A method for predicting spare parts demand in nuclear power plants based on gamma distribution

Abstract

This invention belongs to the field of spare parts management technology, specifically relating to a method for predicting spare parts demand in nuclear power plants based on gamma distribution. It includes the following steps: Step 1: Obtain the rate parameter λ of the gamma distribution based on spare parts lifespan data; Step 2: Obtain the number of spare parts failures within a given time interval based on the gamma distribution; Step 3: Determine the spare parts inventory quota based on the spare parts' service level. The beneficial effects of this invention are: Currently, nuclear power plants determine spare parts inventory quotas manually based on experience, which is highly subjective and the quotas are conservative. The method of this invention enables quantitative calculation of the demand and probability of spare parts with lifespan distributions following a gamma distribution within a given future time interval, reducing subjective human judgment and lowering spare parts inventory.

Description

Technical Field

[0001] This invention belongs to the field of spare parts management technology, specifically relating to a method for predicting spare parts demand in nuclear power plants based on gamma distribution. Background Technology

[0002] Generally, due to technological limitations and economic constraints, it's impossible to design a product that will fully perform its intended function throughout its entire lifecycle. For commercial equipment (such as nuclear power plants, airplanes, and high-speed trains), this could lead to downtime, making spare parts availability crucial. When components are expensive, proper spare parts inventory management is essential. Low inventory increases the likelihood of waiting for spare parts, while excessive inventory ties up too much capital. To ensure a certain safety stock to meet the needs of unplanned spare parts replacements during on-site maintenance, nuclear power plants implement spare parts quota management.

[0003] Spare parts demand is a crucial input for spare parts quota management, and its accurate forecasting is essential for reducing inventory and ensuring on-site maintenance. There are generally two main types of spare parts demand forecasting methods: the first is reliability-based methods, and the second is black-box methods based on historical spare parts consumption data. In some cases, spare parts demand exhibits patterns that traditional methods cannot accurately predict. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the demand for spare parts in nuclear power plants based on gamma distribution. This method can ensure the spare parts consumption needs of nuclear power plants within a certain period of time, rationalize spare parts inventory, and provide support for better management of spare parts quotas in nuclear power plants.

[0005] The technical solution of this invention is as follows: A method for predicting the demand for spare parts in nuclear power plants based on gamma distribution, comprising the following steps:

[0006] Step 1: Obtain the rate parameter λ of the gamma distribution based on the spare parts life data;

[0007] Step 2: Obtain the number of failures of spare parts within a given time interval based on the gamma distribution;

[0008] Step 3: Determine the inventory quota for spare parts based on their service level.

[0009] Step 1 includes,

[0010] Based on reliability theory, the lifespan data of spare parts whose lifespan follows a gamma distribution is fitted to a gamma distribution. The specific process is as follows:

[0011] Step 11: For all complete data t i Using functions Calculate, denoted as LK iFor truncated data t j ,use Calculate, denoted as LK j ;

[0012] Step 12: Put all LK i and LK j Summing these values ​​gives the likelihood value LK.

[0013] Step 13: (Use Excel's Solver function, Matlab's fsolve function, and other tools to solve for the estimated value λ of the rate parameter that makes LK reach its maximum value. λ is the parameter that needs to be fitted.)

[0014] Step 2 includes,

[0015] The expected number of failures within a given interval (0, t) is calculated based on the gamma distribution obtained in step 1. The general formula for the calculation is as follows:

[0016]

[0017] In step 2, a numerical calculation method is designed to calculate M(t), and the steps are as follows:

[0018] Step 21: Divide the interval (0, t) into N equal parts, each with a length Δt, i.e., t = N × Δt. The larger N is, the higher the accuracy of M(t) calculation.

[0019] Step 22: Calculate the expected value of the mean number of failures.

[0020]

[0021] Where F(t) is the cumulative probability density function of the gamma distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i =i×Δt;

[0022] Step 23: Calculate the variance

[0023]

[0024] Step 3 includes,

[0025] Step 31: Assume there are S locations that require a certain spare part, and the lifespan of each spare part is L during prediction. i Then, after time L, the average demand for spare parts at all locations is:

[0026] variance is

[0027] Step 32: Calculate the inventory quota D using the Poisson distribution.p =P -1 (k%,M s ), where P -1 () represents the inverse function of the Poisson cumulative density function, k is the service level that the spare part needs to achieve, and M s Given the parameters of the Poisson distribution, calculate the inventory quota D using the normal distribution. N =N -1 (k%,M s ,var[N s (t)]), where N -1 () represents the inverse function of the cumulative density function of the normal distribution, k is the service level that the spare part needs to achieve, and M s Let N be the mean of a normal distribution. s [(t)] represents the variance of the normal distribution.

[0028] The beneficial effects of this invention are as follows: Currently, nuclear power plants determine spare parts inventory quotas manually based on experience, which is highly subjective and the quotas tend to be conservative. The method of this invention can quantitatively calculate the demand and probability of spare parts with a lifespan distribution that follows a gamma distribution within a given future time interval, reducing subjective human judgment and lowering spare parts inventory. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to specific embodiments.

[0030] This invention is applicable to the demand forecasting of spare parts for nuclear power plants whose lifespan follows a gamma distribution, such as components with a constant failure rate, products that are regularly maintained before wear and tear, components that fail due to random high stress, and components that experience minor wear and tear during their service life.

[0031] A method for predicting spare parts demand in nuclear power plants based on gamma distribution includes the following steps:

[0032] Step 1: Obtain the rate parameter λ of the gamma distribution based on the spare parts life data;

[0033] Based on reliability theory, the lifespan data of spare parts whose lifespan follows a gamma distribution is fitted to a gamma distribution. The specific process is as follows:

[0034] Step 11: For all complete data t i Using functions Calculate, denoted as LK i For truncated data t j ,use Calculate, denoted as LK j ;

[0035] Step 12: Put all LK i and LKj Summing these values ​​gives the likelihood value LK.

[0036] Step 13: (Use Excel's Solver function, Matlab's fsolve function, and other tools to solve for the estimated value λ of the rate parameter that makes LK reach its maximum value. λ is the parameter that needs to be fitted.)

[0037] Step 2: Obtain the number of spare parts failures within a given time interval based on the gamma distribution.

[0038] The expected number of failures within a given interval (0, t) is calculated based on the gamma distribution obtained in step 1. The general formula for the calculation is as follows:

[0039]

[0040] In this embodiment, a numerical calculation method is designed to calculate M(t), and the steps are as follows:

[0041] Step 21: Divide the interval (0, t) into N equal parts, each with a length Δt, i.e., t = N × Δt. The larger N is, the higher the accuracy of M(t) calculation.

[0042] Step 22: Calculate the expected value of the mean number of failures.

[0043]

[0044] Where F(t) is the cumulative probability density function of the gamma distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i = i × Δt.

[0045] Step 23: Calculate the variance

[0046]

[0047] In the formula: var[N[t]] is the variance of the number of times the spare part fails in the time interval (0, t).

[0048] Step 3: Determine the spare parts inventory quota based on the spare parts' service level.

[0049] Step 31: Assume there are S locations that require a certain spare part, and the lifespan of each spare part is L during prediction. i Then, after time L, the average demand for spare parts at all locations is:

[0050] variance is

[0051] Step 32: Calculate the inventory quota D using the Poisson distribution. p =P-1 (k%,M s ), where P -1 () represents the inverse function of the Poisson cumulative density function, k is the service level that the spare part needs to achieve, and M s Given the parameters of the Poisson distribution, calculate the inventory quota D using the normal distribution. N =N -1 (k%,M s ,var[N s (t)]), where N -1 () represents the inverse function of the cumulative density function of the normal distribution, k is the service level that the spare part needs to achieve, and M s Let N be the mean of a normal distribution. s [(t)] represents the variance of the normal distribution.

Claims

1. A method for predicting spare parts demand in a nuclear power plant based on a gamma distribution, characterized by, The method comprises the following steps: Step 1: Obtain the rate parameter of the Gamma distribution from spare parts life data ; The specific process is as follows: Step 11: For all complete data , use the function to calculate, denoted as ; for censored data , use to calculate, denoted as ; Step 12: Sum all and to get the likelihood value ; Step 13: Solve the equations using Excel Solver, Matlab fsolve function tool Rate parameter estimates at the maximum , i.e. parameters to be fitted; Step 2: obtaining the failure times of the spare parts in a given time interval according to the gamma distribution; The step 2 includes calculating the failure number expectation value in the given interval according to the gamma distribution obtained in the step 1, and the general formula is as follows: The step 2 includes calculating the failure number expectation value in the given interval according to the gamma distribution obtained in the step 1, and the general formula is as follows: ， The numerical calculation method designed in step 2 is used to calculate, and the steps are as follows: Step 21: divide the interval into equal parts, each part having a length of , each part having a length of , i.e. , the larger , the higher the calculation accuracy; Step 22: calculating the expected value of the average failure times ， wherein is the cumulative probability density function of a gamma distribution; is the cumulative probability density function of a gamma distribution; is the cumulative probability density function of a gamma distribution; is the cumulative probability density function of a gamma distribution; is the cumulative probability density function of a gamma distribution; is the cumulative probability density function of a gamma distribution; Step 23: calculating the variance ， Step 3: determining the inventory quota of the spare parts according to the service level of the spare parts.

2. The method for predicting the spare parts demand of a nuclear power plant based on the gamma distribution according to claim 1, characterized in that: The step 3 comprises, Step 31 : Assume that there are locations that require a certain spare part, and that the life of each spare part at the time of forecast is Then the average demand for spare parts at all locations after time is ​ Variance is .

3. The method for predicting the spare parts demand of a nuclear power plant based on the gamma distribution according to claim 2, characterized in that: The step 3 comprises, The step 3 comprises, Step 32: Calculate inventory target using Poisson distribution where denotes the inverse function of the cumulative density function of the Poisson distribution, is the service level to be achieved for spare parts, is the parameter of the Poisson distribution, Calculate inventory target using normal distribution where denotes the inverse function of the cumulative density function of the normal distribution, is the service level to be achieved for spare parts, is the mean of the normal distribution, is the variance of the normal distribution.

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