A method and system for estimating the probability distribution of equipment fault repair time

Abstract

The present invention discloses a method and system for estimating the probability distribution of equipment fault repair time, belonging to the field of equipment fault indicator quantification. The method comprises: integrating the gamma distribution density function of the lifespan of each component within the mission time, combined with the cumulative working time of each component, to obtain the probability of each component failing; calculating the repair weight coefficient of each component according to the probability of each component failing within the mission time in the inspection order; calculating the repair completion time array according to the inspection order, based on the time consumed for inspecting the status of each component and the time consumed for repairing each failed component; arranging each element in the repair completion time array in ascending order to obtain the sorted component number and the corresponding repair completion time; and cumulatively calculating the repair weight coefficient of each component in the sorted order to obtain the probability distribution of the equipment fault repair time. The present invention predicts the probability distribution of equipment fault repair time and can more specifically and comprehensively describe the equipment maintainability performance.

Description

Technical Field

[0001] The present invention belongs to the field of equipment failure index quantification, and more specifically, relates to a method and system for estimating the probability distribution of equipment failure repair time. Background Art

[0002] When equipment experiences a malfunction, the first step is to inspect multiple components that may be causing the problem one by one until the faulty component is identified. Repairs are then carried out, such as replacing spare parts. When the fault symptom and cause are in a one-to-many relationship, the uncertainty surrounding the faulty component can lead to varying repair times. Currently, mean time to repair (MTTR) is commonly used to describe equipment maintainability.

[0003] For naval vessels and equipment, crew-level repairs are performed on-site during at-sea missions after equipment failures occur. This type of repair is extremely limited in terms of repair facilities, tools, and the number and skill of repair personnel. Crew-level MTTR metrics are crucial for restoring equipment's combat capability during wartime and are highly valued by equipment manufacturers and the military. Manufacturers have implemented various measures to meet the military's MTTR targets, such as employing automated testing technology to help crews quickly identify fault causes and extensively adopting modular design techniques to enable crews to quickly remove failed components, replace them with spares, and repair equipment. Currently, there are two major issues with the use of MTTR metrics. First, when implementing MTTR metrics, equipment designers / manufacturers and the military generally adopt an approach of assessing MTTR metrics based on a mutually agreed-upon specific fault. This approach fails to estimate MTTR in a more general and comprehensive manner, forcing them to resort to "reflecting" the equipment's overall MTTR performance by "achieving" the mean time to repair for a subset of or representative faults. Second, the mathematical essence of MTTR is a mean, a metric that describes a macro, overall situation. However, even for the same fault, repair times are actually distributed within a certain range due to the varying nature of the failed components and the uncertainty of troubleshooting time. In practice, even if you know something like "The average time to repair this fault is 46 minutes," you'd still prefer to know the answer to questions like "Within what timeframe and with what probability can the repair be completed?" Summary of the Invention

[0004] In view of the defects of the prior art, the purpose of the present invention is to provide a method and system for estimating the probability distribution of equipment fault repair time, aiming to solve the problem that the prior art cannot predict the probability distribution of equipment fault repair time.

[0005] To achieve the above objectives, in a first aspect, the present invention provides a method for estimating the probability distribution of equipment fault repair time, wherein the equipment includes multiple components, the lifespans of the components all obey a gamma distribution, at most one component fails at any time during the entire mission time, and the order of status checks of the components during fault troubleshooting is independent and unrelated, the method comprising:

[0006] S1. Obtain the gamma distribution density function of each component's lifespan, the time it takes to inspect the condition, and the cumulative working time. Obtain the time it takes to repair each failed component and the order in which all components are inspected after a failure occurs. The operating period of the equipment is defined as the task time.

[0007] S2. During the mission time, based on the cumulative operating time of each component, integrate the gamma distribution density function of its lifespan to obtain the probability of failure of each component within the mission time.

[0008] S3. Calculate the repair weight coefficient for each component within the mission time according to the inspection order and the probability of failure of each component within the mission time;

[0009] S4. In accordance with the inspection order, according to the status of each component inspection time and repair time consumed by each failed component, calculate the repair completion time array;

[0010] S5. Arrange the elements in the repair completion time array in ascending order to obtain the sorted part numbers and corresponding repair completion times;

[0011] S6. Accumulate and calculate the repair weight coefficient of each component in the sorted order to obtain the probability distribution of completing the repair within each repair completion time after the equipment fails.

[0012] Preferably, step S2 includes:

[0013] S21. Set component number i = 1;

[0014] S22. Calculate the probability Pf of component i failing within the task time Tw i :

[0015]

[0016] When k=,

[0017] When k≠i,

[0018] Where n represents the number of components, g k (t) represents the conditional probability of component k, a k 、b kThey represent the shape parameter and scale parameter of the gamma distribution density function obeyed by the life of component k, Γ represents the gamma function, t k represents the cumulative working time of component k;

[0019] S23.i=i+1, if i≤n, go to step S22, otherwise go to step S3.

[0020] Preferably, step S3 includes:

[0021] S31. Set component inspection number i = 1;

[0022] S32. Calculate the repair weight coefficient of the component corresponding to inspection number i within the task time:

[0023]

[0024] And assign two intermediate variables as follows:

[0025] Tc i =tc j , Tx i =tx j ;

[0026] Where n represents the number of components, j = gInd i , Pf j represents the probability of failure of component j during its mission time, gInd represents the inspection order of all components after a failure occurs, tc j Indicates the time taken to check the status of component number j, tx j represents the time consumed to repair the failed component with number j;

[0027] S33.i=i+1, if i≤n, go to step S32, otherwise go to step S4.

[0028] Preferably, step S4 includes:

[0029] S41. Set component inspection number i = 1;

[0030] S42. Calculate the repair completion time array

[0031] S43.i=i+1, if i≤n, go to step S42, otherwise go to step S5.

[0032] Preferably, step S6 includes:

[0033] S61. Set the sorting sequence number i=1;

[0034] S62. Calculate at time xt iThe probability of completing repair within 10 seconds Pr i :

[0035]

[0036] Among them, xt i Indicates the repair completion time of the component with sorting number i in the sorting result, Pt i =w j , j = ix i ,ix i Indicates the part number of the sorting result with the sorting sequence number i, w j Indicates the repair weight coefficient of the component within the mission time;

[0037] S63.i=i+1, if i≤n, go to step S52, otherwise, terminate the calculation and output all xt i and Pr i .

[0038] Preferably, the method further comprises:

[0039] S7. Select the expected time and the xt closest to the expected time i The corresponding probability Pr i , as the probability of completing the repair within the expected time;

[0040] Among them, xt i Indicates the repair completion time of the component with sorting number i in the sorting result, Pr i Indicates that at time xt i The probability of completing the repair within 3 days.

[0041] To achieve the above-mentioned objectives, in a second aspect, the present invention provides a system for estimating the probability distribution of equipment fault repair time, comprising a processor and a memory; the memory is used to store computer-executable instructions; and the processor is used to execute the computer-executable instructions so that the method described in the first aspect is executed.

[0042] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0043] The present invention discloses a method and system for estimating the probability distribution of equipment fault repair time. The method calculates the repair weight coefficient of each component within the task time according to the inspection order and the probability of each component failing within the task time. The repair completion time array is calculated according to the inspection time consumed for the status of each component and the repair time consumed for each failed component. The elements in the repair completion time array are arranged in ascending order to obtain sorted component numbers and corresponding repair completion times. The repair weight coefficient of each component is then cumulatively calculated according to the sorted order to obtain the probability distribution of completing the repair within each repair completion time after the equipment fails, thereby realizing the prediction of the probability distribution of the equipment fault repair time and being able to describe the equipment maintainability performance in a more specific and detailed manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flow chart of a method for estimating the probability distribution of equipment fault repair time provided by an embodiment of the present invention.

[0045] Figure 2 The embodiments of the present invention provide probability distribution results of completing repair within the range of 20 to 145 minutes, obtained by using a simulation method and the method of the present invention respectively. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0047] The device involved in the present invention includes multiple components, the lifespans of the components all obey the gamma distribution, at most one component fails at any time during the entire mission time, and the order of status inspection of each component during fault troubleshooting is independent and unrelated. Figure 1 The flowchart of the method for estimating the probability distribution of equipment fault repair time provided by the embodiment of the present invention is as follows. Figure 1 As shown, the method includes:

[0048] Step S1. Obtain the gamma distribution density function, status inspection consumption time and cumulative working time obeyed by the life of each component, obtain the consumption time for repairing each failed component and the inspection order of all components after the failure occurs, and use a period of equipment operation as the task time.

[0049] Gamma distribution is a common distribution type that is suitable for describing the gradual and continuous degradation of equipment performance in engineering practice. For example, tool wear is a typical continuous time and continuous state performance degradation process, and its life can be represented by gamma distribution. Gamma type unit refers to the unit whose life follows the gamma distribution Ga(a,b), and its density function Among them, a is the shape parameter, b is the scale parameter, and Γ() is the gamma function.

[0050] The present invention stipulates that:

[0051] (1) A certain device is composed of multiple gamma-type units. For the convenience of description, the life of each unit is described by time.

[0052] (2) At any given moment, at most one unit will fail. When a unit fails, it will affect the normal operation of the equipment, and the equipment will exhibit certain fault symptoms, requiring repair work.

[0053] (3) When confirming a fault, the order in which the status of these units is checked is independent and unrelated, that is, there is no specific requirement for the inspection order such as "unit A must be checked first, then unit B".

[0054] (4) The life distribution of each unit, the time consumed in checking the status of each unit (normal or not), the repair time of each failed unit, the cumulative working time of each unit, the time to perform the task, and the inspection order of all related units after a certain fault phenomenon occurs are known.

[0055] The relevant variables of the present invention are agreed as follows:

[0056] The number of units is recorded as n; the inspection order is recorded as gInd. The array gInd stores the unit numbers to be inspected. The relevant units are inspected in sequence according to the unit numbers provided in the array until the failed unit is found. The life of unit i follows the gamma distribution Ga(a i ,b i ); The cumulative working time of unit i is recorded as t i ; The status check time of unit i is recorded as tc i ; The time to repair the failed unit i is recorded as tx i ; The task time is recorded as Tw.

[0057] Step S2: During the mission time, the cumulative working time of each component is combined with the integral calculation of the gamma distribution density function obeyed by its life span to obtain the probability of failure of each component during the mission time.

[0058] Preferably, step S2 includes:

[0059] S21. Set component number i = 1;

[0060] S22. Calculate the probability Pf of component i failing within the task time Tw i :

[0061]

[0062] When k=i,

[0063] When k≠i,

[0064] Where n represents the number of components, g k (t) represents the conditional probability of component k, a k 、b k They represent the shape parameter and scale parameter of the gamma distribution density function obeyed by the life of component k, Γ represents the gamma function, t k represents the cumulative working time of component k;

[0065] S23.i=i+1, if i≤n, go to step S22, otherwise go to step S3.

[0066] Step S3. Calculate the repair weight coefficient of each component within the mission time according to the inspection order and the probability of failure of each component within the mission time.

[0067] Preferably, step S3 includes:

[0068] S31. Set component inspection sequence number i=1.

[0069] S32. Calculate the repair weight coefficient of the component corresponding to inspection number i within the task time:

[0070]

[0071] And assign two intermediate variables as follows:

[0072] Tc i =tc j , Tx i =tx j ;

[0073] Where n represents the number of components, j = gInd i , Pf j represents the probability of failure of component j during its mission time, gInd represents the inspection order of all components after a failure occurs, tc j Indicates the time taken to check the status of component number j, tx j It represents the time required to repair the failed component with the number j.

[0074] Sort the elements in Tr, and record the sorted result as xt. The element number of the sorted result in Tr is recorded as ix. For example: Tr = [32 12 45], after reordering, xt = [12 32 45], ix = [2 1 3].

[0075] S33.i=i+1, if i≤n, go to step S32, otherwise go to step S4.

[0076] Step S4. Calculate the repair completion time array according to the inspection order, the inspection time consumed for each component and the repair time consumed for each failed component.

[0077] Preferably, step S4 includes:

[0078] S41. Set component inspection number i = 1;

[0079] S42. Calculate the repair completion time array

[0080] S43.i=i+1, if i≤n, go to step S42, otherwise go to step S5.

[0081] Step S5: Arrange the elements in the repair completion time array in ascending order to obtain sorted component numbers and corresponding repair completion times.

[0082] Step S6. According to the sorted order, the repair weight coefficient of each component is cumulatively calculated to obtain the probability distribution of completing the repair within each repair completion time after the equipment fails.

[0083] Preferably, step S6 includes:

[0084] S61. Set the sorting sequence number i=1;

[0085] S62. Calculate at time xt i The probability of completing repair within 10 seconds Pr i :

[0086]

[0087] Among them, xt i Indicates the repair completion time of the component with sorting number i in the sorting result, Pt i =w j , j = ix i ,ix i Indicates the part number of the sorting result with the sorting sequence number i, w j Indicates the repair weight coefficient of the component within the mission time;

[0088] S63.i=i+1, if i≤n, go to step S52, otherwise, terminate the calculation and output all xt i and Pr i .

[0089] Preferably, the method further includes: S7. selecting the desired time, and setting the xt closest to the desired time i The corresponding probability Pri , as the probability of completing the repair within the expected time; where xt i Indicates the repair completion time of the component with sorting number i in the sorting result, Pr i Indicates that at time xt i The probability of completing the repair within 3 days.

[0090] The present invention provides a system for estimating the probability distribution of equipment fault repair time, comprising a processor and a memory; the memory is used to store computer-executable instructions; the processor is used to execute the computer-executable instructions so that the above method is executed.

[0091] Example: A component is composed of 10 gamma-distributed units, with information about each unit shown in Table 1. It is about to perform a 100-hour task. It is agreed that after a failure occurs, the status of units numbered 2, 9, 8, 6, 1, 4, 10, 7, 5, and 3 will be checked sequentially until the failed unit is found. This unit will then be repaired to complete the repair. Using the above method, calculate the time distribution for repairing this fault and estimate the probability of completing the repair within one and a half hours.

[0092] Table 1 Relevant information of each unit

[0093]

[0094] 1) Calculate the probability Pf of failure of each unit. The probabilities of failure of units 1 to 10 are 0.066, 0.056, 0.155, 0.076, 0.227, 0.094, 0.132, 0.101, 0.006, and 0.019, respectively.

[0095] 2) According to the inspection order gInd, the repair weight coefficient w is traversed and calculated as 0.060, 0.006, 0.108, 0.101, 0.071, 0.081, 0.021, 0.141, 0.244, and 0.166; Tc is 13, 18, 11, 18, 6, 13, 14, 23, 9, and 7; Tx is 7, 5, 21, 19, 10, 14, 6, 9, 10, and 13.

[0096] 3) Calculate the repair completion time array Tr, where Tr is 20, 36, 63, 79, 76, 93, 99, 125, 135, and 145.

[0097] 4) Sort the elements in Tr from small to large. The sorting results xt are 20, 36, 63, 76, 79, 93, 99, 125, 135, 145. The element numbering results ix in Tr of this sorting result are 1, 2, 3, 5, 4, 6, 7, 8, 9, 10.

[0098] 5) Calculate the probability Pr of the repair time distribution, where Pr is 0.06, 0.07, 0.17, 0.24, 0.35, 0.43, 0.45, 0.59, 0.83, 1.00.

[0099] 6) Terminate the calculation and output xt and Pr. By looking up the table, it can be seen that the value in xt closest to one and a half hours is 93 minutes. Therefore, the probability of completing the repair work within one and a half hours is approximately 0.43.

[0100] A simulation model can be established to verify the correctness of the above method. The simulation model is briefly described as follows:

[0101] (1) Generate n random numbers simT i , 1 ≤ i ≤ n, where simT i follows the lifetime distribution law of unit i, and it is required that all simT i > t i holds. Then the remaining lifetime sT of each unit i = simT i - t i .

[0102] (2) Find the minimum number among all sT i , and record the corresponding serial number as m, that is: sT m ≤ sT i , 1 ≤ i ≤ n.

[0103] (3) If sT m < Tw holds, then this simulation is valid. According to the inspection order, the consumed inspection time can be obtained, and the sum of it and the repair time of this unit is the simulation result of the repair time this time.

[0104] After a large number of simulations, the probability distribution result of the time consumed to repair this fault can be statistically obtained.

[0105] After a large number of simulations, the probability distribution of the repair time can be statistically obtained. Figure 2 This is the probability distribution result of the repair time within the range of 20 - 145 minutes obtained by using the simulation method and the method of the present invention respectively in the embodiments of the present invention. Considering the randomness of the simulation, Figure 2 it shows that the results of the two are extremely consistent. The simulation results show that the average repair time of this fault is 106.7 minutes, and the root variance of the repair time is 34.8 minutes. Because the change of the repair time fluctuates greatly, it is still relatively rough to carry out work such as maintenance management plans based on the average repair time.

[0106] A large number of simulation verification results show that the method of the present invention can simultaneously consider the influence of factors such as equipment reliability (life distribution law of each unit), equipment health status (accumulated working time), maintainability of basic components of equipment (status inspection time and repair time of each unit) and mission time, and accurately estimate the probability distribution of repair time. Compared with the MTTR indicator, it can describe the maintainability of equipment in a more specific and detailed manner, and can be used for the evaluation of maintainability design schemes in the equipment design stage and the optimization of maintenance schemes in the equipment use stage.

[0107] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for estimating the probability distribution of equipment failure repair time, characterized in that: The device includes multiple components, the lifespans of the components all obey a gamma distribution, at most one component fails at any time during the entire mission time, and the order of status checks of the components during troubleshooting is independent and unrelated. The method includes: S1. Obtain the gamma distribution density function of each component's lifespan, the time it takes to inspect the condition, and the cumulative working time. Obtain the time it takes to repair each failed component and the order in which all components are inspected after a failure occurs. The operating period of the equipment is defined as the task time. S2. During the mission time, based on the cumulative operating time of each component, integrate the gamma distribution density function of its lifespan to obtain the probability of failure of each component within the mission time. S3. Calculate the repair weight coefficient for each component within the mission time according to the inspection order and the probability of failure of each component within the mission time; S4. In accordance with the inspection order, according to the status of each component inspection time and repair time consumed by each failed component, calculate the repair completion time array; S5. Arrange the elements in the repair completion time array in ascending order to obtain the sorted part numbers and corresponding repair completion times; S6. Accumulate and calculate the repair weight coefficient of each component in the sorted order to obtain the probability distribution of completing the repair within each repair completion time after the equipment fails.

2. The method according to claim 1, wherein Step S2 includes: S21. Set component number i = 1; S22. Calculate the probability Pf of component i failing within the task time Tw i : When k=i, When k≠i, Where n represents the number of components, g k (t) represents the conditional probability of component k, a k 、b k They represent the shape parameter and scale parameter of the gamma distribution density function obeyed by the life of component k, Γ represents the gamma function, t k represents the cumulative working time of component k; S23.i=i+1, if i≤n, go to step S22, otherwise go to step S3.

3. The method according to claim 1, wherein Step S3 includes: S31. Set component inspection number i = 1; S32. Calculate the repair weight coefficient of the component corresponding to inspection number i within the task time: And assign two intermediate variables as follows: Tc i =tc j ,Tx i =tx j ; Where n represents the number of components, j = gInd i , Pf j represents the probability of failure of component j during its mission time, gInd represents the inspection order of all components after a failure occurs, tc j Indicates the time taken to check the status of component number j, tx j represents the time consumed to repair the failed component with number j; S33.i=i+1, if i≤n, go to step S32, otherwise go to step S4.

4. The method according to claim 3, wherein Step S4 includes: S41. Set component inspection number i = 1; S42. Calculate the repair completion time array S43.i=i+1, if i≤n, go to step S42, otherwise go to step S5.

5. The method according to claim 4, wherein Step S6 includes: S61. Set the sorting sequence number i=1; S62. Calculate at time xt i The probability of completing repair within 10 seconds Pr i : Among them, xt i Indicates the repair completion time of the component with sorting number i in the sorting result, Pt i =w j , j = ix i ,ix i Indicates the part number of the sorting result with the sorting sequence number i, w j Indicates the repair weight coefficient of the component within the mission time; S63.i=i+1, if i≤n, go to step S52, otherwise, terminate the calculation and output all xt i and Pr i .

6. The method according to claim 1, wherein The method further includes: S7. Select the expected time and the xt closest to the expected time i The corresponding probability Pr i , as the probability of completing the repair within the expected time; Among them, xt i Indicates the repair completion time of the component with sorting number i in the sorting result, Pr i Indicates that at time xt i The probability of completing the repair within 3 days.

7. A system for estimating the probability distribution of equipment failure repair time, characterized in that: including processor and memory; The memory is used to store computer-executable instructions; The processor is configured to execute the computer-executable instructions so that the method according to any one of claims 1 to 6 is performed.

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