A method for predicting spare parts demand in nuclear power plants based on Weibull 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 the Weibull distribution. It includes the following steps: Step 1: Obtain the shape parameter β and scale parameter η of the Weibull distribution based on spare parts lifespan data; Step 2: Obtain the number of spare parts failures within a given time interval based on the Weibull 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 with lifespan distributions following a Weibull 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 Weibull 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 the Weibull 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 the Weibull distribution, comprising the following steps:

[0006] Step 1: Obtain the shape parameter β and scale parameter η of the Weibull distribution based on the spare parts life data;

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

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

[0009] Step 1, as described above, fits the lifespan data of spare parts whose lifespan follows a Weibull distribution to a Weibull distribution based on reliability theory. The specific process is as follows:

[0010] 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 ;

[0011] Step 12: Put all LK i and LK j Summing these values ​​gives the likelihood value LK.

[0012] Step 13: Use Excel's Solver function or Matlab's fsolve function to find the shape parameter estimate that maximizes the likelihood value LK. and scale parameter estimates

[0013] Step 2 calculates the expected number of failures within a given interval (0, t) based on the Weibull distribution obtained in Step 1. The calculation formula 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 value of the mean number of failures.

[0018] Where F(t) is the cumulative probability density function of the Weibull distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i =i×Δt;

[0019] Step 23: Calculate the variance

[0020]

[0021] In the formula: var[N[t]] is the variance of the number of times the spare part fails in the time interval (0, t).

[0022] Step 3 includes the following:

[0023] 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:

[0024] 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 The parameters are those 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 quantitatively calculate the demand and probability of spare parts with a lifespan distribution that follows a Weibull distribution within a given future time interval, reducing subjective human judgment and lowering spare parts inventory. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of a method for predicting the demand for spare parts in nuclear power plants based on the Weibull distribution, provided by the present invention. 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 used for demand forecasting of spare parts for nuclear power plants whose lifespan follows a Weibull distribution. It is applicable to technical fields such as ball bearings, gyroscopes, electric motors, switches, circuit breakers, certain capacitors, electron tubes, magnetrons, potentiometers, batteries, mechanical-hydraulic constant-speed transmission devices, hydraulic pumps, gears, valves, and material fatigue in nuclear power plants.

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

[0031] Step 1: Obtain the shape parameter β and scale parameter η of the Weibull distribution based on the spare parts life data;

[0032] Based on reliability theory, the lifespan data of spare parts whose lifespan follows a Weibull distribution are fitted to a Weibull distribution. The specific process is as follows:

[0033] Step 11: For all complete data t i Using functions Calculate, denoted as LKi For truncated data t j ,use Calculate, denoted as LK j ;

[0034] Step 12: Put all LK i and LK j Summing these values ​​gives the likelihood value LK.

[0035] Step 13: Use Excel's Solver function or Matlab's fsolve function to find the shape parameter estimate that maximizes the likelihood value LK. and scale parameter estimates

[0036] and These are the parameters that need to be fitted.

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

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

[0039]

[0040] In this embodiment, a numerical calculation method is used 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] Where F(t) is the cumulative probability density function of the Weibull 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:

[0049] variance is

[0050] 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 represents the parameters of the Poisson distribution.

[0051] 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 nuclear power plants based on Weibull distribution, characterized in that, Includes the following steps: Step 1: Obtain the shape parameter β and scale parameter η of the Weibull distribution based on the spare parts life data; The specific process of step 1 is as follows: 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 ; Step 12: Put all LK i and LK j Summing these values ​​gives the likelihood value LK. Step 13: Use Excel's Solver function or Matlab's fsolve function to find the shape parameter estimate that maximizes the likelihood value LK. and scale parameter estimates Step 2: Obtain the number of failures of the spare part within a given time interval based on the Weibull distribution; Step 2 calculates the expected number of failures within a given interval (0, t) based on the Weibull distribution obtained in Step 1. The calculation formula is as follows: Step 2 involves calculating M(t), and the steps are as follows: 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. Step 22: Calculate the expected value of the mean number of failures. Where F(t) is the cumulative probability density function of the Weibull distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i =i×Δt; Step 23: Calculate the variance In the formula: var[N[t]] is the variance of the number of times the spare part fails in the time interval (0, t); Step 3: Determine the inventory quota for spare parts based on their service level; Step 3 includes the following: 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 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 The parameters are those 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.

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