A method for predicting spare parts demand in nuclear power plants based on 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 normal distribution. It includes the following steps: Step 1: Obtain the mean μ and standard deviation σ of the normal distribution based on spare parts lifespan data; Step 2: Obtain the expected number of spare parts failures within a given time interval based on the 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 with a lifespan distribution following a 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 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 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 normal distribution, comprising the following steps:

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

[0007] Step 2: Obtain the expected number of failures of spare parts within a given time interval based on the normal 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 lifespans follow a normal distribution, to a normal 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 ,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 mean estimate that makes LK reach its maximum value. Sum of standard deviation estimates

[0013] Step 2 calculates the expected number of failures within the given interval (0, t) based on the normal 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]

[0019] Where F(t) is the cumulative probability density function of the 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,

[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:

[0025] variance is

[0026] 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.

[0027] 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 with a lifespan distribution that follows a normal distribution within a given future time interval, reducing subjective human judgment and lowering spare parts inventory. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of a method for predicting the demand for spare parts in nuclear power plants based on normal distribution, provided by the present invention. Detailed Implementation

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

[0030] This invention is applicable to the demand forecasting of spare parts for nuclear power plants whose lifespan follows a normal distribution, such as vehicle tire wear, transformers, and alarm bulbs.

[0031] like Figure 1 As shown, a method for predicting spare parts demand in nuclear power plants based on normal distribution includes the following steps:

[0032] Step 1: Obtain the mean μ and standard deviation σ of the normal distribution based on the spare parts life data;

[0033] Based on reliability theory, the lifespan data of spare parts whose lifespan follows a normal distribution are fitted to a normal 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 ,in

[0035] Step 12: Put all LK i and LK j Summing, we get LK

[0036] Step 13: Use tools such as Excel's Solver function and Matlab's fsolve function to find the mean estimate that makes LK reach its maximum value. Sum of standard deviation estimates

[0037] and These are the parameters that need to be fitted.

[0038] Step 2: Obtain the expected number of failures of spare parts within a given time interval based on the normal distribution.

[0039] The expected number of failures within the given interval (0, t) is calculated based on the normal distribution obtained in step 1. The calculation formula is as follows:

[0040]

[0041] In this embodiment, a numerical calculation method is designed to calculate M(t), and the steps are as follows:

[0042] 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.

[0043] Step 22: Calculate the expected value of the mean number of failures.

[0044]

[0045] Where F(t) is the cumulative probability density function of the normal distribution; t i Let t be the position of the i-th Δt in the interval (0, t). i = i × Δt.

[0046] Step 23: Calculate the variance

[0047]

[0048] In the formula: var[N[t]] is the variance of the number of times the spare part fails in the time interval (0, t).

[0049] Step 3: Determine the spare parts inventory quota based on the spare parts' service level.

[0050] 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:

[0051] variance is

[0052] 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 normal distribution-based method for predicting spare parts demand in a nuclear power plant, characterized by, The method comprises the following steps: Step 1: Obtain the mean value of the normal distribution from the spare part life data and the standard deviation ; 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 , where ; Step 12: Sum all and ;​ Step 13: Solve the equations using Excel Solver, Matlab fsolve function Mean estimate at maximum and standard deviation estimate ; Step 2: obtaining the expected value of the failure times of the spare parts in a given time interval according to the normal distribution; Step 2 calculates the given interval based on the normal distribution obtained in step 1. The expected number of failures within the time limit is calculated using the following formula: ， The step 2 is as follows The calculation is as follows: Step 21: divide the interval into equal parts, each of length , i.e. , The larger is, the higher the accuracy of the calculation. Step 22: calculating the expected value of the average failure times ， wherein is a cumulative probability density function of a normal distribution; is the th portion of the interval ; Step 23: calculating the variance ， In the formula: the time interval for spare parts the variance of the number of failures Step 3: determining the inventory quota of the spare parts according to the service level of the spare parts.

2. The normal distribution-based spare parts demand forecasting method for nuclear power plants of claim 1, wherein: 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 a time is , variance is .

3. The normal distribution based spare parts demand forecasting method for nuclear power plants of claim 2, wherein: 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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