steps of:
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 Parameters that are poisson distribution;inventory quota D using normal distribution calculator 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.
CN202111461386.2A 2021-12-03 2021-12-03 Nuclear power plant spare part demand prediction method based on Weibull distribution Pending CN116258219A (en)

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