CN114692087A - Product reliability evaluation method, readable storage medium and electronic device - Google Patents

Product reliability evaluation method, readable storage medium and electronic device Download PDF

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CN114692087A
CN114692087A CN202210412499.1A CN202210412499A CN114692087A CN 114692087 A CN114692087 A CN 114692087A CN 202210412499 A CN202210412499 A CN 202210412499A CN 114692087 A CN114692087 A CN 114692087A
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郭超
黄洪钟
邓智铭
童辉
刁庆
李彦锋
余奥迪
米金华
史慧楠
汪邦军
于爽
吴强
海洋
柳思源
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Abstract

A reliability evaluation method of a product, a readable storage medium and an electronic device, the method comprising: obtaining a product cumulative failure function based on life data corresponding to a plurality of experimental samples of the product; acquiring the cumulative failure rate of the experimental sample at each moment based on the concavity and convexity of the product cumulative failure function; and obtaining the parameter value of the product life distribution by using a parameter estimation method based on the accumulated failure rate of the experimental sample at each moment, and predicting the reliable life or the reliability of the product. The method and the device are suitable for the life prediction and reliability evaluation process of the life data of various sample quantities including small samples, and the prediction result is accurate.

Description

Product reliability evaluation method, readable storage medium and electronic device
Technical Field
The disclosure belongs to the technical field of reliability experiment evaluation, and particularly relates to a product reliability evaluation method, a readable storage medium and electronic equipment.
Background
For manufacturing enterprises, the product life determination is not only a rated life obtained through theoretical calculation, but also needs to be combined with actual working conditions, however, the actual life data of some products with complex service environments are difficult to collect, and the specific failure time of the products cannot be known, so that the traditional parameter estimation method cannot be directly used for predicting the life interval. Meanwhile, the yield of some products is extremely small, but the production system is very critical. When such life data integrating small samples and no failure characteristics are counted, how to establish a life prediction and reliability evaluation model is very critical to predict and evaluate the life and reliability of such products as possible.
The reliability and the service life prediction of the product can improve the maintenance efficiency of the product, reduce the use risk of the product and ensure the safety of users. The product is influenced by a plurality of uncertain factors in the design, processing and use processes, so that the condition that the failure time is dispersed can still occur even if the working condition of the product reliability experiment is strictly controlled, and sometimes, whether the product fails or not can not be even directly observed. Therefore, it is necessary to process experimental data of such products and establish a more accurate reliability evaluation and life prediction model.
Disclosure of Invention
In order to solve the above technical problems, an object of the present disclosure is to provide a method for evaluating reliability of a product, which is capable of processing experimental data of the product and establishing a more accurate reliability evaluation and life prediction model.
In order to realize the purpose of the disclosure, the technical scheme adopted by the disclosure is as follows:
a reliability evaluation method of a product includes:
obtaining a product cumulative failure function based on life data corresponding to a plurality of experimental samples of the product;
acquiring the cumulative failure rate of each moment in a plurality of moments of the experimental sample based on the concavity and convexity of the product cumulative failure function;
and obtaining the parameter value of the product life distribution by using a parameter estimation method based on the accumulated failure rate of the experimental sample at each moment, and predicting the reliable life or the reliability of the product.
Optionally, the lifetime data of the product is obtained by:
acquiring life data corresponding to a plurality of experimental samples based on experimental data of the plurality of experimental samples of the product;
and when the life data are less than the preset number, expanding the number of the experimental samples and the corresponding life data.
Optionally, the number of lifetime data is augmented with a gray self-help model.
Optionally, the experimental data includes experimental time, failure number and total amount of samples input at each experimental time.
Optionally, obtaining the cumulative failure rate of the experimental sample at each moment based on the concave-convex property of the product cumulative failure function includes:
estimating the failure probability of each experimental sample when the experimental termination time is reached through the distribution of the failure probability of the final working moment of the product and the concave-convex property of the cumulative failure function of the product, and obtaining the prior distribution of the cumulative failure probability of each experimental sample at each moment;
obtaining posterior distribution of the cumulative failure probability when each experimental sample reaches the experimental termination time based on the prior distribution of each cumulative failure probability;
and obtaining the expected value of the time accumulated failure probability of each failed product based on the posterior distribution of each accumulated failure probability, and thus obtaining the accumulated failure rate of each experimental sample at each moment.
Optionally, the prior distribution of the cumulative failure probability, the posterior distribution of the cumulative failure probability, and/or the cumulative failure rate of the experimental sample at each moment are obtained by a bayesian estimation model.
Optionally, based on the cumulative failure rate at each moment, using a parameter estimation method to obtain a parameter value of the product life distribution, and predicting the reliable life or reliability of the product according to the parameter value, including;
constructing a loss function of the product based on the posterior estimation value of the cumulative failure rate of the experimental sample at each moment;
obtaining a distribution parameter of the product life when the loss function is minimum based on the loss function;
and obtaining the reliable service life or the reliability of the product based on the distribution parameters of the service life of the product.
Optionally, the lifetime data is failure data or no failure data.
The present disclosure also provides a readable storage medium having executable instructions thereon, which when executed, cause a computer to perform the steps of the reliability evaluation method of the product described above.
The present disclosure also provides an electronic device comprising a processor and a memory, said memory having stored therein computer program instructions adapted to be executed by said processor, said computer program instructions, when executed by said processor, performing the steps of the reliability evaluation method of the product as described above.
The method is based on life data (failure data or no failure data) of a plurality of experimental samples of the product, provides a product cumulative failure function based on the life data, obtains the cumulative failure rate of the experimental samples at each moment by combining the concavity and convexity of the product failure function, and obtains key parameters of the product life distribution by combining a parameter estimation method. The method and the device are suitable for the service life prediction and reliability evaluation process of the service life data of various sample quantities including small samples, and the prediction result is accurate.
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The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the principles of the disclosure.
FIG. 1 is a method flow diagram of a method of reliability evaluation of a product in the present disclosure;
FIG. 2 is a schematic diagram of a data sample after expansion of a gray self-help model in the method of the present disclosure;
FIG. 3 is a graphical illustration of the cumulative probability of failure values for each sample in the method of the present disclosure;
FIG. 4 is a graphical illustration of a cumulative probability of failure function in the method of the present disclosure.
Detailed Description
The present disclosure will be described in further detail with reference to the drawings and embodiments. It is to be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limitations of the present disclosure. It should be further noted that, for the convenience of description, only the portions relevant to the present disclosure are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict. The present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Referring to fig. 1, the present disclosure of an embodiment of the present disclosure provides a method for evaluating reliability of a product, as shown in fig. 1, including the following steps:
and S1, counting and sorting the experimental data corresponding to the plurality of experimental samples of the product to obtain life data corresponding to the plurality of experimental samples, and sorting the life data into failure data or non-failure data to be used as the input of the product life prediction model. The present disclosure takes the non-failure data as an example, and the principle is the same when the lifetime data is the failure data.
The experimental data of the product are mainly obtained by the service life experiment of the product under the same working condition, different tail-cutting times are taken to group experimental samples, and non-failure data are obtained through statistics after the experiment.
In the embodiment of the present disclosure, the non-failure data of the product may include three factors:
(1) the experimental tail-biting time T of the product under each experimental group;
(2) number r of failed products at experimental truncation under each experimental groupi；
(3) Experimental sample size n of product under each experimental groupi。
In the embodiment of the disclosure, a product is a bearing of a certain model, and the experimental data is non-failure data of the bearing under a certain acceleration working condition, as shown in the following table.
T ri ni
50 3 3
70 3 3
150 3 3
300 3 3
450 3 3
750 2 3
S2, when the service life data are less than the preset number, according to the failure data or no failure data arranged in the step S1, a gray self-help model is used for carrying out capacity expansion on the no failure data, the no failure statistical data are input, and the expanded no failure data are output; the method for expanding the capacity of the non-failure data sample needs to expand the experimental time, the failure number and the total amount of the sample input in each experimental time, and when the total amount of the sample input in each experimental time is the same, the items do not need to be fused.
In the embodiment of the disclosure, because the number of the experimental samples of each experimental group is the same, the gray self-service model is selected to fuse the experimental truncation time T and the number r of the invalid products during the experimental truncation under each experimental groupiIt is used as an input sample Y (T, r) of the gray self-help modeli). At this time, it is assumed that: the number of ash self-help samples B is 80, and the number of self-help samples m extracted each time is 45。
One grey self-help sample value can be calculated by every m self-help samples, and the total required calculation B is 80 grey self-help sample values. The m bootstrap samples taken at each time are given by:
Yb＝(yb(1),yb(2),L,yb(k),L,yb(m)),b＝1,2,L,B (1)
wherein, YbFor the b-th bootstrap sample, yb(k) The kth data of the b-th bootstrap sample. According to the principle of gray prediction GM (1,1), these data are accumulated once to generate a new sequence vector:
Figure BDA0003604253720000051
and then, generating an adjacent mean value of the sequence generated by accumulation, namely, constructing and generating new data by using the mean value of adjacent data, wherein the calculation method comprises the following steps:
Figure BDA0003604253720000052
then constructing a data matrix D and a data vector Yb：
Figure BDA0003604253720000053
Yb＝[yi(2) yi(3)L yi(m)](5)
Due to z in the matrixi(m) is the average of the neighboring data calculated by equation (3), so this time taken only from the last 2 to m terms y of the helper sampleiOpposite thereto (k + 1). The ash generation model can be expressed as:
Figure BDA0003604253720000054
wherein k is a continuous variable, c1And c2Are parameters. Initial conditions are xb(1)＝yb(1) The solution of the differential equation is:
Figure BDA0003604253720000055
wherein
(c1,c2)T＝(DTD)-1DT(Yb)T (8)
From the summation equation (3) can be generated:
xb(k+1)-xb(k)＝yb(k+1) (9)
from this, the predicted value of the w-th measurement can be obtained:
Figure BDA0003604253720000061
the B data of the w-th measurement can form the following vector
Figure BDA0003604253720000062
Fig. 2 is a schematic diagram of a sample of the expansion of the gray self-help model without failure.
S3, acquiring the cumulative failure rate of each moment in the multiple moments of the expanded non-failure sample based on the concave-convex property of the product cumulative failure function;
compared with the traditional probability statistical method, the Bayesian estimation model can be adopted in the step, and the Bayesian method has the advantages that the prior information representation is introduced, the parameter to be estimated is preliminarily estimated, and the prior information is further updated through the experimental information, so that the posterior distribution of the parameter to be estimated is obtained. Aiming at non-failure data under the condition of small samples, extended samples are obtained based on a self-help method and a gray prediction model, statistical distribution of parameters to be estimated is obtained through the extended samples, distribution types are determined through inspection and selection, prior distribution is further fitted, posterior distribution is calculated through a Bayesian method, and estimation results are obtained.
The method comprises the following steps:
s31, determining the distribution of the probability of failure of the product at the final moment of operation, wherein the distribution can be obtained by experience and is generally uniform.
As shown in Table 1, the final time tk750h, cumulative probability of failure p of the productkAt [0, λ ]k]Subject to uniform distribution, p can be obtainedkPrior distribution:
Figure BDA0003604253720000063
for this type of bearing, the parameter values are given artificially: lambda [ alpha ]k＝0.88。
And S32, estimating the failure probability of each experimental sample when the experimental termination time is reached through the distribution of the failure probability of the product at the final working moment and the concave-convex property of the cumulative failure function of the product, and obtaining the prior distribution of the cumulative failure probability of each experimental sample at each moment, wherein the prior distribution is the prior distribution of a Bayesian estimation model.
At the time of obtaining tkTime point failure probability p of 750hkAfter a priori distribution of (a), t can be determinedkProbability of time of failure piThe logarithm of the cumulative failure function of the weibull distribution has the concavity and convexity:
Figure BDA0003604253720000071
in the formula ti≤tk，F(ti)＝pi，F(tk)＝pkFrom this, it can be inferred that:
Figure BDA0003604253720000072
in practical engineering, the failure probability p can be considered conservativelyiAnd pkThe following relationships exist:
Figure BDA0003604253720000073
due to probability of failure piAnd pkThe relationship (b) is relatively conservative, and thus the conclusion will tend to be more conservative and more acceptable to the engineer, and with equation (15), we find piThe prior distribution of (a) is:
Figure BDA0003604253720000074
wherein λ isiIs tiThe upper bound on the probability of failure at a moment,
Figure BDA0003604253720000075
and S33, obtaining posterior distribution of the cumulative failure probability when each non-failure sample reaches the experiment termination time based on the prior distribution of each cumulative failure probability.
After the gray self-help expansion, the sample truncation time is the augmented non-failure sample truncation time tiThe input sample amount is the sample amount n of the non-failure sample after expansioniFor the extended samples, to tiUntil moment riFailure of individual product, si＝ni-riNo failure occurred in any of the products, therefore, at tiAt a moment of siThe conditional probability of individual product failure is:
Figure BDA0003604253720000076
then s can be obtainediConditional probability distribution of individual product failure:
Figure BDA0003604253720000077
from piThe prior distribution (18) and the Bayesian formula (I) can know that p isiThe posterior distribution of (a) is:
Figure BDA0003604253720000078
wherein 0<pi<λi；
And S34, obtaining the expected value of the time cumulative failure probability of each failed product based on the posterior distribution of each cumulative failure probability, obtaining the cumulative failure rate of each non-failure sample at each moment, and integrating and calculating the expected value of the time cumulative failure probability of each sample.
At a loss of square, p can be obtainediThe bayesian estimate of (a) is:
Figure BDA0003604253720000081
referring to fig. 3, a schematic diagram of an accumulated failure probability value of each sample obtained by bayesian estimation of a non-failure sample expanded by the gray self-help model is shown.
And the prior distribution of the cumulative failure probability, the posterior distribution of the cumulative failure probability and/or the cumulative failure rate of each moment of the experimental sample can be obtained by a Bayesian estimation model.
And S4, obtaining the parameter value of the product life distribution by using a parameter estimation method based on the cumulative failure rate of the non-failure sample at each moment, and predicting the reliable life or reliability of the product.
For multiple time-posterior probability sample points
Figure BDA0003604253720000082
In the present method, the probability curve of the double-parameter Weibull cumulative failure of the bearing which is as close as possible to all the sample points is obtained
Figure BDA0003604253720000083
Wherein, the two-parameter Weibull cumulative failure probability of the bearing is as follows:
Figure BDA0003604253720000084
therefore, the loss function is constructed first, and then the unknown parameters are calculated by using an optimization method.
And S41, constructing a loss function of the product based on the posterior estimated value of the cumulative failure rate of the experimental sample at each moment.
Fitting the shape parameter beta and the scale parameter eta by using a least square method, and enabling:
Figure BDA0003604253720000085
find out to satisfy
Figure BDA0003604253720000086
Is estimated from the parameters
Figure BDA0003604253720000087
Which is a key parameter of the product life distribution.
And S42, obtaining the distribution parameter of the product life when the loss function is minimum based on the loss function, and obtaining the reliable life or reliability of the product based on the distribution parameter of the product life.
Taking Q (beta, eta) as an analysis object of the Gibbs method, and finding the minimum value point in a two-dimensional case comprises the following algorithm steps:
(1) initial state η ═ η of random initialization0；
(2) Setting a minimum iteration error epsilon;
(3) the following process is repeated for sampling:
a) at the loss function Q (beta | eta)0) Find a point beta around the minimum of the function1；
b) At the loss function Q (η | beta)1) InFinding a point η near the minimum of the function1；
c) Calculate the difference L ═ Q (β)0,η0)-Q(β1,η1)|；
d) Record the calculated point (beta) at that time1，η1) Let η0＝η1。
(4) Circulate until L<ε, output (. beta.)1，η1) As a result of the solution.
The final iteration result shape parameter estimation result is
Figure BDA0003604253720000091
The scale parameter estimation result is
Figure BDA0003604253720000092
The service life value of the bearing under the acceleration stress is 25.0579h, the reliability of the bearing is 0.9, the difference between the service life value and the service life value 26.09h calculated by using the ISO281 standard of the bearing is not great, and the accuracy of the service life prediction of the model is illustrated.
Referring to fig. 4, the solution result is substituted into a function curve of the cumulative failure function F (t, β, η) by the iterative solution result.
An exemplary embodiment of the present disclosure provides a readable storage medium, on which executable instructions are stored, and when the executable instructions are executed, the computer is caused to execute the steps of the reliability evaluation method of the product described above. The computer-readable storage medium may be: an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system or propagation medium. The computer-readable storage medium may also include a semiconductor or solid state memory, magnetic tape, a removable computer diskette, a Random Access Memory (RAM), a read-only memory (ROM), a rigid magnetic disk and an optical disk. Optical disks may include compact disk-read only memory (CD-ROM), compact disk-read/write (CD-RW), and DVD.
An electronic device provided by the exemplary embodiments of the present disclosure includes a processor and a memory, where a computer program instruction suitable for being executed by the processor is stored in the memory, and when the computer program instruction is executed by the processor, the method performs the steps of the reliability evaluation method of the product. The processor may be a general-purpose processor, and includes a Central Processing Unit (CPU), a Network Processor (NP), and the like; the processor can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, for example, the processor adopts a multi-core digital signal processor 3713, embeds a plurality of DSP cores with 500MHz dominant frequency, and controls the time precision by using an interrupt manner; the memory may include a Random Access Memory (RAM), and may further include a Non-volatile memory (Non-volatile memory), such as at least one disk memory. The memory may also be an internal memory of Random Access Memory (RAM) type, and the processor and the memory may be integrated into one or more independent circuits or hardware, such as: application Specific Integrated Circuit (ASIC). It should be noted that the computer program in the memory may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand-alone product. Based on such understanding, the technical solution of the present invention or a part thereof which contributes to the prior art in essence can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, an electronic device, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention.
In the description herein, reference to the description of the terms "one embodiment/mode," "some embodiments/modes," "example," "specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment/mode or example is included in at least one embodiment/mode or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to be the same embodiment/mode or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments/modes or examples. Furthermore, the various embodiments/aspects or examples and features of the various embodiments/aspects or examples described in this specification can be combined and combined by one skilled in the art without conflicting therewith.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
It will be understood by those skilled in the art that the foregoing embodiments are merely for clarity of illustration of the disclosure and are not intended to limit the scope of the disclosure. Other variations or modifications may occur to those skilled in the art, based on the foregoing disclosure, and are still within the scope of the present disclosure.

Claims (10)

1. A method for evaluating reliability of a product, comprising:
obtaining a product cumulative failure function based on life data corresponding to a plurality of experimental samples of the product;
acquiring the cumulative failure rate of each moment in a plurality of moments of the experimental sample based on the concavity and convexity of the product cumulative failure function;
and obtaining the parameter value of the product life distribution by using a parameter estimation method based on the accumulated failure rate of the experimental sample at each moment, and predicting the reliable life or the reliability of the product.
2. The reliability evaluation method of a product according to claim 1, wherein the life data of the product is obtained by:
acquiring life data corresponding to a plurality of experimental samples based on experimental data of the plurality of experimental samples of the product;
and when the life data are less than the preset number, expanding the number of the experimental samples and the corresponding life data.
3. The reliability evaluation method of a product according to claim 2, characterized in that: and expanding the number of the service life data by adopting a gray self-help model.
4. The reliability evaluation method of a product according to claim 3, characterized in that: the experimental data includes experimental time, failure number and total amount of samples input at each experimental time.
5. The method for evaluating the reliability of a product according to claim 1, wherein obtaining the cumulative failure rate of the experimental sample at each moment based on the ruggedness of the cumulative failure function of the product comprises:
estimating the failure probability of each experimental sample when reaching the termination time of the experiment by the distribution of the failure probability of the product at the final working moment and the concave-convex property of the cumulative failure function of the product, and obtaining the prior distribution of the cumulative failure probability of each experimental sample at each moment;
obtaining posterior distribution of the cumulative failure probability when each experimental sample reaches the experimental termination time based on the prior distribution of each cumulative failure probability;
and obtaining the expected value of the time cumulative failure probability of each failed product based on the posterior distribution of each cumulative failure probability, and thus obtaining the cumulative failure rate of each experimental sample at each moment.
6. The method for reliability evaluation of a product according to claim 5, wherein the prior distribution of the cumulative failure probability, the posterior distribution of the cumulative failure probability and/or the cumulative failure rate of the experimental sample at each moment are obtained by a Bayesian estimation model.
7. The method for evaluating the reliability of a product according to claim 1, wherein the method for estimating the parameters is used to obtain the parameter values of the life distribution of the product based on the cumulative failure rate at each moment, and thereby predict the reliable life or reliability of the product, including;
constructing a loss function of the product based on the posterior estimation value of the accumulated failure rate of the experimental sample at each moment;
obtaining a distribution parameter of the product life when the loss function is minimum based on the loss function;
and obtaining the reliable service life or the reliability of the product based on the distribution parameters of the service life of the product.
8. The reliability evaluation method of a product according to claim 1, characterized in that: the lifetime data is failure data or no failure data.
9. A readable storage medium having executable instructions thereon which, when executed, cause a computer to perform the steps of the method of reliability assessment of a product according to any of claims 1-7.
10. An electronic device, characterized in that it comprises a processor and a memory in which computer program instructions are stored, adapted to be executed by the processor, the computer program instructions, when executed by the processor, performing the steps of the reliability evaluation method of the product according to any one of claims 1-7.
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