CN116258222A - Nuclear power plant spare part demand prediction method based on lognormal distribution - Google Patents

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

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CN116258222A
CN116258222A CN202111463780.XA CN202111463780A CN116258222A CN 116258222 A CN116258222 A CN 116258222A CN 202111463780 A CN202111463780 A CN 202111463780A CN 116258222 A CN116258222 A CN 116258222A
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lognormal distribution
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姚昊
杜君尧
吴宝华
蔡胜武
胡文勇
熊伟
李志鹏
李强
汤奔
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 lognormal distribution. The method comprises the following steps: step 1: acquiring mu and sigma of parameters of the lognormal distribution according to spare part life data, wherein mu is a logarithmic mean value of the lognormal distribution, and sigma is a logarithmic standard deviation of the lognormal distribution; step 2: acquiring an expected value of failure times of the spare part in a given time interval according to the lognormal 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 the nuclear power plant manually according to experience, 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 lognormal distribution in a given time interval in the future can be realized by the method provided by the invention, 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 lognormal 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 lognormal 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 lognormal distribution, which can ensure spare part consumption needs of a nuclear power plant in a certain time, rationalize 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 lognormal distribution comprises the following steps:
step 1: acquiring mu and sigma of parameters of the lognormal distribution according to spare part life data, wherein mu is a logarithmic mean value of the lognormal distribution, and sigma is a logarithmic standard deviation of the lognormal distribution;
step 2: acquiring an expected value of failure times of the spare part in a given time interval according to the lognormal distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
The specific process of the step 1 is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003390445750000021
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 BDA0003390445750000022
Calculate, recorded as LK j Wherein->
Figure BDA0003390445750000023
Step 12: all LK is taken i And LK (sum of LK) j Summing to obtain LK;
step 13: solving the logarithmic mean estimated value when LK is maximized by using Excel programming solving function, matlab fsolve function and other tools
Figure BDA0003390445750000024
And logarithmic standard deviation estimate +.>
Figure BDA0003390445750000025
And->
Figure BDA0003390445750000026
I.e. the parameters that need to be fitted.
The step 2 includes calculating expected values of failure times in a given interval (0, t) according to the lognormal distribution obtained in the step 1, wherein the general formula is as follows:
Figure BDA0003390445750000027
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 expected value of failure times
Figure BDA0003390445750000028
Wherein F (t) is a cumulative probability density function of the lognormal 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 BDA0003390445750000031
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 BDA0003390445750000032
Variance is
Figure BDA0003390445750000033
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.
The invention has the beneficial effects that: at present, the inventory quota of spare parts is determined by the nuclear power plant manually according to experience, 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 lognormal distribution in a given time interval in the future can be realized by the method provided by the invention, so that the manual subjective judgment is reduced, and the inventory of the spare parts is reduced.
Drawings
Fig. 1 is a flowchart of a method for predicting the demand of a spare part of a nuclear power plant based on lognormal distribution.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples.
The invention is applicable to demand prediction of nuclear power plant spare parts with life obeying log-normal distribution, such as spare parts of a nuclear power plant related to the following components and failure modes: electrical winding insulation, semiconductor devices, silicon transistors, metal fatigue, etc.
As shown in fig. 1, a nuclear power plant spare part demand prediction method based on lognormal distribution includes the following steps:
step 1: and acquiring mu and sigma of parameters of the lognormal distribution according to the spare part life data, wherein mu is the logarithmic mean value of the lognormal distribution, and sigma is the logarithmic standard deviation of the lognormal distribution.
Fitting life data of spare parts with life obeying the lognormal distribution to the lognormal distribution according to the reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
Figure BDA0003390445750000041
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 BDA0003390445750000042
Calculate, recorded as LK j Wherein->
Figure BDA0003390445750000043
Step 12: all LK is taken i And LK (sum of LK) j Summing to obtain LK.
Step 13: solving the logarithmic mean estimated value when LK is maximized by using Excel programming solving function, matlab fsolve function and other tools
Figure BDA0003390445750000044
And logarithmic standard deviation estimate +.>
Figure BDA0003390445750000045
Figure BDA0003390445750000046
And->
Figure BDA0003390445750000047
I.e. the parameters that need to be fitted.
Step 2: and obtaining the expected value of the failure times of the spare part in a given time interval according to the lognormal distribution.
And (2) calculating expected values of failure times in a given interval (0, t) according to the lognormal distribution obtained in the step (1), wherein the calculated general formula is as follows:
Figure BDA0003390445750000048
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, and the greater the interval length Δt, i.e., t=n×Δt, the greater the calculation accuracy of M (t).
Step 22: calculating expected value of failure times
Figure BDA0003390445750000051
Wherein F (t) is a cumulative probability density function of the lognormal 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 BDA0003390445750000052
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 BDA0003390445750000053
Variance is
Figure BDA0003390445750000054
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 lognormal distribution is characterized by comprising the following steps of:
step 1: acquiring mu and sigma of parameters of the lognormal distribution according to spare part life data, wherein mu is a logarithmic mean value of the lognormal distribution, and sigma is a logarithmic standard deviation of the lognormal distribution;
step 2: acquiring an expected value of failure times of the spare part in a given time interval according to the lognormal 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 lognormal distribution as claimed in claim 1, wherein the specific process of the step 1 is as follows:
step 11: for all complete data t i Using functions
Figure FDA0003390445740000011
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 FDA0003390445740000012
Calculate, recorded as LK j Wherein->
Figure FDA0003390445740000013
3. The method for predicting the demand of spare parts of a nuclear power plant based on lognormal distribution as claimed in claim 2, wherein the specific process of the step 1 is as follows:
step 12: all LK is taken i And LK (sum of LK) j Summing to obtain LK.
4. The method for predicting the demand of spare parts of a nuclear power plant based on lognormal distribution as claimed in claim 2, wherein the specific process of the step 1 is as follows:
step 13: solving the logarithmic mean estimated value when LK is maximized by using Excel programming solving function, matlab fsolve function and other tools
Figure FDA0003390445740000014
And logarithmic standard deviation estimate +.>
Figure FDA0003390445740000015
And->
Figure FDA0003390445740000016
I.e. the parameters that need to be fitted.
5. The method for predicting the demand of spare parts of a nuclear power plant based on lognormal distribution as claimed in claim 1, wherein: the step 2 includes calculating expected values of failure times in a given interval (0, t) according to the lognormal distribution obtained in the step 1, wherein the general formula is as follows:
Figure FDA0003390445740000021
6. the method for predicting the demand of spare parts of a nuclear power plant based on lognormal distribution as set forth 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 lognormal distribution as set forth in claim 6, wherein said step 2 calculates M (t) as follows:
step 22: calculating expected value of failure times
Figure FDA0003390445740000022
Wherein F (t) is a cumulative probability density function of the lognormal distribution; 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 spare parts in a nuclear power plant based on lognormal distribution as set forth in claim 7, wherein said step 2 calculates M (t) as follows:
step 23: calculating variance
Figure FDA0003390445740000023
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 of a nuclear power plant based on lognormal 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 FDA0003390445740000024
Variance is
Figure FDA0003390445740000031
10. The method for predicting the demand of spare parts in a nuclear power plant based on lognormal 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 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.
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