CN107967398A - A kind of product reliability analysis method and device - Google Patents

Abstract

The invention discloses a product reliability analysis method and device. The method includes: collecting the failure and maintenance history information of various parts in multiple samples of the product to be analyzed, modeling the failure of the fully repairable parts as a complete maintenance failure statistical model, and making the minimum maintenance The failure modeling of the parts and components is the minimum maintenance failure statistical model; the complete maintenance failure statistical model or the minimum maintenance failure statistical model of each type of parts obtained through modeling is tested; Complete maintenance failure statistical model or minimum maintenance failure statistical model, conduct Monte Carlo simulation on the product to be analyzed; conduct statistical analysis on the simulation data obtained by using Monte Carlo simulation, calculate the average time between failures of the product to be analyzed and the product to be analyzed Unconditional failure strength for each fixed time interval. It can reduce the modeling difficulty in reliability analysis.

Description

A product reliability analysis method and device

technical field

The invention relates to the field of reliability analysis. More specifically, the present invention relates to a product reliability analysis method and device.

Background technique

All kinds of products need reliability analysis before they are used or sold. For example, as the core component of various CNC machine tools, the CNC system is the key to the realization of CNC machining, and its quality and reliability level directly affect the reliability level of CNC machine tools. With the rapid development of machine tool industry and numerical control technology, the reliability research of numerical control system is becoming more and more important.

Reliability analysis and modeling is an important part of reliability research. Its main purpose is to evaluate various indicators of system or product reliability and provide guidance for realizing reliability design and reliability growth. For general repairable systems, the reliability analysis modeling mainly includes two aspects, one is to study the distribution model, and the other is to consider the influence of the maintenance process on the system reliability. For the numerical control system, due to the limitations of maintenance methods, maintenance time, mechanical fatigue and other reasons, the system cannot be completely repaired in many cases, but maintenance and replacement of system parts and other maintenance activities have a greater impact on the recovery of system reliability. Although it does not achieve "repair as new", it is better than "repair as old", that is, its repair process conforms to incomplete repair, and the failure rate reduction model or life reduction model can usually be used to model its reliability. However, whether it is the scheduled reduction or reduction ratio in the failure rate reduction model, or the service age regression factor in the life reduction model, its value is generally set as a constant, ignoring the impact of specific maintenance methods and maintenance times on it, and The actual engineering situation does not match. Moreover, with the introduction of new parameters such as service age regression factor, the parameter estimation of the above model becomes more and more difficult, and traditional parameter estimation methods such as maximum likelihood estimation cannot be solved.

Therefore, for complex repairable systems or products, considering the types of incomplete maintenance models such as failure rate reduction model and life reduction model and the estimation of model parameters are too complicated, it is urgent to propose a system reliability analysis method that avoids incomplete maintenance models .

Contents of the invention

The purpose of the present invention is achieved through the following technical solutions.

Product reliability analysis method according to the present invention comprises:

Step 1: Collect the failure and maintenance history information of various components in multiple samples of the product to be analyzed, and model the failure of the fully repairable component as a complete maintenance failure based on the failure and maintenance history information Statistical model, modeling the failure of minimally repairable parts as a statistical model of minimally repairable failures;

Step 2: Check the complete maintenance failure statistical model or the minimum maintenance failure statistical model of various types of components obtained through modeling;

Step 3: Use the tested complete maintenance failure statistical model or the minimum maintenance failure statistical model of each type of parts to perform Monte Carlo simulation on the operating status of each type of parts of the product to be analyzed;

Step 4: Statistically analyze the simulation data obtained by Monte Carlo simulation, calculate the average time between failures of the product to be analyzed and the unconditional failure intensity of the product to be analyzed within each fixed time interval,

Among them, according to the type of maintenance after failure, each type of parts in the product to be analyzed is divided into two types: parts that can be completely repaired and parts that can be repaired minimally. Repairs that can be completed by replacing parts after a fault occurs, other repair methods that do not belong to the complete repairs belong to the minimal repairs, and the faults of parts that can be completely repaired are complete repair faults, and parts that can be repaired minimally Component failures are minimal maintenance failures.

According to the product reliability analysis method of the present invention, the complete maintenance failure statistical model adopts a Weibull distribution model, and the failure and maintenance history information of the parts that can be fully maintained includes at least one of the following: specific types of zero The failure repair method of components, the number of failures of specific types of parts samples, the interval time between failures of specific types of parts samples, whether the specific types of parts samples are running normally until the cut-off time, the cut-off interval time of specific types of parts samples ;

The minimum maintenance failure statistical model adopts the Weibull process model, and the failure and maintenance history information of the components that can be subjected to minimum maintenance includes at least one of the following: failure maintenance methods of specific types of components, specific types of components The test cut-off time of the sample, the occurrence time of each failure of a specific type of component sample, the total number of samples of a specific type of component, the total number of failures of a specific sample of a specific type of component, the total number of failures of all samples of a specific type of component.

According to the product reliability analysis method of the present invention, in step 1:

The complete repair failure statistical model for each class of fully repairable components is modeled by the following formula:

in, is the estimated value of the scale parameter of the failure rate function in the Weibull distribution model, is the estimated value of the shape parameter of the failure rate function in the Weibull distribution model, n is the number of failures of a specific type of component, x _i is the i-th failure interval time of a specific type of component, r is the censored value of a specific type of component The number of times, x _sj is the censored interval time of the jth sample of a specific type of component;

The statistical model of minimal maintenance failures for each class of components that can be minimally maintained is modeled by the following formula:

in, an estimate of the intensity parameter of the intensity function in the Weibull process model, The estimated value of the shape parameter in the Weibull process model, t _si is the censored time of the i-th sample test of a specific type of component, S _ij is the j-th failure time of the i-th sample of a specific type of component, and K is The total number of samples of a specific type of parts, n _i is the total number of failures of the i-th sample of a specific type of parts, n is the total number of failures of all samples of a specific type of parts.

According to the product reliability analysis method of the present invention, in step 2:

The Weibull distribution model is tested by Mann test criterion, and the Weibull process model is tested by Cramer-von Mises test criterion.

According to the product reliability analysis method of the present invention, in step 3:

The Weibull distribution model is simulated by the following formula:

Among them, r' is a random variable uniformly distributed on the (0,1) interval, t is the fault time interval, is the estimated value of the scale parameter, is the estimated value of the shape parameter;

The Weibull process model is simulated by:

Among them, z _i is the working failure time after the i-th minimum maintenance, y ₀ =ξ ₀ , t=F ^-1 (ξ ₀ ), ξ _i (i=0,1,2,3,…) A sequence of random numbers independent of each other on the (0,1) interval obtained by counting seeds.

According to the product reliability analysis method of the present invention, in step 4:

Calculate the mean time between failures for the product under analysis using the following formula:

Among them, M is the number of simulations, T is the running time of a single simulation, and N _m is the number of failures of the product to be analyzed in the mth simulation;

Calculate the unconditional failure strength for each fixed time interval of the product to be analyzed using the following formula:

Wherein, M is the number of simulations, and ΔW _m (t) is the number of failures of the product to be analyzed within (t,t+Δt).

A product reliability analysis device according to the present invention, comprising:

The data acquisition and modeling module is used to collect the failure and maintenance history information of various parts in multiple samples of the product to be analyzed, and based on the failure and maintenance history information, the failure of the fully repairable parts It is modeled as a statistical model of complete maintenance failure, and the failure of parts that can be repaired minimally is modeled as a statistical model of minimum maintenance failure;

The model checking module is used to test the complete maintenance failure statistical model or the minimum maintenance failure statistical model of various types of components obtained through modeling;

The simulation module is used to perform Monte Carlo simulation on the operating state of various types of components of the product to be analyzed by using the tested statistical model of complete maintenance failure or minimum maintenance failure statistical model of various types of components;

The data analysis module is used to perform statistical analysis on the simulation data obtained by Monte Carlo simulation, calculate the average time between failures of the product to be analyzed and the unconditional failure intensity of the product to be analyzed within each fixed time interval,

Among them, according to the type of maintenance after failure, each type of parts in the product to be analyzed is divided into two types: parts that can be completely repaired and parts that can be repaired minimally. Repairs that can be completed by replacing parts after a fault occurs, other repair methods that do not belong to the complete repairs belong to the minimal repairs, and the faults of parts that can be completely repaired are complete repair faults, and parts that can be repaired minimally Component failures are minimal maintenance failures.

Another product reliability analysis device according to the present invention includes a processor and a memory storing executable instructions, and the processor executes the executable instructions to complete the steps in the method described above.

The invention has the advantage that it can reduce the difficulty of modeling when performing reliability analysis.

Description of drawings

Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the specific embodiments. The drawings are only for the purpose of illustrating specific embodiments and are not to be considered as limiting the invention. Also throughout the drawings, the same reference numerals are used to designate the same components. In the attached picture:

Fig. 1 shows a schematic flowchart of a product reliability analysis method according to an embodiment of the present invention.

Fig. 2 shows a schematic flowchart of Monte Carlo simulation used in the product reliability analysis method according to the embodiment of the present invention.

Fig. 3 shows a schematic block diagram of a first product reliability analysis device according to an embodiment of the present invention.

Detailed ways

Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided for more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

Fig. 1 shows a schematic flowchart of a product reliability analysis method 100 according to an embodiment of the present invention.

As shown in FIG. 1 , the product reliability analysis method 100 includes the following steps:

Step S102: Collect the failure and maintenance history information of various components in multiple samples of the product to be analyzed, and model the failure of the fully repairable component as a complete maintenance failure based on the failure and maintenance history information A statistical model that models the failure of minimally repairable components as a statistical model of minimally repairable failures.

For example, parts with the same model number can be grouped into parts of the same kind.

S104: Verify the complete maintenance failure statistical model or the minimum maintenance failure statistical model of each type of parts obtained through modeling.

S106: Using the tested statistical model of complete maintenance failure or minimum maintenance failure of each type of component, Monte Carlo simulation is performed on the running state of each type of component of the product to be analyzed.

S108: Statistically analyze the simulation data obtained by Monte Carlo simulation, and calculate the Mean Time Between Failure (MTBF) of the product to be analyzed and the unconditional failure intensity of the product to be analyzed within each fixed time interval.

Among them, according to the type of maintenance after failure, each type of parts in the product to be analyzed is divided into two types: parts that can be completely repaired and parts that can be repaired minimally. Repairs that can be completed by replacing parts after a fault occurs, other repair methods that do not belong to the complete repairs belong to the minimal repairs, and the faults of parts that can be completely repaired are complete repair faults, and parts that can be repaired minimally Component failures are minimal maintenance failures.

1. Fault classification

Starting from the fault data, the system (more precisely, including the above-mentioned products to be analyzed such as electronic products, mechanical products, electromechanical products, etc.) Included systems or subsystems such as numerical control systems) are abstractly divided, according to whether the system (including its components or subsystems) fails, whether the maintenance process replaces parts, and the system (including its components or subsystems) fails Divided into: complete maintenance failure and minimal maintenance failure, that is, when the maintenance activity is the replacement of parts, the failure is regarded as a complete maintenance failure, otherwise it is regarded as a minimum maintenance failure.

That is, the above-mentioned components may also be member subsystems constituting a system, or member systems constituting a larger system.

Optionally, according to the product reliability analysis method 100 of the present invention, the complete maintenance failure statistical model adopts a Weibull distribution model, and the failure and maintenance history information of the components that can be fully maintained includes at least one of the following Items: failure repair methods of specific types of parts, failure times of specific types of parts samples, interval time between failures of specific types of parts samples, whether specific types of parts samples are running normally until the cut-off time, specific types of parts samples The censoring interval of .

The minimum maintenance failure statistical model adopts the Weibull process model, and the failure and maintenance history information of the components that can be subjected to minimum maintenance includes at least one of the following: failure maintenance methods of specific types of components, specific types of components The test cut-off time of the sample, the occurrence time of each failure of a specific type of component sample, the total number of samples of a specific type of component, the total number of failures of a specific sample of a specific type of component, the total number of failures of all samples of a specific type of component.

2. System modeling

According to the above classification of system faults, the system abstraction is divided into two subsystems (namely, the two types of parts that can be fully repaired and the parts that can be repaired minimally), one of which is a fully repairable subsystem, and the other The subsystem is a minimum maintenance subsystem, and the two are connected in series. The complete maintenance subsystem and the minimal maintenance subsystem adopt the Weibull distribution model and the Weibull process model respectively, and the two subsystems are systematically modeled according to the following formula:

(1) Weibull distribution:

Its failure rate function

reliability function

The probability density function is

Among them, θ is the scale parameter, β is the shape parameter, and t is the fault time interval.

(2) Weibull process:

Its strength function is as follows

ω(t')＝abt' ^b-1 , a>0, b>0, t'≥0 (4)

Among them, a is the strength parameter, b is the shape parameter, t' is the fault time, and when b>1, the strength function is an increasing function, indicating the system degradation; when b=1, the strength function is constant, and the system failure trend remains Constant; when b<1, the intensity function is a decreasing function, indicating that the system is improved.

3. Distribution function determination and inspection

In the reliability simulation, the life distribution function is the basis of the simulation. For the two distribution models that have been determined above: Weibull distribution and Weibull process, it is necessary to collect the failure time data and use the maximum similarity method on the basis of classification. Then estimate the parameters and fit them separately.

Therefore, optionally, according to the product reliability analysis method 100 of the present invention, in step S102:

Statistical models of complete repair failures for each class of fully repairable components are modeled (i.e., (1) Weibull distribution parameter estimates are performed) by the following formula:

in, is the estimated value of the scale parameter of the failure rate function in the Weibull distribution model, is the estimated value of the shape parameter of the failure rate function in the Weibull distribution model, n is the number of failures of a specific type of component, x _i is the i-th failure interval time of a specific type of component, r is the censored value of a specific type of component The number of times, x _sj is the censored interval time of the jth sample of a specific type of component.

The statistical model of minimum maintenance failures for each class of components that can be minimally maintained is modeled (i.e., (2) Weibull process parameter estimation is performed) by the following formula:

in, an estimate of the intensity parameter of the intensity function in the Weibull process model, The estimated value of the shape parameter in the Weibull process model, t _si is the censored time of the i-th sample test of a specific type of component, S _ij is the j-th failure time of the i-th sample of a specific type of component, and K is The total number of samples of a specific type of parts, n _i is the total number of failures of the i-th sample of a specific type of parts, n is the total number of failures of all samples of a specific type of parts.

Optionally, according to the product reliability analysis method 100 of the present invention, in step S104:

The Weibull distribution model is tested by Mann test criterion, and the Weibull process model is tested by Cramer-von Mises test criterion.

For example, in order to ensure the effectiveness of later reliability analysis, it is necessary to perform a goodness-of-fit test on the above-mentioned reliability distribution model. The specific inspection methods are as follows:

(1) Mann test

A specific test for the Weibull distribution. Assumed to be

H ₀ : Failure time obeys Weibull distribution;

H ₁ : The failure time does not obey the Weibull distribution;

The test statistic is

in, M _i =Z _i+1 -Z _i , is the integer part of x, r is the total number of faults, n is the number of test systems (here equal to the sum of the total number of faults and the censored number), X _i is the interval time between the _ith faults, and Mi is an approximate value. H ₀ is accepted if M < F _crit is satisfied. If the degree of freedom of the numerator is 2k ₂ and the degree of freedom of the denominator is 2k ₁ , the value of F _crit can be obtained from the F distribution table.

(2) Cramer-von Mises test

For the Weibull process, Cramer-von Mises was used for goodness-of-fit tests. Supposed to be:

H ₀ : use Weibull process to describe failure time data;

H ₁ : The Weibull process cannot describe the data;

The test statistic is

Among them, n is the total number of faults, S _i is the time sequence of fault occurrence, t _s is the timing censoring time, is the maximum likelihood estimate of the parameter b.

Given the significance level α, look up the table to get critical value of if satisfied It is considered that the Weibull process fits the failure time data acceptable.

4. Monte Carlo programming and simulation

Optionally, according to the product reliability analysis method 100 of the present invention, in step S106:

The Weibull distribution model is simulated by the following formula:

Among them, r' is a random variable uniformly distributed on the (0,1) interval, t is the fault time interval, is the estimated value of the scale parameter, is an estimate of the shape parameter.

The Weibull process model is simulated by:

Among them, z _i is the working failure time after the i-th minimum maintenance, y ₀ =ξ ₀ , t=F ^-1 (ξ ₀ ), ξ _i (i=0,1,2,3,…) A sequence of random numbers independent of each other on the (0,1) interval obtained by counting seeds.

This is because, after the distribution function of the random variable is determined, a simple and reasonable random variable sampling method is usually selected to realize the sampling of the known distribution function.

For complete maintenance, that is, the Weibull distribution model, the inverse transformation method can be used to generate random numbers. The Weibull distribution function obtained from formula (2)

Let r be a random variable uniformly distributed on the (0,1) interval, solve the equation r=1-exp[-(t/θ) ^β ], and r is the same distribution as 1-r on the interval (0,1), The above sampling formula (9) of the Weibull distribution can be obtained.

For minimal maintenance, that is, Weibull process, the residual distribution sampling method should be used for life sampling. The cumulative intensity function of the Weibull process is obtained from formula (4)

The first failure time distribution function

F(t')=1-R(t')=1-exp{-W(t')}=1-exp(-at' ^b ) (13)

Among them, R(t') represents reliability, P{N(t')=0} represents the probability of normal operation within time t', namely

Given any random number ξ ₀ in the (0,1) interval, the sampling value of the first failure time is obtained by the inverse transformation method

Any random number ξ ₁ in the (0,1) interval is given, and the working failure time z ₁ after the first minimum maintenance satisfies

Let y ₁ =ξ ₀ +(1-ξ ₀ )ξ ₁ , then z ₁ =F ^-1 (y ₁ )-t'.

Any given random number ξ ₂ in the (0,1) interval, the working failure time z ₂ after the second minimum maintenance satisfies

Let y ₂ =y ₁ +(1-y ₁ )ξ ₂ , then z ₂ =F ^-1 (y ₂ )-(z ₁ +t').

In the same way, it can be obtained that the sampling formula of working failure time zi after the _i -th minimum maintenance is the above formula (10).

Based on the above sampling method, system simulation can be carried out. Fig. 2 shows a schematic flowchart of Monte Carlo simulation used in the product reliability analysis method according to the embodiment of the present invention.

As shown in Fig. 2, taking a system (or product to be analyzed) including a fully repairable part and a minimally repairable part as an example, the Monte Carlo simulation used may include the following steps:

1) Set the number of simulation times M and the running time T of a single simulation, so that the number of times of simulation m=0;

2) m=m+1, judge whether m>M is established, if established, turn to step 9), otherwise execute 3);

3) Start a single simulation. At the beginning, the system is running normally, the running time is t=0, and the number of failures is N=0;

4) Sampling the failure time of Weibull distribution and Weibull process respectively, get _t1 and _t2 ;

5) Take the smaller t _min =min{t ₁ ,t ₂ } for comparison;

6) Propel running time t=t+t _min ;

7) When t ₁ <t ₂ , carry out complete maintenance, next Weibull process sampling failure time t ₂ '=t ₂ -t _min , Weibull distribution for re-sampling; when t ₁ ≥ t ₂ , perform minimum maintenance , the next Weibull distribution sampling failure time t ₁ '=t ₁ -t _min , the Weibull process performs residual distribution sampling, and records the number of failure occurrences;

8) Judging that t>T, if it is true, go to 2), otherwise go to 4) to continue sampling;

9) Perform statistical analysis on the data recorded by the simulation.

5. Statistical analysis (that is, the above simulation step 9)

Optionally, according to the product reliability analysis method 100 of the present invention, in step S108:

Calculate the mean time between failures for the product under analysis using the following formula:

Among them, M is the number of simulations, T is the running time of a single simulation, and N _m is the number of failures of the product to be analyzed in the mth simulation.

Calculate the unconditional failure strength for each fixed time interval of the product to be analyzed using the following formula:

Wherein, M is the number of simulations, and ΔW _m (t) is the number of failures of the product to be analyzed within (t,t+Δt). By dividing the single simulation running time T into several time intervals, counting the average number of failures of the system in each time interval, and dividing the average number of failures by the time interval, the unconditional failure of the system in each fixed time interval can be obtained strength.

That is, the system is simulated according to the above-mentioned simulation process, and after obtaining enough data, the reliability index of the system is statistically solved. The above technical solution of the present invention ignores the maintenance time, and only focuses on the fault occurrence time or fault interval time. Therefore, in the above simulation process, only the number of system fault occurrences is recorded.

In combination with the above product reliability analysis method 100 according to the present invention, two product reliability analysis devices are also proposed.

Fig. 3 shows a schematic block diagram of a first product reliability analysis device 300 according to an embodiment of the present invention.

As shown in FIG. 3 , the first product reliability analysis device 300 includes a data collection and modeling module 302 , a model checking module 304 , a simulation module 306 and a data analysis module 308 .

The data collection and modeling module 302 is used to collect the failure and maintenance history information of various parts in multiple samples of the product to be analyzed, and based on the failure and maintenance history information, the components that can be completely repaired The fault is modeled as a complete repair fault statistical model, and the fault of the parts that can be repaired minimally is modeled as a minimal repair fault statistical model.

The model verification module 304 is used to verify the complete maintenance failure statistical model or the minimum maintenance failure statistical model of various types of components obtained through modeling.

The simulation module 306 is used for performing Monte Carlo simulation on the running state of each type of component of the product to be analyzed by using the verified complete maintenance failure statistical model or the minimum maintenance failure statistical model of each type of component.

The data analysis module 308 is used for performing statistical analysis on the simulation data obtained by Monte Carlo simulation, and calculating the average time between failures of the product to be analyzed and the unconditional failure intensity of the product to be analyzed within each fixed time interval.

Among them, according to the type of maintenance after failure, each type of parts in the product to be analyzed is divided into two types: parts that can be completely repaired and parts that can be repaired minimally. Repairs that can be completed by replacing parts after a fault occurs, other repair methods that do not belong to the complete repairs belong to the minimal repairs, and the faults of parts that can be completely repaired are complete repair faults, and parts that can be repaired minimally Component failures are minimal maintenance failures.

Another product reliability analysis device according to the present invention includes a processor and a memory storing executable instructions, and the processor executes the executable instructions to complete the product reliability analysis method 100 described above. A step of.

According to the above-mentioned technical scheme of the present invention, a reliability analysis method of a numerical control system (that is, a product to be analyzed) based on fault distribution is proposed. The method starts from the fault data and abstractly divides the system. After a fault occurs in the system, its maintenance Whether the process replaces parts or not, the system faults are divided into: complete maintenance faults and minimal maintenance faults. For the complete maintenance failure time data and the minimum maintenance failure time data after the above classification, the common Weibull distribution and Weibull process model are used to fit the distribution function respectively. Furthermore, the Mann test and the Cramer-von Mises test are used to test the goodness of fit for the above reliability distribution model, and finally the reliability index of the system is evaluated based on Monte Carlo simulation. The above technical solution of the present invention avoids incomplete maintenance models such as failure rate reduction models and life reduction models, and the solution process is simple and clear, and the parameter estimation of the distribution function can be completed only by using the maximum likelihood, which reduces the parameter estimation of the model Difficulty, and to a certain extent, can be extended to general repairable systems, which provides a new idea for the reliability analysis of repairable systems. Has the following advantages:

1. The overall incomplete maintenance process of the system is regarded as a mixture of complete maintenance and minimal maintenance, and system failures are divided into complete maintenance failures and minimal maintenance failures according to whether parts are replaced during the maintenance process.

2. Incomplete maintenance models such as the failure rate reduction model and the life reduction model are avoided, and the difficulty of parameter estimation of the model is reduced.

3. Starting from the fault data, abstractly divide the system, and use Monte Carlo simulation to solve the system reliability index.

4. The solution process is simple and clear, and the parameter estimation of the distribution function can be completed only by using the maximum likelihood, and to a certain extent, it can be extended and applied to general repairable systems, providing a new method for the reliability analysis and research of repairable systems ideas.

Optionally, the above-mentioned technical solution of the present invention may also include the following steps:

Step 1, fault classification, starting from the fault data, abstractly divides the system, and divides the system faults into complete maintenance faults and minimal maintenance faults according to whether the maintenance process replaces parts after a system fault occurs, that is, when the maintenance activity is When parts are replaced, its failure is considered as a complete maintenance failure, otherwise it is regarded as a minimal maintenance failure.

Step 2, system modeling, according to the fault classification of the CNC system, the system is abstracted into two subsystems, one of which is a complete maintenance subsystem, and the other is a minimum maintenance subsystem, and the two are connected in series.

Step three, distribution function determination and inspection.

Step 4, Monte Carlo program design and simulation, after determining the distribution model of the random variable, choose a simple and reasonable random variable sampling method to realize the sampling of the known distribution function.

Step five, statistical analysis, after obtaining enough simulation data, statistically solve the reliability index of the system, calculate the average time between failures of the system and the unconditional failure intensity of the system in each fixed time interval.

The above description is only an exemplary embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily conceive of changes or changes within the technical scope disclosed in the present invention. Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims (8)

1. A product reliability analysis method, characterized in that, comprising: Step 1: Collect the failure and maintenance history information of various components in multiple samples of the product to be analyzed, and model the failure of the fully repairable component as a complete maintenance failure based on the failure and maintenance history information Statistical model, modeling the failure of minimally repairable components as a statistical model of minimally repairable failures; Step 2: Check the complete maintenance failure statistical model or the minimum maintenance failure statistical model of various types of parts obtained through modeling; Step 3: Use the tested complete maintenance failure statistical model or the minimum maintenance failure statistical model of each type of parts to perform Monte Carlo simulation on the operating status of each type of parts of the product to be analyzed; Step 4: Statistically analyze the simulation data obtained by Monte Carlo simulation, calculate the average time between failures of the product to be analyzed and the unconditional failure intensity of the product to be analyzed within each fixed time interval, Among them, according to the type of maintenance after failure, each type of parts in the product to be analyzed is divided into two types: parts that can be completely repaired and parts that can be repaired minimally. Repairs that can be completed by replacing parts after a fault occurs, other repair methods that do not belong to the complete repairs belong to the minimal repairs, and the faults of parts that can be completely repaired are complete repair faults, and parts that can be repaired minimally Component failures are minimal maintenance failures. 2. The product reliability analysis method according to claim 1, characterized in that, the complete repair failure statistical model adopts a Weibull distribution model, and the fault and repair history information of the parts that can be completely repaired includes at least the following At least one of: the failure repair method of specific types of parts, the number of failures of specific types of parts samples, the interval time between failures of specific types of parts samples, whether the specific types of parts samples are running normally until the cut-off time, specific The censored interval time of the type component samples; The minimum maintenance failure statistical model adopts the Weibull process model, and the failure and maintenance history information of the components that can be subjected to minimum maintenance includes at least one of the following: failure maintenance methods of specific types of components, specific types of components The test cut-off time of the sample, the occurrence time of each failure of a specific type of component sample, the total number of samples of a specific type of component, the total number of failures of a specific sample of a specific type of component, the total number of failures of all samples of a specific type of component. 3. the product reliability analysis method according to claim 2, is characterized in that, in step 1: The complete repair failure statistical model for each class of fully repairable components is modeled by the following formula: <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mo>(</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><msub><mi>x</mi><mi>i</mi></msub><mover><mi>&amp;beta;</mi><mo>^</mo></mover></msup><msub><mi>lnx</mi><mi>i</mi></msub><mo>+</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></munderover><msup><msub><mi>x</mi><mrow><mi>s</mi><mi>j</mi></mrow></msub><mover><mi>&amp;beta;</mi><mo>^</mo></mover></msup><msub><mi>lnx</mi><mrow><mi>s</mi><mi>j</mi></mrow></msub><mo>)</mo><mo>/</mo><mo>(</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><msub><mi>x</mi><mi>i</mi></msub><mover><mi>&amp;beta;</mi><mo>^</mo></mover></msup><mo>+</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></munderover><msup><msub><mi>x</mi><mrow><mi>s</mi><mi>j</mi></mrow></msub><mover><mi>&amp;beta;</mi><mo>^</mo></mover></msup><mo>)</mo><mo>-</mo><mfrac><mn>1</mn><mover><mi>&amp;beta;</mi><mo>^</mo></mover></mfrac><mo>=</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>lnx</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><mover><mi>&amp;theta;</mi><mo>^</mo></mover><mo>=</mo><msup><mrow><mo>(</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mfrac><mrow><msup><msub><mi>x</mi><mi>i</mi></msub><mover><mi>&amp;beta;</mi><mo>^</mo></mover></msup></mrow><mi>n</mi></mfrac><mo>+</mo><munderover><mi>&amp;Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>r</mi></munderover><mfrac><mrow><msup><msub><mi>x</mi><mrow><mi>s</mi><mi>j</mi></mrow></msub><mover><mi>&amp;beta;</mi><mo>^</mo></mover></msup></mrow><mi>n</mi></mfrac><mo>)</mo></mrow><mfrac><mn>1</mn><mover><mi>&amp;beta;</mi><mo>^</mo></mover></mfrac></msup></mrow></mtd></mtr></mtable></mfenced> in, is the estimated value of the scale parameter of the failure rate function in the Weibull distribution model, is the estimated value of the shape parameter of the failure rate function in the Weibull distribution model, n is the number of failures of a specific type of component, x _i is the i-th failure interval time of a specific type of component, r is the censored value of a specific type of component The number of times, x _sj is the censored interval time of the jth sample of a specific type of component; The statistical model of minimal maintenance failures for each class of components that can be minimally maintained is modeled by the following formula: <mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><mover><mi>b</mi><mo>^</mo></mover><mo>=</mo><mfrac><mi>n</mi><mrow><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mi>mo><mn>1</mn></mrow><mi>K</mi></munderover><munderover><mi>&amp;Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>n</mi><mi>i</mi></msub></munderover><mi>ln</mi><mfrac><msub><mi>t</mi><mrow><mi>s</mi><mi>i</mi></mrow></msub><msub><mi>S</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mfrac></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mover><mi>a</mi><mo>^</mo></mover><mo>=</mo><mfrac><mi>n</mi><mrow><munderover><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>K</mi></munderover><msup><msub><mi>t</mi><mrow><mi>s</mi><mi>i</mi></mrow></msub><mover><mi>b</mi><mo>^</mo></mover></msup></mrow></mfrac></mrow></mtd></mtr></mtable></mfenced> in, an estimate of the intensity parameter of the intensity function in the Weibull process model, The estimated value of the shape parameter in the Weibull process model, t _si is the censored time of the i-th sample test of a specific type of component, S _ij is the j-th failure time of the i-th sample of a specific type of component, and K is The total number of samples of a specific type of parts, n _i is the total number of failures of the i-th sample of a specific type of parts, n is the total number of failures of all samples of a specific type of parts. 4. the product reliability analysis method according to claim 3, is characterized in that, in step 2: The Weibull distribution model is tested by Mann test criterion, and the Weibull process model is tested by Cramer-von Mises test criterion. 5. the product reliability analysis method according to claim 3, is characterized in that, in step 3: The Weibull distribution model is simulated by the following formula: <mrow><mi>t</mi><mo>=</mo><mover><mi>&amp;theta;</mi><mo>^</mo></mover><msup><mrow><mo>(</mo><mo>-</mo><msup><mi>lnr</mi><mo>&amp;prime;</mo></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mover><mi>&amp;beta;</mi><mo>^</mo></mover></mrow></msup></mrow> Among them, r' is a random variable uniformly distributed on the (0,1) interval, t is the fault time interval, is the estimated value of the scale parameter, is the estimated value of the shape parameter; The Weibull process model is simulated by: <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>y</mi><mi>i</mi></msub><mo>=</mo><msub><mi>y</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mrow><mo>(</mo><mn>1</mn><mo>-</mo><msub><mi>y</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>)</mo></mrow><msub><mi>&amp;xi;</mi><mi>i</mi></msub></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>z</mi><mi>i</mi></msub><mo>=</mo><msup><mi>F</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><msub><mi>y</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><munderover><mo>&amp;Sigma;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></munderover><msub><mi>z</mi><mi>j</mi></msub><mo>+</mo><mi>t</mi><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>...</mo></mrow> Among them, z _i is the working failure time after the i-th minimum maintenance, y ₀ =ξ ₀ , t=F ^-1 (ξ ₀ ), ξ _i (i=0,1,2,3,…) A sequence of random numbers independent of each other on the (0,1) interval obtained by counting seeds. 6. the product reliability analysis method according to claim 3, is characterized in that, in step 4: Calculate the mean time between failures for the product under analysis using the following formula: <mrow><msub><mi>T</mi><mrow><mi>M</mi><mi>T</mi><mi>B</mi><mi>F</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>M</mi><mi>T</mi></mrow><mrow><munderover><mo>&amp;Sigma;</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><msub><mi>N</mi><mi>m</mi></msub></mrow></mfrac></mrow> Among them, M is the number of simulations, T is the running time of a single simulation, and N _m is the number of failures of the product to be analyzed in the mth simulation; Calculate the unconditional failure strength for each fixed time interval of the product to be analyzed using the following formula: <mrow><mi>&amp;lambda;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mi>M</mi></mfrac><munderover><mo>&amp;Sigma;</mo><mrow><mi>m</mi><mo>=</mo><mn>1</mn></mrow><mi>M</mi></munderover><mfrac><mrow><msub><mi>&amp;Delta;W</mi><mi>m</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>&amp;Delta;</mi><mi>t</mi></mrow></mfrac></mrow> Wherein, M is the number of simulations, and ΔW _m (t) is the number of failures of the product to be analyzed within (t,t+Δt). 7. A product reliability analysis device, characterized in that, comprising: The data acquisition and modeling module is used to collect the failure and maintenance history information of various parts in multiple samples of the product to be analyzed, and based on the failure and maintenance history information, the failure of the fully repairable parts It is modeled as a statistical model of complete maintenance failure, and the failure of parts that can be repaired minimally is modeled as a statistical model of minimum maintenance failure; The model checking module is used to test the complete maintenance failure statistical model or the minimum maintenance failure statistical model of various types of components obtained through modeling; The simulation module is used to perform Monte Carlo simulation on the operating state of various types of components of the product to be analyzed by using the tested statistical model of complete maintenance failure or minimum maintenance failure statistical model of various types of components; The data analysis module is used to perform statistical analysis on the simulation data obtained by Monte Carlo simulation, calculate the average time between failures of the product to be analyzed and the unconditional failure intensity of the product to be analyzed within each fixed time interval, Among them, according to the type of maintenance after failure, each type of parts in the product to be analyzed is divided into two types: parts that can be completely repaired and parts that can be repaired minimally. Repairs that can be completed by replacing parts after a fault occurs, other repair methods that do not belong to the complete repairs belong to the minimal repairs, and the faults of parts that can be completely repaired are complete repair faults, and parts that can be repaired minimally Component failures are minimal maintenance failures. 8. A product reliability analysis device, which includes a processor and a memory storing executable instructions, wherein the processor executes the executable instructions to complete the process according to claims 1 to 8. The step in the method described in any one of 6.