Ship equipment spare parts configuration method based on spare parts utilization rate

Abstract

This invention proposes a spare parts configuration method for ship equipment based on spare parts utilization rate. For spare parts with non-exponential life distribution, the method first calculates the equivalent failure rate of the spare parts using the failure rate equivalence method. Then, it calculates indicators such as spare parts support probability, spare parts utilization rate, and warehouse spare parts cost ratio using the calculation method for exponential spare parts. Finally, it constructs a warehouse spare parts configuration optimization model and solves the optimization model using the marginal benefit method to obtain the final spare parts optimization scheme.

Description

Technical Field

[0001] This invention relates to the field of equipment spare parts configuration technology, and specifically to a method for configuring ship equipment spare parts based on spare parts utilization rate. Background Technology

[0002] Spare parts are a crucial resource for ensuring the availability of naval equipment. Precise support must be achieved in spare parts allocation, not only by increasing the probability of spare parts availability so that they are readily available when needed for repairs, but also by controlling the scale of allocation to avoid unnecessary equipment support costs. Therefore, when allocating spare parts for naval equipment, both spare parts utilization rate and spare parts availability probability should be comprehensively considered to optimize the quantity of spare parts allocated and improve the efficiency of equipment maintenance and support. Summary of the Invention

[0003] To address the aforementioned problems, this invention proposes a method for configuring ship equipment spare parts based on spare parts utilization rate. When multiple configuration options are available, the spare parts utilization rate is used as an auxiliary indicator to determine the configuration option.

[0004] The technical solution to achieve the purpose of this invention is as follows:

[0005] A method for configuring spare parts for ship equipment based on spare parts utilization rate, characterized in that it includes:

[0006] Step 1: Determine the number of spare parts required for ship equipment based on the probability of spare parts availability. If the lifespan of all spare parts follows an exponential distribution, proceed to Step 2 to calculate the spare parts utilization rate. If the lifespan of all spare parts follows a non-exponential distribution, proceed to Step 3 to calculate the spare parts utilization rate.

[0007] Step 2: Establish a probabilistic model for the exponential distribution of spare parts utilization rate and calculate the spare parts utilization rate;

[0008] Step 3: Establish a non-exponential distribution spare parts utilization probability model and calculate the spare parts utilization rate using the λ equivalent method;

[0009] Step 4: Construct a warehouse spare parts configuration optimization model based on spare parts utilization rate;

[0010] Step 5: Solve the warehouse spare parts configuration optimization model to obtain the equipment spare parts configuration scheme.

[0011] Furthermore, the specific operations of step 2 include:

[0012] Step 21: The spare parts follow an exponential distribution with parameter λ, denoted as Exp(λ), with a task time of T and a spare parts guarantee probability requirement of p;

[0013] Step 22: Determine the number of spare parts to be configured, m, based on the spare parts availability probability requirement p:

[0014]

[0015] Where P(s,T) is the spare parts availability probability within task time T when s spare parts are configured, and

[0016] Step 23: If m = 0, no spare parts are needed; if m ≥ 1, calculate the spare parts utilization rate L(m, T):

[0017]

[0018] Where P(m,T) is the spare parts availability probability within task time T when m spare parts are configured, and

[0019] Furthermore, the specific operations in step 3 include:

[0020] Step 31: Determine the type of non-exponential distribution that the equipment spare parts follow and its corresponding parameters;

[0021] Step 32: Given the spare parts availability probability requirement p and the availability task time T;

[0022] Step 33: Based on the non-exponential distribution type of the spare parts, calculate the equivalent failure rate λ using the λ-equivalence method. * ;

[0023] Step 34: Based on the equivalent failure rate λ * According to equation (2), the spare parts utilization rate is calculated. If λ * If T < 100, then the spare parts configuration number is determined using the spare parts availability probability calculation formula. If λ * If T≥100, then the normal distribution is used to approximate the calculation to determine the number of spare parts and the equivalent utilization rate.

[0024] Furthermore, the non-exponential distribution types followed by the equipment spare parts include the Weibull distribution and the gamma distribution.

[0025] Furthermore, the specific operational steps of step 33 include:

[0026] Step 331: When the spare part life follows a Weibull distribution, proceed to step 332 to calculate the equivalent failure rate; when the spare part life follows a gamma distribution, proceed to step 333 to calculate the equivalent failure rate.

[0027] Step 332: Denote the two-parameter Weibull distribution with parameters (m, η) as W(m, η), and its probability density function is:

[0028]

[0029] Where T1 is the spare parts life;

[0030] Then, based on the failure rate calculation formula, we get λ1(t)=m / η(t / η). m-1 And by λ, we have get:

[0031] λ1 * (t)=t m-1 / η m (3)

[0032] Based on equation (3), the equivalent failure rate is expressed as λ1 * =λ1 * (T), where T is the task time;

[0033] Step 333: Let the gamma distribution following parameters (α,λ) be denoted as Ga(α,λ), and its probability density function is:

[0034]

[0035] Where T2 is the spare parts life;

[0036] From λ, we obtain the equivalent:

[0037]

[0038] in,

[0039] Based on equation (4), the equivalent failure rate is obtained: λ2 * =λ2 * (T), where T is the task time.

[0040] Furthermore, step 4 includes the following specific steps:

[0041] Step 41: Determine the total guarantee probability requirement p0 for the warehouse, the number of spare parts types n, and the unit price f of the i-th spare part. i Number of spare parts (m) i , guarantee probability P i And the spare parts utilization rate L of the i-th type of spare parts under the condition of meeting the guarantee probability requirements. i The spare parts configuration scheme is then m = (m1, m2, ..., m n );

[0042] Step 42: The cost percentage of warehouse spare parts (Pm) is:

[0043]

[0044] Step 43: The spare parts configuration optimization scheme with the goal of maximizing the cost percentage (Pm) and ensuring that the availability probability of various spare parts meets the total availability probability requirement is as follows:

[0045]

[0046] stP i ≥P0, (i=1,2,…,n)

[0047] Furthermore, step 5 uses the marginal benefit method to solve the warehouse spare parts configuration optimization model. The specific steps of the solution include:

[0048] Step 51: Determine the initial spare parts plan, let m = 0 1×n ;

[0049] Step 52: Calculate the spare parts availability probability P i If P i If ≥P0, (i=1,2,…,n), then no spare parts are needed; otherwise, proceed to step 53.

[0050] Step 53: Determine the candidate spare parts schemes. There are n candidate spare parts schemes. In the i-th candidate spare parts scheme, the number of spare parts of type i is the number of spare parts of type i in the current scheme plus 1. The other spare parts schemes remain unchanged. Calculate the spare parts availability probability P of each type of spare parts in the candidate spare parts schemes. i Spare parts utilization rate L i And the percentage of expenses, Pm;

[0051] Step 54: If the probability of spare parts availability among the candidate spare parts solutions satisfies P i If a scheme with a cost ratio of ≥P0 (i=1,2,…,n) is found, the calculation is terminated, and the scheme with the largest cost ratio among the schemes that meet the conditions is the final optimized scheme; otherwise, the scheme with the largest cost ratio Pm among the candidate schemes is taken as the current scheme, and the process proceeds to step 53.

[0052] Compared with existing technologies, this method has the following advantages:

[0053] First, this invention studies the calculation of spare parts utilization rate when spare parts life follows an exponential distribution, and gives an analytical calculation formula for spare parts utilization rate. Compared with existing calculation methods, this method is simple to calculate and gives the relationship with spare parts availability probability.

[0054] Second, this invention employs the λ-equivalence method to study the equivalent calculation of spare parts utilization when spare parts life follows Weibull and Gamma distributions, and provides a calculation method, thus providing technical support for the calculation of spare parts utilization when spare parts life follows a non-exponential distribution.

[0055] Third, this invention provides an optimization model for warehouse spare parts configuration based on spare parts availability probability and spare parts utilization rate, which provides technical support for the precise allocation of ship spare parts and is conducive to improving the efficiency of equipment maintenance and support. Attached Figure Description

[0056] Figure 1This is a flowchart of the present invention; Detailed Implementation

[0057] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0058] This invention proposes a spare parts configuration method for ship equipment based on spare parts utilization rate. The core idea is to simultaneously consider spare parts utilization rate and spare parts availability probability during the spare parts configuration process, thereby improving equipment maintenance and support efficiency. The method calculates spare parts utilization rates following exponential and non-exponential distributions using both methods. These spare parts utilization rates and spare parts availability probability are then used as indicators to determine the current spare parts warehouse configuration scheme.

[0059] I. Probabilistic Model and Properties of Exponentially Distributed Spare Parts Utilization

[0060] 1. Spare parts utilization rate probability model

[0061] Assuming a ship's equipment has m (≥1) spare parts, whose lifespan follows an exponential distribution with parameter λ, denoted as Exp(λ), the mission time is T, and the number of spare parts required during the mission time is a random variable X, then the statistical definition of the spare parts utilization rate of the ship's equipment, Y, is as follows:

[0062]

[0063] Where m = 0 indicates that no spare parts are provided, and there is no spare parts utilization issue in this case;

[0064] The statistical definition of spare parts utilization rate is that Y is a random variable. In engineering practice, its average value is usually called the spare parts utilization rate. In this invention, the spare parts utilization rate is denoted as L(m,T), and is obtained through calculation:

[0065]

[0066] Where P(m,T) is the spare parts availability probability within task time T when m spare parts are configured, and

[0067] As shown above, the utilization rate of ship equipment spare parts is determined by the number of spare parts configured, m, and the mean number of failures, λT. If the required support probability is p, then under the given mission time T, the utilization rate is determined by... Determine the number of spare parts that need to be configured.

[0068] 2. Engineering significance of spare parts utilization rate

[0069] For shipboard spare parts, according to the relevant statistics on equipment reliability, more than half of the spare parts have an average number of failures λT of less than 0.1 per year, and the vast majority of spare parts have an average number of failures of less than 0.5 per year. Taking the support probability requirements as 0.7, 0.8 and 0.9, the spare parts utilization rate is calculated as shown in Table 1.

[0070] Table 1 Spare parts utilization rates under different assurance probability requirements and different average failure numbers.

[0071]

[0072] As shown in Table 1, when the average number of failures λT ≤ 0.1, there is no need to consider the utilization rate since spare parts are not required. When the average number of failures is 0.5, the spare parts utilization rate is 0.3935. Therefore, it is not appropriate to consider the spare parts utilization rate requirement during the spare parts configuration process. When formulating a spare parts configuration plan for ships, priority should be given to configuring spare parts that have a significant impact on the combat readiness of the equipment. Only when there are multiple spare parts configuration plans for ships can the spare parts utilization rate be used as an auxiliary indicator to compare the advantages and disadvantages of different plans.

[0073] When the average number of failures of spare parts is high, the corresponding spare parts utilization rate of the spare parts configuration scheme is also high. In engineering practice, due to the large number of objects supported by the spare parts warehouse, the average annual number of failures of spare parts is high, and the corresponding turnover spare parts utilization rate is high. At this time, the spare parts utilization rate index can be used to examine whether the spare parts configured in the spare parts warehouse is reasonable, and can be further used to optimize the ship's turnover spare parts procurement scheme and improve the efficiency of ship spare parts support.

[0074] II. Non-exponential distribution spare parts utilization probability model

[0075] The common distributions that ship equipment lifespan follows are the Weibull and Gamma distributions. However, the analytical expression for spare parts utilization rate, which is not based on an exponential distribution, is relatively complex to derive. To facilitate engineering applications, this invention uses the λ-equivalence method to study the calculation of spare parts utilization rate when spare parts lifespan follows the Weibull and Gamma distributions.

[0076] 1. λ equivalent of non-exponential distribution

[0077] (1) Calculation of the equivalent of the Weibull distribution λ

[0078] The Weibull distribution is often used to describe the product lifespan in which the failure rate changes over time, and to explain the statistical laws of failures caused by aging and wear. It is applicable to electromechanical products such as ball bearings, relays, electron tubes, magnetrons, electric motors, and hydraulic pumps.

[0079] Assume the device life T1 follows a two-parameter Weibull distribution with parameters (m, η), denoted as W(m, η), and its probability density function is:

[0080]

[0081] Where t represents the time during which the spare part is used.

[0082] From the failure rate calculation formula We obtain λ1(t) = m / η(t / η). m-1 From λ, we have the equivalent: get:

[0083] λ1 * (t)=t m-1 / η m (3)

[0084] Therefore, if the task time is T, the equivalent failure rate is λ1. * =λ1 * (T).

[0085] (2) Calculation of the equivalent of the gamma distribution λ

[0086] Gamma distribution is often used to describe faults caused by "impacts," such as power surges in the power grid. Some electronic components will fail when they are subjected to a certain number of power surges.

[0087] Assume the device lifetime T2 follows a Gamma distribution with parameters (α,λ), denoted as Ga(α,λ), and its probability density function is:

[0088]

[0089] Where α is a parameter,

[0090] From λ, we obtain the equivalent:

[0091]

[0092] Therefore, if the task time is T, the equivalent failure rate is λ². * =λ2 * (T).

[0093] 2. Calculation method for non-exponential spare parts utilization rate

[0094] For non-index spare parts, the λ-equivalence method can be used to transform them and calculate the spare part utilization rate. The results are then compared and analyzed with the utilization rate simulation results. The spare part utilization rate calculation steps and simulation analysis steps are as follows:

[0095] Step 1: Determine the distribution type and corresponding parameters that non-exponentially distributed spare parts follow;

[0096] Step 2: Give the spare parts availability probability requirement p and the availability task time T;

[0097] Step 3: Based on the λ equivalence method, select the corresponding calculation method from equation (3) or equation (4) to determine the failure rate λ of the equivalent exponential distribution. * ;

[0098] Step 4: Calculate the spare parts utilization rate according to the spare parts utilization rate calculation method (2) based on the exponential distribution. During the calculation process, if λ... * If T < 100, then the spare parts configuration number is determined using the spare parts availability probability calculation formula. If λ * If T≥100, then the spare parts configuration number m can be approximated using a normal distribution, and the following can be obtained:

[0099]

[0100] Where f(t) is a normal distribution N(λ) * T,λ * The probability density function of T), where p is the probability requirement to be guaranteed. This is for rounding up.

[0101] At this point, the spare parts availability probability is The equivalent utilization rate of the spare parts is then calculated using equation (2).

[0102] Step 5: Using simulation, determine the non-exponentially distributed spare parts configuration quantity m and spare parts utilization rate L1 under the condition of meeting the guarantee probability requirements, and compare them with the result L2 calculated by the equivalent method. The specific comparison process is as follows: numerical analysis.

[0103] 3. Numerical Analysis

[0104] The utilization rate of spare parts when their lifespan follows common Weibull, normal, and gamma distributions is calculated using the λ-equivalence method, and the results are compared and analyzed with those obtained from simulation calculations.

[0105] (1) Spare parts life follows a Weibull distribution.

[0106] Taking the shape parameter m of the Weibull distribution as 1.5 and 2.0, and the average lifespan of spare parts as 5, the corresponding values ​​of parameter η were determined. The required support probabilities were 0.8 and 0.9, and the support task intensity was taken as 4, 6, 8, 10, 20, 30, 40, and 50. The spare part utilization rates L1 and L2, the equivalent average number of failures, and the error were calculated using simulation and equivalent methods under different support task intensities. The results are shown in Tables 2 and 3. The simulation was performed 10,000 times, and the error value err was:

[0107] err = |L1 - L2|

[0108] Table 2. Weibull type spare parts (m, η) = (1.5, 5.5387), p = 0.8, spare parts utilization rate, λ * T * and error

[0109]

[0110] Table 3. Weibull type component (m, η) = (2.0, 5.642), p = 0.9, spare parts utilization rate, λ * T * and error

[0111]

[0112] As shown in Tables 2 and 3, for Weibull-type spare parts, the spare part utilization rate calculated using the λ equivalent method is close to the simulation results, with an error not exceeding 11%; when the equivalent average number of failures λ * T * When the value is large, the probability of guarantee may be infinitely large during the calculation process. Therefore, a normal distribution is used for approximate calculation. The equivalent calculation result of the utilization rate is very close to the simulation result. Therefore, when configuring spare parts in the spare parts warehouse, it is feasible to use the λ equivalent method to calculate the spare parts utilization rate for Weibull type spare parts.

[0113] (2) Spare parts life follows a gamma distribution.

[0114] With parameters λ set to 0.15 and 0.8 in the gamma distribution and the average lifespan of spare parts set to 5, the corresponding values ​​of parameter α were determined. The guarantee probability requirements were 0.8 and 0.9, respectively. The guarantee task intensity was set to 4, 6, 8, 10, 20, 30, 40, and 50. The spare parts utilization rate, equivalent average number of failures, and error under different guarantee task intensities were calculated using simulation and equivalent methods, as shown in Tables 4 and 5. The simulation was performed 10,000 times, and the error value err was calculated in accordance with the method for spare parts conforming to the Weibull type.

[0115] Table 4. Gamma-type spare parts (α,λ)=(0.75,0.15), p=0.8 Spare parts utilization rate, λ * T * and error

[0116]

[0117]

[0118] Table 5. Spare parts utilization rate and λ for gamma-type spare parts (α,λ)=(4,0.8), p=0.9 * T * and error

[0119]

[0120] As shown in Tables 4 and 5, for gamma-type spare parts, the spare part utilization rate calculated using the λ equivalent method is very close to the simulation results, with an error of no more than 9%. Similar to Weibull-type spare parts, gamma-type spare parts also exhibit similar utilization rates in terms of the equivalent mean failure number λ. * T * When the value is large, the utilization rate of the equivalent calculation is very close to the simulation result, and this equivalent calculation method is feasible when configuring spare parts in the spare parts warehouse.

[0121] III. Spare Parts Configuration Optimization Plan

[0122] 1. Warehouse Spare Parts Configuration Optimization Model

[0123] As the previous analysis shows, the utilization rate index is suitable for optimizing the spare parts configuration of the spare parts warehouse. When configuring spare parts, the spare parts warehouse should not only consider the spare parts utilization rate, but also other indicators such as spare parts availability probability and funding requirements.

[0124] For the problem of determining the annual turnover spare parts configuration plan for a spare parts warehouse, let the total guarantee probability requirement of the warehouse be p0, the number of spare parts types be n, and the unit price of the i-th type of spare parts be f. i The number of spare parts is m i The guarantee probability is P i The utilization rate of the i-th type of spare parts under the condition of meeting the guarantee probability requirement is L. i Where i = 1, 2, ..., n, the spare parts configuration scheme is m = (m1, m2, ..., m n The cost percentage of warehouse spare parts (Pm) is:

[0125]

[0126] The optimal spare parts configuration scheme, with the goal of maximizing the cost percentage and constrained by ensuring that the availability probability of various spare parts meets the overall availability probability requirement, is as follows:

[0127]

[0128] stP i ≥P0, (i=1,2,…,n)

[0129] 2. Calculation of Warehouse Spare Parts Configuration Plan

[0130] The marginal benefit method is used to calculate and determine the warehouse spare parts configuration scheme. The optimization process of the spare parts scheme is as follows:

[0131] (1) Determine the initial spare parts plan, let m = 0 1×n ;

[0132] (2) Calculate the spare parts availability probability P iIf P i If the value is greater than or equal to P0 (i = 1, 2, ..., n), then no spare parts are needed, where p0 is the preset total guarantee probability requirement; otherwise, proceed to the next step.

[0133] (3) Determine each candidate spare parts scheme. There are n candidate spare parts schemes. The number of spare parts of type i in the i-th candidate spare parts scheme is the number of spare parts of type i in the current scheme plus 1. The other spare parts schemes remain unchanged. Calculate the spare parts availability probability P of each type of spare parts in the candidate spare parts schemes. i Spare parts utilization rate L i And the percentage of expenses, Pm;

[0134] (4) If there is a spare parts guarantee probability among the candidate spare parts schemes that satisfies P i If the scheme is ≥P0, (i=1,2,…,n), then the calculation is terminated, and the scheme with the largest cost ratio among the schemes that meet the conditions is the final optimized scheme; otherwise, the scheme with the largest cost ratio Pm among the candidate schemes is the current scheme, and the process is switched to (3).

[0135] Example

[0136] To further verify the effectiveness of this invention, a configuration scheme for the annual turnover of six types of spare parts in a warehouse was determined. The lifespan distribution types and unit prices of the nine types of spare parts are shown in Table 6, and the overall guarantee probability requirement p0 is set to 0.8. For spare parts with non-exponential lifespan distributions, the equivalent failure rate of the spare parts is first calculated using the failure rate equivalence method. Then, the spare part guarantee probability, spare part utilization rate, and warehouse spare part cost ratio are calculated using the calculation method for exponential spare parts.

[0137] Table 6: Warehouse Spare Parts Lifespan Distribution Types and Prices

[0138]

[0139]

[0140] Determine the quantity of spare parts to be configured according to the warehouse spare parts configuration plan:

[0141] 1) The mission duration is 365*24=8760h; the initial spare parts configuration quantity is set to 0.

[0142] 2) Using formulas (3) and (4), the equivalent failure rates of the four types of non-exponential warehouse spare parts are calculated as λ2 = 0.3313 × 10 -3 λ3=0.8312×10 -3 λ5=0.1632×10 -3 λ6=0.2921×10 -3 The failure rate of the indexed spare parts is λ1 = 0.1 × 10⁻⁶. -3λ4=0.2×10 -3 .

[0143] 3) When the number of spare parts is 0, the calculated guarantee probabilities are 0.4164, 0.0549, 0.0007, 0.1734, 0.2395, and 0.0774, respectively. The guarantee probabilities do not meet the total guarantee probability requirement p0 = 0.8.

[0144] 4) Using the marginal benefit method, the calculated spare parts configuration quantities are 2, 4, 9, 5, 6, 5.

[0145] As can be seen from the above, when storing spare parts in a spare parts warehouse, the spare parts configuration plan can be determined by comprehensively considering two indicators: spare parts availability probability and spare parts utilization rate, so as to achieve the goal of precise support.

[0146] Contents not described in detail in this specification are existing technologies known to those skilled in the art. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A spare parts allocation method for a naval vessel equipment based on spare parts utilization, characterized by, The application relates to a method for determining the number of spare parts of a ship equipment configuration according to a spare part guarantee probability demand, and the method comprises the following steps: step 1, determining the number of spare parts of a ship equipment configuration according to a spare part guarantee probability demand; if the life of all spare parts obeys an exponential distribution, entering step 2 to calculate the spare part utilization rate; if the life of all spare parts obeys a non-exponential distribution, entering step 3 to calculate the spare part utilization rate; step 2, establishing a probability model of the exponential distribution spare part utilization rate and calculating the spare part utilization rate; step 4, constructing a warehouse spare part configuration optimization model based on the spare part utilization rate; step 5, solving the warehouse spare part configuration optimization model to obtain a configuration scheme of the equipment spare parts; wherein the specific operation of step 2 comprises the following steps: step 21, determining the exponential distribution type of the equipment spare parts and corresponding parameters; step 22, calculating the exponential distribution type of the equipment spare parts; step 3, the specific operation of step 3 comprises the following steps: step 31, determining the non-exponential distribution type of the equipment spare parts and corresponding parameters; step 32, calculating the non-exponential distribution type of the equipment spare parts; step 4, the specific steps of step 4 comprise the following steps: step 41, determining the non-exponential distribution type of the equipment spare parts; step 42, calculating the non-exponential distribution type of the equipment spare parts; step 5, solving the warehouse spare part configuration optimization model by using a marginal benefit method, and the specific steps of the solution comprise the following steps: step 51, determining the non-exponential distribution type of the equipment spare parts; step 52, calculating the non-exponential distribution type of the equipment spare parts; wherein the non-exponential distribution type of the equipment spare parts comprises a Weibull distribution and a gamma distribution; step 33, the specific operation steps of step 33 comprise the following steps: step 331, when the life of the spare parts obeys the Weibull distribution, entering step 332 to calculate an equivalent failure rate; when the life of the spare parts obeys the gamma distribution, entering step 333 to calculate the equivalent failure rate; step 34, the specific operation steps of step 34 comprise the following steps: step 341, when the life of the spare parts obeys the Weibull distribution, entering step 342 to calculate the equivalent failure rate; when the life of the spare parts obeys the gamma distribution, entering step 343 to calculate the equivalent failure rate; step 35, the specific operation steps of step 35 comprise the following steps: step 351, when the life of the spare parts obeys the Weibull distribution, entering step 352 to calculate the equivalent failure rate; when the life of the spare parts obeys the gamma distribution, entering step 353 to calculate the equivalent failure rate. ​ ​ ​ Step 3: Establish a non-exponential distribution of spare parts utilization probability model, using Equivalent method to calculate the utilization rate of spare parts; ​ ​ ​ Step 21: The spare parts compliance parameter is an exponential distribution and is denoted by , the mission time is , and the spare parts support probability requirement is ; Step 22: Determine spare parts configuration number based on the probability of support requirement Determine spare parts configuration number : （1） wherein, is configured the task time the spare parts support probability within the spare parts, and ; Step 23: If spares are not needed, if spares utilization is calculated : （2） wherein, to configure the task time the spare parts guarantee probability, and ; ​ ​ Step 32: Given spare part support probability requirement and support mission time ; Step 33: According to the type of non-exponential distribution that the spare parts comply with, the equivalent failure rate is calculated using the equivalent method ; Step 34: based on equivalent failure rate , according to formula (2) to calculate spare parts utilization rate, if , using spare parts security probability calculation formula to determine the number of spare parts configuration, if , using normal distribution to approximate calculation to determine the number of spare parts configuration and equivalent utilization rate value; ​ Step 41: determining total guarantee probability requirement of the warehouse , number of spare part categories , unit price of the first category spare part , number of spare part configurations , guarantee probability , and spare part utilization rate of the first category spare part under the guarantee probability requirement , then the spare part configuration scheme is ; Step 42: Cost proportion of warehouse spare parts For: ； Step 43: constructing the target for the cost proportion The maximum is reached, and the support probability of each type of spare part reaches the total requirement of the support probability. The spare part configuration optimization scheme is constrained by: （5） s.t. ; ​ Step 51 : Determine initial spare parts scheme, let ; Step 52: Calculate spare parts security probability If No spare parts are needed, otherwise go to step 53; Step 53: Determine the candidate spare parts solutions. The candidate spare parts solutions are: The, the The first of the candidate spare parts solutions The number of spare parts configured in a given category is the number of spare parts configured in the current scheme plus 1, while other spare parts schemes remain unchanged. Calculate the spare parts availability probability for each type of spare part in the candidate spare parts schemes. Spare parts utilization rate and the percentage of expenses ; Step 54: If the probability of spare parts availability in the candidate spare parts solution meets the requirements... If the proposed solution fails, the calculation terminates, and the solution with the largest cost percentage among the satisfying options is selected as the final optimized solution; otherwise, the solution with the largest cost percentage among the candidate solutions is selected. The largest set of solutions is the current solution, and we proceed to step 53.

2. The spare parts allocation method for naval equipment based on spare parts utilization rate according to claim 1, characterized in that, ​ 3. The spare parts allocation method for naval equipment based on spare parts utilization rate according to claim 2, characterized in that, ​ ​ Step 332: Let the two-parameter Weibull distribution with parameters be denoted by with the probability density function given by ； wherein, spare parts life; According to the failure rate calculation formula, we get And by Equivalent to , we get: （3） Based on equation (3), the equivalent failure rate is expressed as where is the task time; Step 333: Let the Gamma distribution with parameters be denoted by with probability density function ； wherein, spare parts life; By equivalently: （4） wherein ; Based on equation (4), the equivalent failure rate is obtained as: where is the task time.

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