CN115688025A - Method and system for estimating probability distribution of equipment fault repair time - Google Patents
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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
Technical Field
The invention belongs to the field of equipment fault index quantification, and particularly relates to a method and a system for estimating probability distribution of equipment fault repair time.
Background
When a certain fault phenomenon occurs in equipment, a plurality of parts which possibly cause the fault phenomenon are generally checked one by one until a failed part is found, and then the failed part is repaired by adopting repair modes such as replacement of spare parts and the like. When the failure phenomenon and the failure cause are in a one-to-many relationship, the time for completing the repair is different due to the uncertainty of the failure element. Mean Time To Repair (MTTR) is currently used to describe equipment serviceability.
For naval vessel equipment, crew-level repairs are those performed at the equipment site during marine missions, after equipment failure, and are also very limited in terms of repair facilities, repair tools, repair crew number and level, etc. The crew MTTR index is very important for recovering the equipment operational capacity in wartime, and is highly valued by equipment producers and military parties. The production party adopts various measures to meet the MTTR index of the military party, for example, an automatic testing technology is adopted to help a naval crew to quickly find out the fault reason, and a modularization technology is widely adopted to design equipment, so that the naval crew can quickly dismantle a failure part and replace a spare part so as to repair the equipment. Currently when MTTR is used, there are two major problems: firstly, when the MTTR index is implemented, the equipment design/production party and the military party mostly adopt a mode of carrying out MTTR index assessment aiming at a certain specific fault agreed by the two parties. The reason behind this approach is that the MTTR cannot be estimated in the more general, more extensive cases, but rather to "embody" the overall MTTR performance of the equipment by "achieving" the mean time to repair of partial or representative failures. Secondly, the mathematical nature of MTTR is mean value, and it is an index that describes in macroscopic and overall level, but actually even if the same fault phenomenon occurs, the repair time is actually distributed in a certain range due to the different failure parts and the uncertainty of the troubleshooting time. In actual practice, even if one knows a conclusion like "average time taken to repair the fault is 46 minutes", it is still more desirable to get "within which times and with what probability the repair can be done? "answers to such questions.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method and a system for estimating the probability distribution of equipment fault repairing time, and aims to solve the problem that the probability distribution of the equipment fault repairing time cannot be predicted in the prior art.
In order to achieve the above object, in a first aspect, the present invention provides a method for estimating a probability distribution of a time for repairing a failure of a device, where the device includes 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 status check of the components is independent and irrelevant when troubleshooting, the method includes:
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, calculating a repair completion time array according to the state checking time consumption of each part and the repair time consumption of each failed part;
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.
Preferably, 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 the number k is = b, the current ratio,
when k is not equal to i, the number of the bits is less than or equal to i,
wherein n represents the number of parts, g k (t) represents the conditional probability of component k, a k 、b k Shape parameters and scale parameters in a gamma distribution density function representing the lifetime compliance of a component k, gamma representing the 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.
Preferably, 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 represents 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 State check elapsed time, tx, for the part numbered j 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.
Preferably, 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.
Preferably, step S6 includes:
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 。
Preferably, the method further comprises:
s7, selecting expected time, and enabling xt closest to the expected time i Corresponding probability Pr i As desiredProbability of completing repair within 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.
To achieve the above object, in a second aspect, the present invention provides a system for estimating a probability distribution of a device failure recovery time, including a processor and a memory; the memory is used for storing computer execution instructions; the processor is configured to execute the computer-executable instructions to cause the method of the first aspect to be performed.
Generally, 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 a system for estimating probability distribution of equipment fault repairing time, which calculate repairing weight coefficients of all parts in task time according to the probability of all parts in the task time of faults according to an inspection sequence, calculate a repairing completion time array according to the state inspection consumption time of all parts and the repairing consumption time of all failed parts, arrange all elements in the repairing completion time array in an ascending order, obtain the ordered part numbers and the corresponding repairing completion time, and then calculate the repairing weight coefficients of all parts in an accumulating manner according to the ordered sequence to obtain the probability distribution of completing repairing in all repairing completion time after the equipment faults, thereby realizing the prediction of the probability distribution of the equipment fault repairing time and describing the maintainability of equipment in more detail.
Drawings
Fig. 1 is a flowchart of a method for estimating probability distribution of device fault repairing time according to an embodiment of the present invention.
Fig. 2 is a probability distribution result of the repair completed within 20 to 145 minutes by using the simulation method and the method of the present invention, respectively, according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The equipment comprises a plurality of components, the service lives of the components are subject to 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 in troubleshooting. Fig. 1 is a flowchart of a method for estimating probability distribution of device fault recovery time according to an embodiment of the present invention. As shown in fig. 1, the method includes:
s1, obtaining a gamma distribution density function, state inspection consumption time and accumulated working time of the service life obeying of each component, obtaining the inspection sequence of all the components after the consumption time and the faults of each failed component are repaired, and taking a working period of the equipment as task time.
The gamma distribution is a common distribution type and is suitable for describing the process of gradual and continuous degradation of the performance of equipment in engineering practice, for example, the wear of a cutter is a typical continuous-time and continuous-state performance degradation process, and the service life of the cutter can be represented by the gamma distribution. Gamma type cell means that the life of the cell obeys the gamma distribution Ga (a, b) as a function of its density
Where a is a shape parameter, b is a scale parameter, and Γ () is a gamma function.
The invention appoints that:
(1) A piece of equipment consists of a plurality of gamma type units, and for convenience of description, the life of each unit is described in terms of time.
(2) At most 1 cell failed at any time. When a certain unit breaks down, the normal work of equipment can be influenced, certain failure phenomena can occur to the equipment, and repair work needs to be carried out at the moment.
(3) When fault confirmation is performed, the order of status checks on these units is independent and irrelevant, namely: there are no cases where there are specific requirements on the checking order, such as "unit a must be checked first and then unit B".
(4) The life distribution rule of each unit, the time consumed for performing (normal or abnormal) state check on each unit, the repair time of each failed unit, the accumulated working time of each unit, the time to execute a task and the check sequence of all relevant units after a certain fault phenomenon occurs are known.
The related variable conventions of the present invention are as follows:
the number of units is recorded as n; the checking sequence is recorded as gInd, the unit number to be checked is stored in the array gInd, and related units are checked in sequence according to the unit numbers provided in the array until a failure part is found; the lifetime of the cell i obeys the gamma distribution Ga (a) i ,b i ) (ii) a The cumulative on time of cell i is recorded as t i (ii) a The state check time for cell i is denoted as tc i (ii) a The time to repair the failed cell i is recorded as tx i (ii) a The task time is denoted as Tw.
And 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 being in fault is obtained.
Preferably, step S2 comprises:
s21, setting a part number i =1;
s22, calculating the fault probability Pf of the component i in the task time Tw i ：
When k = i, the number of the terminals is increased,
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 Individual watchShape and scale parameters in a gamma distribution density function that obeys the lifetime of a component k, Γ represents the 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.
And 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.
Preferably, step S3 comprises:
s31, set component check 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 represents 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 to repair the failed part numbered j.
And (4) sorting the elements in the Tr, recording a sorting result as xt, and recording an element number result of the sorting result in the Tr as ix. For example: tr = [32 12 45], after reordering, xt = [12 45], ix = [ 23 ].
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.
And S4, according to the checking sequence, checking the consumed time according to the states of all the parts and the consumed time for repairing all the failed parts, and calculating a repair completion time array.
Preferably, 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.
And S5, arranging the 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.
Preferably, step S6 includes:
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 Denotes repair completion time, pt, of parts having sequence number i in the sequence result 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 。
Preferably, the method further comprises: 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.
The invention provides an estimation system of probability distribution of equipment fault repair time, which comprises a processor and a memory, wherein the processor is used for processing equipment fault repair time; the memory is used for storing computer execution instructions; the processor is used for executing the computer execution instruction so as to execute the method.
Example (b): it is known that a component is composed of 10 gamma distribution units, and the relevant information of each unit is shown in table 1, i.e. 100 hours of tasks are to be executed. After the convention fails, the state is checked according to the unit serial numbers 2, 9, 8, 6, 1, 4, 10, 7, 5 and 3 in sequence until a failed unit is found, and the unit is repaired to complete the repair. Using the above method, calculate the time distribution results of repairing the fault and estimate what is the probability of completing the repair within one and a half hours?
TABLE 1 information about units
1) And (3) calculating the failure probability Pf of each unit in a traversing way, wherein the failure probabilities of the units 1 to 10 are respectively as follows: 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 order gInd, the repair weight coefficients w are calculated in a traversing mode and are 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, 7; tx is 7, 5, 21, 19, 10, 14, 6, 9, 10, 13.
3) And calculating a repair completion time array Tr, wherein Tr is 20, 36, 63, 79, 76, 93, 99, 125, 135 and 145.
4) Sorting the elements in the Tr from small to large, wherein xt is 20, 36, 63, 76, 79, 93, 99, 125, 135 and 145 as a sorting result; the element number result ix of the sorting result in Tr is 1, 2, 3, 5, 4, 6, 7, 8, 9 and 10.
5) And calculating the repair time distribution probability Pr which is 0.06, 0.07, 0.17, 0.24, 0.35, 0.43, 0.45, 0.59, 0.83 and 1.00.
6) And stopping calculation and outputting xt and Pr. As can be seen from the table lookup, the nearest half hour of xt is 93 minutes, so the probability of completing the repair work in one and a half hours is approximately 0.43.
A simulation model can be established to verify the correctness of the method, and the simulation model is briefly described as follows:
(1) Generating n random numbers simT i ，1≤i≤n，simT i Obey the life distribution rule of the unit i and require all simT i >t i If true, the remaining lifetime sT of each cell i ＝simT i -t i 。
(2) At all sT i The minimum number is found in the sequence number, the corresponding sequence number is marked as m, namely: sT m ≤sT i ,1≤i≤n。
(3) If sT m <Tw is established, the simulation is valid, the consumed inspection time can be obtained according to the inspection sequence, and the sum of the consumed inspection time and the repair time of the unit is the simulation result of the repair time.
After a large number of simulations, the probability distribution result of the time consumed to repair the fault can be obtained statistically.
After a large number of simulations, the probability distribution of the repair time can be statistically obtained. Fig. 2 is a probability distribution result of the repair completed within 20 to 145 minutes by using the simulation method and the method of the present invention, respectively, according to an embodiment of the present invention. In view of the randomness of the simulation, FIG. 2 shows that the results are very consistent. The simulation result shows that: the mean time to repair for this failure was 106.7 minutes, and the root variance for the time to repair was 34.8 minutes. Because the change fluctuation of the repair time is large, the work in the aspects of developing maintenance management plans by the average repair time is rough.
A large number of simulation verification results show that: the method can simultaneously consider the influences of the factors such as the reliability of the equipment (the service life distribution rule of each unit), the health state of the equipment (accumulated working time), the maintainability of basic component units of the equipment (the state inspection time and the repair time of each unit), the task time and the like, accurately estimate the probability distribution of the repair time, can describe the maintainability of the equipment in more detail compared with an MTTR index, and can be used for the maintainability design scheme evaluation in the equipment design stage and the maintainability scheme optimization in the equipment use stage.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the 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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| CN116579494A (en) * | 2023-05-23 | 2023-08-11 | 中国人民解放军海军工程大学 | Spare part inventory prediction method and system based on electromechanical equipment under maintenance time consumption |
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| CN116579494A (en) * | 2023-05-23 | 2023-08-11 | 中国人民解放军海军工程大学 | Spare part inventory prediction method and system based on electromechanical equipment under maintenance time consumption |
| CN116579494B (en) * | 2023-05-23 | 2024-03-19 | 中国人民解放军海军工程大学 | Spare part inventory prediction method and system based on electromechanical equipment under maintenance time consumption |
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