CN116258221A - Nuclear power plant spare part demand prediction method based on normal distribution - Google Patents
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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 normal distribution. The method comprises the following steps: step 1: acquiring a parameter mean mu and a standard deviation sigma of normal distribution according to spare part life data; step 2: acquiring expected values of failure times of spare parts in a given time interval according to normal 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 normal 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
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 normal 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 normal distribution, which can ensure spare part consumption requirements 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 normal distribution comprises the following steps:
step 1: acquiring a parameter mean mu and a standard deviation sigma of normal distribution according to spare part life data;
step 2: acquiring expected values of failure times of spare parts in a given time interval according to normal distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
Step 1 fits the life data of spare parts with life obeying normal distribution to normal distribution according to reliability theory, and the specific process is as follows:
step 11: for all complete data t i Using functions
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 +.>
Calculate, recorded as LK j Wherein->
Step 12: all LK is taken i And LK (sum of LK) j Summing to obtain LK;
step 13: solving the mean value estimated value when LK takes the maximum value by using Excel programming solving function, matlab fsolve function and other tools
And standard deviation estimate +.>
Step 2 calculates expected failure times in a given interval (0, t) according to the normal distribution obtained in step 1, wherein the calculation formula is as follows:
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 an expected value of the average number of failures
Wherein F (t) is a normal distributed cumulative probability density function; 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
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 includes 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
Variance is
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 Calculating inventory quota D for parameters of poisson distribution using normal distribution 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 normal 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.
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Fig. 1 is a schematic flow chart of a method for predicting the demand of spare parts of a nuclear power plant based on normal distribution.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings and specific examples.
The invention is suitable for demand prediction of spare parts of the nuclear power plant, such as vehicle tyre wear, transformers, alarm bulbs and the like, with the service life obeying normal distribution.
As shown in fig. 1, a nuclear power plant spare part demand prediction method based on normal distribution includes the following steps:
step 1: acquiring a parameter mean mu and a standard deviation sigma of normal distribution according to spare part life data;
fitting life data of spare parts with life obeying normal distribution to normal distribution according to reliability theory, wherein the specific process is as follows:
step 11: for all complete data t i Using functions
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 +.>
Calculate, recorded as LK j Wherein->
Step 12: all LK is taken i And LK (sum of LK) j Summing to obtain LK
Step 13: solving the mean value estimated value when LK takes the maximum value by using Excel programming solving function, matlab fsolve function and other tools
And standard deviation estimate +.>
Step 2: and obtaining the expected value of the failure times of the spare part in a given time interval according to the normal distribution.
And (2) calculating expected values of failure times in a given interval (0, t) according to the normal distribution obtained in the step (1), wherein a calculation formula is as follows:
in this embodiment, the design numerical calculation method calculates M (t), and includes the following steps:
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 an expected value of the average number of failures
Wherein F (t) is a normal distributed cumulative probability density function; 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
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
Variance is
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 Calculating inventory quota D for parameters of poisson distribution using normal distribution 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 normal distribution is characterized by comprising the following steps of:
step 1: acquiring a parameter mean mu and a standard deviation sigma of normal distribution according to spare part life data;
step 2: acquiring expected values of failure times of spare parts in a given time interval according to normal distribution;
step 3: inventory quota for the spare parts is determined based on the service level of the spare parts.
2. The nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 1, wherein: step 1 fits the life data of spare parts with life obeying normal distribution to normal distribution according to reliability theory, and the specific process is as follows:
step 11: for all complete data t i Using functions
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 +.>
Calculate, recorded as LK j Wherein->
3. The nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 2, wherein: step 1 fits the life data of spare parts with life obeying normal distribution to normal distribution according to reliability theory, and the specific process is as follows:
step 12: all LK is taken i And LK (sum of LK) j Summing to obtain LK.
4. The nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 3, wherein: step 1 fits the life data of spare parts with life obeying normal distribution to normal distribution according to reliability theory, and the specific process is as follows:
step 13: solving the mean value estimated value when LK takes the maximum value by using Excel programming solving function, matlab fsolve function and other tools
And standard deviation estimate +.>
5. The nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 1, wherein: step 2 calculates expected failure times in a given interval (0, t) according to the normal distribution obtained in step 1, wherein the calculation formula is as follows:
6. the nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 5, wherein: and the step 2 is used for calculating M (t), and comprises the following steps:
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 nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 6, wherein: and the step 2 is used for calculating M (t), and comprises the following steps:
step 22: calculating an expected value of the average number of failures
Wherein F (t) is a normal distributed cumulative probability density function; t is t i For the position of the ith part Deltat in the interval (0, t), t i ＝i×Δt。
8. The nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 7, wherein: and the step 2 is used for calculating M (t), and comprises the following steps:
step 23: calculating variance
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 nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 1, wherein: the step 3 includes 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
Variance is
10. The nuclear power plant spare part demand prediction method based on normal distribution as claimed in claim 9, wherein: the step 3 includes the steps of,
step 32: using poissonDistribution computing inventory quota D 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 Calculating inventory quota D for parameters of poisson distribution using normal distribution 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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