A method for predicting spare parts demand in nuclear power plants based on log-normal 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 a log-normal distribution. It includes the following steps: Step 1: Obtain the parameters μ and σ of the log-normal distribution based on spare parts lifespan data, where μ is the logarithmic mean of the log-normal distribution and σ is the logarithmic standard deviation of the log-normal distribution; Step 2: Obtain the expected number of spare parts failures within a given time interval based on the log-normal 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 provided by this invention can quantitatively calculate the demand and probability of spare parts whose lifespan distribution follows a log-normal 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 log-normal 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 log-normal 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 log-normal distribution, comprising the following steps:

[0006] Step 1: Obtain the parameters μ and σ of the log-normal distribution based on the spare parts life data, where μ is the log mean of the log-normal distribution and σ is the log standard deviation of the log-normal distribution;

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

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

[0009] The specific process of step 1 is as follows:

[0010] Step 11: For all complete data t i Using functions Calculate, denoted as LK i For truncated data tj ,use Calculate, denoted as LK j ,in

[0011] Step 12: Put all LK i and LK j Summing gives LK;

[0012] Step 13: Use tools such as Excel's Solver function and Matlab's fsolve function to find the logarithmic mean estimate that maximizes LK. Sum of logarithmic standard deviation estimates and These are the parameters that need to be fitted.

[0013] Step 2 includes calculating the expected number of failures within a given interval (0, t) based on the log-normal distribution obtained in step 1. The general formula for the calculation is as follows:

[0014]

[0015] Step 2 involves calculating M(t), and the steps are as follows:

[0016] 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.

[0017] Step 22: Calculate the expected number of failures

[0018]

[0019] Where F(t) is the cumulative probability density function of the log-normal distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i =i×Δt;

[0020] Step 23: Calculate the variance

[0021]

[0022] In the formula: var[N[t]] is the variance of the number of times the spare part fails in the time interval (0, t).

[0023] Step 3 includes the following steps:

[0024] 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: variance is

[0025] 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 Here are the parameters of the Poisson distribution. The inventory quota D is calculated 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.

[0026] 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 provided by this invention can realize the quantitative calculation of the demand and probability of spare parts whose lifespan distribution follows a log-normal distribution within a given future time interval, reducing subjective human judgment and lowering spare parts inventory. Attached Figure Description

[0027] Figure 1 The flowchart of a method for predicting spare parts demand in nuclear power plants based on log-normal distribution provided by the present invention is shown. Detailed Implementation

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] This invention is applicable to demand forecasting for spare parts in nuclear power plants whose lifespan follows a log-normal distribution, such as spare parts associated with the following components and failure modes: electric winding insulation, semiconductor devices, silicon transistors, metal fatigue, etc.

[0030] like Figure 1 As shown, a method for predicting spare parts demand in nuclear power plants based on log-normal distribution includes the following steps:

[0031] Step 1: Obtain the parameters μ and σ of the log-normal distribution based on the spare parts life data, where μ is the log mean of the log-normal distribution and σ is the log standard deviation of the log-normal distribution.

[0032] Based on reliability theory, the lifespan data of spare parts that follow a log-normal distribution are fitted to a log-normal distribution. The specific process is as follows:

[0033] 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 ,in

[0034] Step 12: Put all LK i and LK j Summing gives LK.

[0035] Step 13: Use tools such as Excel's Solver function and Matlab's fsolve function to find the logarithmic mean estimate that maximizes LK. Sum of logarithmic standard deviation estimates and These are the parameters that need to be fitted.

[0036] Step 2: Obtain the expected number of failures of spare parts within a given time interval based on the log-normal distribution.

[0037] The expected number of failures within a given interval (0, t) is calculated based on the log-normal distribution obtained in step 1. The general formula for the calculation is as follows:

[0038]

[0039] In this embodiment, a numerical calculation method is designed to calculate M(t), and the steps are as follows:

[0040] 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.

[0041] Step 22: Calculate the expected number of failures

[0042]

[0043] Where F(t) is the cumulative probability density function of the log-normal distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i = i × Δt.

[0044] Step 23: Calculate the variance

[0045]

[0046] In the formula: var[N[t]] is the variance of the number of times the spare part fails in the time interval (0, t).

[0047] Step 3: Determine the spare parts inventory quota based on the spare parts' service level.

[0048] 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: variance is

[0049] 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 Here are the parameters of the Poisson distribution. The inventory quota D is calculated 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 spare parts demand forecasting in a nuclear power plant based on a lognormal distribution, characterized by, The method comprises the following steps: Step 1: obtaining the parameters of the lognormal distribution, i.e. μ and σ, according to the spare part life data, wherein μ is the log mean of the lognormal distribution, and σ is the log standard deviation of the lognormal distribution; The specific process of step 1 is as follows: Step 11: For all complete data t i , compute using the function denoted as LK i ; for censored data t j , compute using denoted as LK j , where Step 12: Sum all LK i and LK j to get LK; Step 13: Use Excel Solver function, Matlab fsolve function to solve the log mean estimate value when LK gets maximum value and log standard deviation estimate value and That is the parameters to be fitted; Step 2: obtaining the expected value of the failure times of the spare part in a given time interval according to the lognormal distribution; The step 2 comprises: calculating the expected value of the failure times in the given interval (0, t) according to the lognormal distribution obtained in step 1, and the general formula for the calculation is as follows: The step 2 calculates M(t), and the steps are as follows: Step 21: dividing the interval (0, t) into N equal parts, and the length of each part is Δt, i.e. t=N×Δt, and the greater N is, the higher the calculation accuracy of M(t) is; Step 22: calculating the expected value of the failure times where F(t) is the cumulative probability density function of the lognormal distribution; t i is the position of the ith Δt in the interval (0, t), t i = i x Δt; Step 23: calculating the variance In the formula, var[N[t]] is the variance of the failure times of the spare part in the time interval (0, t); Step 3: determining the inventory quota of the spare part according to the service level of the spare part; The step 3 comprises the following steps: Step 31 : Assume that there are S locations that require a certain spare part, and that the life of each spare part is L at the time of the forecast i Then the average demand for the spare part over all locations after time L is variance is 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.

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