CN115688025A - Method and system for estimating probability distribution of equipment failure repair time - Google Patents

Abstract

The invention discloses a method and a system for estimating probability distribution of equipment fault repairing time, and belongs to the field of equipment fault index quantification. The method comprises the following steps: in the task time, the cumulative working time of each component is combined, and the gamma distribution density function integral subject to the service life is calculated to obtain the failure probability of each component; according to the inspection sequence and the probability of the fault of each component in the task time, calculating the repair weight coefficient of each component; according to the checking sequence, checking the consumed time according to the state of each component and the consumed time for repairing each failed component, and calculating a repair completion time array; arranging elements in the repair completion time array in an ascending order to obtain the ordered part numbers and the corresponding repair completion time; and according to the sequence after sequencing, cumulatively calculating the repair weight coefficients of all the parts to obtain the probability distribution of the equipment fault repair time. The invention realizes the prediction of the probability distribution of the equipment fault repairing time, and can describe the equipment maintainability performance in more detail.

Description

Method and system for estimating probability distribution of equipment failure repair time

technical field

The 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 technique

When a certain fault occurs in the equipment, generally the multiple parts that may cause the fault are checked one by one until the failed parts are found, and then the failed parts are repaired by replacing spare parts and other repair methods. When the fault phenomenon and the fault cause are in a one-to-many relationship, due to the uncertainty of the failed parts, the time to complete the repair will be different each time. At present, the mean time to repair (MTTR) is often used to describe the maintainability of equipment.

For naval ship equipment, crew-level repair is a kind of repair at the equipment site after the equipment fails during the mission at sea. Very limited repairs. Crew-level MTTR indicators are crucial to recovering equipment combat capabilities during wartime, and are highly valued by equipment manufacturers and the military. The manufacturer takes various measures to meet the military's MTTR index, such as using automatic testing technology to help the crew find the cause of the failure quickly, and widely adopting modular technology to design equipment, so that the crew can quickly remove failed parts and replace spare parts to repair equipment . Currently, there are two major problems in the use of MTTR: First, when implementing MTTR indicators, equipment design/manufacturers and the military mostly adopt the method of "assessing MTTR indicators for a specific failure agreed upon by both parties". The reason behind this method is that MTTR cannot be estimated in a more general and broader situation, so we have to settle for the next best thing and "reflect" the overall MTTR performance of equipment by "realizing" the average repair time of partial or representative failures . The second is that the mathematical essence of MTTR is the mean value, which is an indicator for describing at the macro and overall level, but in fact, even for the same fault phenomenon, due to the different failed parts and the uncertainty of troubleshooting time, the repair time is actually distributed within a certain range. In actual work, even if you know the conclusion like "the average time to repair the fault is 46 minutes", you still hope to get the answer to the question "in which time and with what probability can the repair be completed?".

Contents of the invention

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

In order to achieve the above object, in the first aspect, the present invention provides a method for estimating the probability distribution of equipment fault repair time. The equipment includes a plurality of components, and the life of the components all obeys the gamma distribution. At most one component fails at any time, and the order of status checks of each component is independent and irrelevant during troubleshooting. The method includes:

S1. Obtain the gamma distribution density function that the life of each component obeys, the time spent on state inspection and the cumulative working time, and the time spent on repairing each failed component and the order of inspection of all components after the failure occurs, and a certain working period of the equipment as task time;

S2. During the task time, combined with the cumulative working time of each component, the integral calculation of the gamma distribution density function obeyed by its life expectancy, the probability of failure of each component within the task time is obtained;

S3. According to the inspection sequence, according to the failure probability of each component within the task time, calculate the repair weight coefficient of each component within the task time;

S4. According to the inspection order, calculate the repair completion time array according to the state inspection time of each component and the repair time of each failed component;

S5. Sort the elements in the repair completion time array in ascending order, and obtain the sorted part numbers and corresponding repair completion time;

S6. Calculate the repair weight coefficients of each component accumulatively according to the sorted order, and obtain the probability distribution of repair completion within each repair completion time after the equipment fails.

Preferably, step S2 includes:

S21. Set part number i=1;

S22. Calculate the probability Pf _i of failure of internal component i within the task time Tw:

When k=,

When k≠i,

Among them, n represents the number of components, g _k (t) represents the conditional probability of component k, a _k and b _k represent the shape parameters and scale parameters in the gamma distribution density function that the lifetime of component k obeys, Γ represents the gamma function, t _k represents the accumulative working time of component k;

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

Preferably, step S3 includes:

S31. Set the component inspection sequence number i=1;

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

And assign the two intermediate variables as follows:

Tc _i =tc _j , Tx _i =tx _j ;

Among them, n represents the number of components, j=gInd _i , Pf _j represents the failure probability of the component numbered j within the mission time, gInd represents the inspection order of all components after the fault occurs, tc _j represents the component number j Status inspection time consumption, tx _j represents the time consumed to repair the failed component numbered j;

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

Preferably, step S4 includes:

S41. Set the component inspection sequence number i=1;

S42. Calculate repair completion time array

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

Preferably, step S6 includes:

S61. Set the sorting sequence number i=1 after sorting;

S62. Calculate the probability Pr _i of completing the restoration within the time xt _i :

Among them, xt _i represents the repair completion time of the component with the sequence number i in the sorting result, Pt _i =w _j , j=ix _i , ix _i represents the component number with the sequence number i in the sorting result, and w _j represents the component number with the sequence number i in the task time The repair weight factor of the component;

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

Preferably, the method also includes:

S7. Select the expected time, and use the probability Pr _i corresponding to the xt _i closest to the expected time as the probability of completing the restoration within the expected time;

Among them, xt _i represents the repair completion time of the component with the sort number i in the sorting result, and Pr _i represents the probability of completing the repair within time xt _i .

In order to achieve the above object, in the second aspect, the present invention provides a system for estimating the probability distribution of equipment failure repair time, including a processor and a memory; the memory is used to store computer execution instructions; the processor is used to Execution of the computer-implemented instructions causes the method described in the first aspect to be performed.

Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

The invention discloses a method and system for estimating the probability distribution of equipment failure repair time. According to the inspection sequence, according to the failure probability of each component within the task time, the repair weight coefficient of each component within the task time is calculated, and according to the state of each component Check the time consumed and the time consumed to repair each failed component, calculate the repair completion time array, arrange the elements in the repair completion time array in ascending order, obtain the sorted part number and the corresponding repair completion time, and then calculate the cumulative calculation of each component according to the sorted order The repair weight coefficient of the equipment can be used to obtain the probability distribution of repair completion within each repair completion time after the equipment fails, so as to realize the prediction of the probability distribution of equipment repair time and describe the maintainability performance of equipment more specifically and in detail.

Description of drawings

Fig. 1 is a flow chart of a method for estimating the probability distribution of equipment failure repair time provided by an embodiment of the present invention.

Fig. 2 shows the probability distribution results of the restoration within the range of 20 to 145 minutes obtained by using the simulation method and the method of the present invention respectively provided by the embodiment of the present invention.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

The equipment involved in the present invention includes a plurality of components, and the service life of the components is subject to the gamma distribution. At most one component fails at any time during the entire task time, and the order of status inspection of each component is independent and irrelevant during troubleshooting. Fig. 1 is a flow chart of a method for estimating the probability distribution of equipment failure repair time provided by an embodiment of the present invention. As shown in Figure 1, the method includes:

Step S1. Obtain the gamma distribution density function that the service life of each component obeys, the time spent on status inspection and the cumulative working time, obtain the time spent on repairing each failed component and the order of inspection of all components after the failure occurs, and set a working period of the equipment as task time.

其中，a为形状参数，b为尺度参数，Γ()为伽马函数。Gamma distribution is a common distribution type, which is suitable for describing the process of 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 calculated by gamma distribution. express. The gamma type unit means that the unit life obeys 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.

The present invention agrees:

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

(2) At any moment, at most one unit fails. When a unit breaks down, it will affect the normal operation of the equipment, and some failures will occur in the equipment, and repair work is required at this time.

(3) When performing fault confirmation, the order of checking the status of these units is independent and irrelevant, that is, there is no special requirement for the inspection order such as "you must check unit A first, and then check unit B". .

(4) The life distribution of each unit is known, the time it takes to check the status (normal or not) of each unit, the repair time of each failed unit, the accumulated working time of each unit, and the time to perform the task and the inspection sequence of all related units after a certain fault phenomenon occurs.

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

The number of units is recorded as n; the inspection sequence is recorded as gInd, and the number of units to be inspected is stored in the array gInd, and the relevant units are checked in turn according to the unit numbers provided in the array until a failure is found; the life of unit i obeys the gamma distribution Ga (a _i , b _i ); the cumulative working time of unit i is recorded as t _i ; the status inspection time of unit i is recorded as tc _i ; the time of repairing failed unit i is recorded as txi _; the task time is recorded as Tw.

Step S2. During the task time, combined with the cumulative working time of each component, the integral calculation of the gamma distribution density function obeyed by the service life is performed to obtain the failure probability of each component within the task time.

Preferably, step S2 includes:

S21. Set part number i=1;

S22. Calculate the probability Pf _i of failure of internal component i within the task time Tw:

When k=i,

When k≠i,

Among them, n represents the number of components, g _k (t) represents the conditional probability of component k, a _k and b _k represent the shape parameters and scale parameters in the gamma distribution density function that the lifetime of component k obeys, Γ represents the gamma function, t _k represents the accumulative working time of component k;

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

Step S3. According to the inspection sequence, the repair weight coefficient of each component within the task time is calculated according to the failure probability of each component within the task time.

Preferably, step S3 includes:

S31. Set the component inspection sequence number i=1.

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

And assign the two intermediate variables as follows:

Tc _i =tc _j , Tx _i =tx _j ;

Among them, n represents the number of components, j=gInd _i , Pf _j represents the failure probability of the component numbered j within the mission time, gInd represents the inspection order of all components after the fault occurs, tc _j represents the component number j The status check takes time, and tx _j represents the time spent in repairing the failed component with the number j.

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

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

Step S4. According to the inspection order, calculate the repair completion time array according to the state inspection time of each component and the repair time of each failed component.

Preferably, step S4 includes:

S41. Set the component inspection sequence number i=1;

S42. Calculate repair completion time array

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

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

Step S6. According to the sorted order, the repair weight coefficients of each component are calculated accumulatively, and the probability distribution of repair completion within each repair completion time after the equipment fails is obtained.

Preferably, step S6 includes:

S61. Set the sorting sequence number i=1 after sorting;

S62. Calculate the probability Pr _i of completing the restoration within the time xt _i :

Among them, xt _i represents the repair completion time of the component with the sequence number i in the sorting result, Pt _i =w _j , j=ix _i , ix _i represents the component number with the sequence number i in the sorting result, and w _j represents the component number with the sequence number i in the task time The repair weight factor of the component;

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

Preferably, the method further includes: S7. Selecting the expected time, taking the probability Pr _i corresponding to the xt _i closest to the expected time as the probability of completing the repair within the expected time; wherein, xt _i represents the number i in the sorting result Completion time of component repair, Pr _i represents the probability of completing repair within time xt _i .

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

Example: It is known that a certain component is composed of 10 gamma distribution units, and the relevant information of each unit is shown in Table 1, and a task of 100 hours is about to be performed. It is agreed that after a fault occurs, the status inspection shall be carried out according to the unit serial number 2, 9, 8, 6, 1, 4, 10, 7, 5, and 3, until the failed unit is found, and the unit shall be repaired to complete the repair. Using the above method, calculate the time distribution result of repairing the fault, and estimate the probability that the repair will be completed within one and a half hours?

Table 1 Relevant information of each unit

1) Traversingly calculate the failure probability Pf of each unit, the failure probability of unit 1 to unit 10 is respectively: 0.066, 0.056, 0.155, 0.076, 0.227, 0.094, 0.132, 0.101, 0.006, 0.019.

2) According to the inspection sequence gInd, the traversal calculation repair weight coefficient w is 0.060, 0.006, 0.108, 0.101, 0.071, 0.081, 0.021, 0.141, 0.244, 0.166; Tc is 13, 18, 11, 18, 6, 13, 14, 23, 9, 7; Tx is 7, 5, 21, 19, 10, 14, 6, 9, 10, 13.

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

4) Sort the elements in Tr from small to large, and the sorting result xt is 20, 36, 63, 76, 79, 93, 99, 125, 135, 145; the sorting result is the element number result ix in Tr 1, 2, 3, 5, 4, 6, 7, 8, 9, 10.

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

6) Terminate the calculation and output xt, Pr. It can be seen from the table lookup that the closest one and a half hours in xt is 93 minutes, so the probability of completing the repair work within one and a half hours is about 0.43.

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

(1) Generate n random numbers simT _i , 1≤i≤n, simT _i obeys the life distribution law of unit i, and requires all simT _i >t _i to be established, then the remaining life of each unit sT _i =simT _i - t _i .

(2) Find the smallest number among all sT _i , and record the corresponding number as m, namely: sT _m ≤ sT _i , 1≤i≤n.

(3) If sT _m < Tw holds true, this simulation is valid, and the sum of the consumed inspection time and the repair time of the unit is obtained according to the inspection order, which is the simulation result of this repair time.

After a large number of simulations, the probability distribution results of the time consumed to repair the fault can be obtained statistically.

After a large number of simulations, the probability distribution of repair time can be obtained statistically. Fig. 2 shows the probability distribution results of the restoration completed in the range of 20 to 145 minutes by using the simulation method and the method of the present invention respectively provided by the embodiment of the present invention. Considering the randomness of the simulation, Figure 2 shows that the results of the two are very consistent. The simulation results show that the average repair time of the fault is 106.7 minutes, and the root variance of the repair time is 34.8 minutes. Because the change of repair time fluctuates greatly, it is relatively rough to use the average repair time to carry out maintenance management planning and other aspects.

A large number of simulation verification results show that: the method of the present invention can simultaneously consider the reliability of the equipment (the life distribution law of each unit), the health status of the equipment (accumulated working time), the maintainability of the basic components of the equipment (the state inspection time of each unit) and repair time) and task time, and accurately estimate the probability distribution of repair time. Compared with the MTTR index, it can describe the maintainability of equipment more specifically and in detail, and can be used in the evaluation of maintainability design schemes and equipment Maintenance program optimization in the phase of use.

It is easy for those skilled in the art to understand that the above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention, All should be included within the protection scope of the present invention.

Claims (7)

1. A method for estimating a probability distribution of a time for failure recovery of a device, wherein the device comprises a plurality of components, the lives of the components are subject to a gamma distribution, at most one component fails at any time in the whole task time, and the order of state checking of the components is independent and irrelevant when troubleshooting, the method comprising:

s1, acquiring a gamma distribution density function, state inspection consumption time and accumulated working time of the service life obeying of each component, acquiring the inspection sequence of all components after the consumption time and the fault of each failed component are repaired, and taking a working period of equipment as task time;

s2, in the task time, the accumulated working time of each component is combined, the gamma distribution density function integral subject to the service life is calculated, and the probability of each component in the task time of failure is obtained;

s3, according to the inspection sequence and according to the probability of the faults of all the components in the task time, calculating the repair weight coefficient of all the components in the task time;

s4, according to the checking sequence, checking the time consumption of each component according to the state of each component and the time consumption of repairing each failed component, and calculating a repair completion time array;

s5, arranging elements in the repair completion time array in an ascending order to obtain the ordered part numbers and the corresponding repair completion time;

and S6, according to the sequence after sequencing, cumulatively calculating the repair weight coefficients of all the parts to obtain the probability distribution of completing repair within each repair completion time after the equipment fails.

2. The method of claim 1, wherein step S2 comprises:

s21, setting a part number i =1;

s22, calculating the failure probability Pf of the component i in the task time Tw _i ：

When k = is set to a value of k = b,

when k ≠ i, it is,

wherein n represents the number of parts, g _k (t) represents the conditional probability of component k, a _k 、b _k Shape parameter and scale parameter in gamma distribution density function respectively representing life obeys of component k, gamma represents gamma function, t _k Represents the cumulative operating time of the component k;

s23.I = i +1, if i ≦ n, go to step S22, otherwise, go to step S3.

3. The method of claim 1, wherein step S3 comprises:

s31, setting a component checking serial number i =1;

s32, calculating the repair weight coefficient of the component corresponding to the inspection serial number i in the task time:

and two intermediate variables are assigned as follows:

Tc _i ＝tc _j ，Tx _i ＝tx _j ；

wherein,n denotes the number of parts, j = gInd _i ，Pf _j Indicates the probability of failure occurrence in the component task time of number j, gInd indicates the inspection order for all components after failure occurrence, tc _j The time consumed for checking the state of the part denoted by the number j, tx _j Indicating the elapsed time for repairing the failed part numbered j;

and S33.I = i +1, if i is less than or equal to n, the step S32 is carried out, otherwise, the step S4 is carried out.

4. The method of claim 3, wherein step S4 comprises:

s41, setting a component checking serial number i =1;

s42, calculating a repair completion time array

S43.I = i +1, if i ≦ n, proceed to step S42, otherwise, proceed to step S5.

5. The method of claim 4, wherein step S6 comprises:

s61, setting a sorted sorting serial number i =1;

s62, calculating the time xt _i Probability Pr of internal completion repair _i ：

Wherein xt is _i Represents the repair completion time of the component with the sequence number i in the sequencing result, pt _i ＝w _j ，j＝ix _i ，ix _i The part number with the sequence number i in the sequencing result, w _j A repair weight coefficient representing the component at the mission time;

s63.I = i +1, if i is less than or equal to n, the step S52 is entered, otherwise, the calculation is terminated, and all xt are output _i And Pr _i 。

6. The method of claim 1, further comprising:

s7, selecting expected time, and enabling xt closest to the expected time _i Corresponding probability Pr _i As the probability of completing the repair within the desired time;

wherein xt is _i Representing the repair completion time, pr, of the component with the sequence number i in the sequencing result _i Is expressed at time xt _i Probability of completing the repair internally.

7. A system for estimating a probability distribution of device failure recovery times, comprising a processor and a memory;

the memory is used for storing computer execution instructions;

the processor, configured to execute the computer-executable instructions to cause the method of any one of claims 1 to 6 to be performed.

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