Product storage life evaluation method based on multi-stage success and failure data

Abstract

The invention provides a product storage life evaluation method based on multi-stage success and failure data, which evaluates the storage life of a product by adopting a discrete parameter algorithm according to multi-stage success and failure natural storage test data of the product, and comprises the following steps: S1, performing zero-moment failure probability distribution fitting and mean value estimation, and according to prior information and factory data, calculating a failure probability distribution value; performing fitting on zero-moment failure probability distribution by adopting beta distribution, and calculating expected mean estimation of the zero-moment failure probability distribution; s2, abnormal value screening and order-preserving processing of fusion data are carried out, multi-stage data are combined, an error threshold value is set, abnormal points are eliminated, and order-preserving processing is carried out; s3, discretizing position parameters, and carrying out Weibull parameter estimation; the interval range of the position parameters is determined, equal interval division is carried out, and corresponding translation processing is carried out on the data; and S4, life parameter selection and abnormal point consistency judgment. According to the method, multi-stage success and failure data can be fully utilized, and the product evaluation precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of product storage life assessment, and in particular to a product storage life assessment method based on multi-stage success / failure data. Background Art

[0002] At present, the life assessment of a certain product is usually carried out in two ways: the first way is to conduct random inspections on each batch of products through special tests and carry out quality monitoring, and evaluate the storage life and storage reliability of the batch products based on the results. The test sample size of this method is usually limited, and the quality monitoring parameters are vague, the standards are lacking, the method is single, and the confidence level of the evaluation results is low; the second way is to conduct a statistical evaluation of the storage life and storage reliability of batch products through user usage data. However, due to the diversity of product batches and differences in test conditions, the reasons for the failure of some samples are complex and difficult to determine, and it is impossible to directly use the existing success or failure data evaluation standards to carry out the evaluation work. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a product storage life assessment method based on multi-stage success / failure data, which integrates multiple existing success / failure data such as factory verification data, regular sampling data, user usage data and return to factory repair data for accurate life assessment.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A product storage life evaluation method based on multi-stage success-failure data, which uses a discrete parameter algorithm to evaluate the storage life of the product based on the multi-stage success-failure natural storage test data of the product. The specific evaluation process includes the following steps:

[0006] S1: Fitting and mean estimation of zero-time failure probability distribution. Based on prior information and factory data, the zero-time failure probability distribution is fitted using the β distribution, and its probability density function is:

[0007]

[0008] In the formula, p0 represents the failure probability of the sample, a, b represent the parameters in the distribution model;

[0009] And calculate its expected mean estimate, that is:

[0010]

[0011] In the formula, E(p0) represents the expectation of p0, a and b represent the parameters in the distribution model;

[0012] To improve the estimation efficiency, b is set to 1;

[0013] S2: Outlier screening and order-keeping processing of fused data: merge regular inspection data, user usage data and return maintenance data, set error threshold to eliminate outliers, and perform order-keeping processing;

[0014] S3: Discretize the location parameters and perform Weibull parameter estimation; determine the interval range of the location parameters, divide the intervals into equal intervals, and the median of the intervals is γ1,γ2,…,γ n , perform corresponding translation processing on the data, that is, the new failure time t ij =t i +γ j ; Based on the two-parameter Weibull distribution, the sample weighted least squares regression method is used for parameter estimation, and the weights are:

[0015]

[0016] In the formula, ω i represents the weight of the i-th sampling, t i represents the time of the i-th sampling inspection, n i represents the sample size of the ith random inspection, and k represents the total number of random inspections;

[0017] S4: Life parameter selection and abnormal point consistency judgment; calculation of zero-time failure probability p for each parameter combination 0i , define the index φ ij , which means that the larger the correlation coefficient is and the closer it is to the estimated point of the distribution mean at time zero, the larger the index is and the better the parameter fitting effect is; the parameter that maximizes the index is selected as the model parameter of the product storage life distribution function.

[0018] Furthermore, in step S1, the beta distribution parameters can be estimated based on prior information and discrete parameter methods; after estimating the parameters a and b, the expected mean of the zero-time failure probability can be estimated by the beta distribution properties or the Bootstrap resampling method. Used to evaluate subsequent parameter estimates.

[0019]

[0020] In the formula, μ represents the expectation of β distribution, σ 2 represents the variance of the beta distribution, a and b represent the parameters in the beta distribution;

[0021] Furthermore, the Bootstrap resampling includes the following steps:

[0022] S11: Perform multiple sampling based on the estimated parameter distribution and randomly select some samples to get the average value

[0023] S12: Take the expectation of the mean sample as the point estimate of the probability of failure at time zero

[0024] Furthermore, in step S2, the order-preserving process is to put the periodic sampling data and the user usage data together. The merged data may have an "inverted" phenomenon, and an order-preserving algorithm can be used for adjustment. The order-preserving algorithm is: if adjacent samples f in the sample i ,…,f i+l Reverse order, and record the order-preserving failure frequency value of the sample as f i * , then it satisfies:

[0025]

[0026] Where n i represents the sample size of the i-th random inspection;

[0027] Calculate the corresponding sample order-preserving failure number

[0028]

[0029] In the formula, f i * represents the order-preserving failure frequency value of the i-th sampling, n i represents the sample size of the i-th random inspection;

[0030] Furthermore, in step S3, the process of fitting the two-parameter Weibull distribution is:

[0031] S31: Linearizing the two-parameter Weibull distribution function yields:

[0032]

[0033] Where, t ij represents the sampling time after translation, p i represents the failure probability of the product at the i-th random inspection, η, m represent the scale parameter and shape parameter in the Weibull distribution respectively;

[0034] Let y i =ln t′ ij , x i =ln ln(1-p i ) -1 , μ=lnη,σ=β -1 ,but:

[0035] y i =μ+σx i +ε i (8)

[0036] In the formula, μ represents the intercept of the linearized model, σ represents the slope of the linearized model, and ε i represents the fitting residual for the i-th sampling;

[0037] For periodic sampling data, the larger the sample size of a single sampling, the higher the credibility. Therefore, weighted least squares can be used for parameter estimation, and the weight value is:

[0038]

[0039] In the formula, ω i represents the weight of the i-th sampling, t i represents the time of the i-th sampling inspection, n i represents the sample size of the ith random inspection, and k represents the total number of random inspections;

[0040] The least squares estimates of the parameters μ and σ are:

[0041]

[0042] In the formula, Represents x i The mean of Represents y i The mean of They represent the estimated values ​​of parameters μ and σ respectively, and ρ represents the correlation coefficient;

[0043] Furthermore, in step S4, the position parameter interval γ can be calculated according to the above method. i Next ρ i , and solve the zero-time failure probability p under each set of parameters 0i ,Right now:

[0044]

[0045] In the formula, γ i Indicates the currently selected position parameter, m i ,η i They are the shape parameter and scale parameter of the Weibull distribution corresponding to the currently selected location parameter;

[0046] Define the indicator φ ij is the correlation coefficient ρ i and the probability of failure at time zero p 0i The ratio of the difference between the mean estimate at time zero and the correlation coefficient is larger, and the closer to the mean point, the larger the indicator is:

[0047]

[0048] In the formula, ρ i represents the correlation coefficient, p0i represents the probability of failure at time zero, represents the estimated value of the mean probability of failure at time zero;

[0049] Select φ i The largest parameter is used as the life distribution parameter to deduce the storage life of the product:

[0050]

[0051] In the formula, They represent the location parameter, scale parameter and shape parameter of the i-th group of Weibull distribution, φ i represents the index under the i-th group of position parameters, Represents the best estimates of the location parameter, scale parameter, and shape parameter of the Weibull distribution;

[0052] After determining the optimal parameter combination, recalculate the errors of each data point in step 2 to determine the data points to be eliminated. If the data points to be eliminated twice are consistent, the algorithm is valid; otherwise, re-screen the error points.

[0053] Furthermore, the discrete parameter algorithm adopts a discrete weighted least squares regression parameter estimation method.

[0054] Furthermore, in step S1, in order to improve estimation efficiency, b is set to 1.

[0055] The beneficial effects of adopting the above technical solution are:

[0056] The present invention mainly establishes a method based on multi-stage success-failure data information, according to which the product storage life and storage reliability assessment method is used to improve the accuracy of product storage life assessment, integrates various existing success-failure data such as factory verification data, regular sampling data, user usage data and return to factory repair data to accurately assess the life, solves the difficult problems in the prior art such as the inability to directly assess the storage life, and provides a point estimate or confidence limit estimate result of the storage life. DETAILED DESCRIPTION

[0057] The present invention provides a product storage life assessment method based on multi-stage success-failure data. The main application assessment object is a long-term stored, one-time use hazardous chemical product, such as chemical products, ammunition, etc. The product storage life is assessed using a discrete parameter algorithm based on the multi-stage success-failure natural storage test data of the product. The specific assessment process includes the following steps:

[0058] S1: Fitting and mean estimation of zero-time failure probability distribution. Based on prior information and factory data, the zero-time failure probability distribution is fitted using the β distribution, and its probability density function is:

[0059] In the formula, p0 represents the failure probability of the sample, a, b represent the parameters in the distribution model;

[0060] And calculate its expected mean estimate, that is:

[0061]

[0062] In the formula, E(p0) represents the expectation of p0, a and b represent the parameters in the distribution model;

[0063] To improve the estimation efficiency, b is set to 1;

[0064] S2: Outlier screening and order-keeping processing of fused data: merge regular inspection data, user usage data and return maintenance data, set error threshold to eliminate outliers, and perform order-keeping processing;

[0065] S3: Discretize the location parameters and perform Weibull parameter estimation; determine the interval range of the location parameters, divide the intervals into equal intervals, and the median of the intervals is γ1,γ2,…,γ n , perform corresponding translation processing on the data, that is, the new failure time t ij =t i +γ j ; Based on the two-parameter Weibull distribution, the sample weighted least squares regression method is used for parameter estimation, and the weights are:

[0066]

[0067] In the formula, ω i represents the weight of the i-th sampling, t i represents the time of the i-th sampling inspection, n i represents the sample size of the ith random inspection, and k represents the total number of random inspections;

[0068] S4: Life parameter selection and abnormal point consistency judgment; calculation of zero-time failure probability p for each parameter combination 0i , define the index φ ij , which means that the larger the correlation coefficient is and the closer it is to the estimated point of the distribution mean at time zero, the larger the index is and the better the parameter fitting effect is; the parameter that maximizes the index is selected as the model parameter of the product storage life distribution function.

[0069] In step S1, the beta distribution parameters can be estimated based on prior information and discrete parameter methods; after estimating the parameters a and b, the expected mean of the zero-time failure probability can be estimated by the beta distribution properties or the Bootstrap resampling method. Used to evaluate subsequent parameter estimates.

[0070]

[0071] In the formula, μ represents the expectation of β distribution, σ 2 represents the variance of the beta distribution, a and b represent the parameters in the beta distribution;

[0072] The Bootstrap resampling includes the following steps:

[0073] S11: Perform multiple sampling based on the estimated parameter distribution and randomly select some samples to get the average value

[0074] S12: Take the expectation of the mean sample as the point estimate of the probability of failure at time zero

[0075] In step S2, the order-preserving process is to put the periodic sampling data and the user usage data together. The merged data may have an "inverted" phenomenon, and the order-preserving algorithm can be used for adjustment. The order-preserving algorithm is: if the adjacent samples f in the sample i ,…,f i+l Reverse order, and record the order-preserving failure frequency value of the sample as f i * , then it satisfies:

[0076]

[0077] Where n i represents the sample size of the i-th random inspection;

[0078] Calculate the corresponding sample order-preserving failure number

[0079]

[0080] In the formula, f i * represents the order-preserving failure frequency value of the i-th sampling, n i represents the sample size of the i-th random inspection;

[0081] In step S3, the process of fitting the two-parameter Weibull distribution is as follows:

[0082] S31: Linearizing the two-parameter Weibull distribution function yields:

[0083]

[0084] Where, t ij represents the sampling time after translation, p i represents the failure probability of the product at the i-th random inspection, η, m represent the scale parameter and shape parameter in the Weibull distribution respectively;

[0085] Let y i= lnt′ ij , x i =lnln(1-p i ) -1 , μ=lnη,σ=β -1 ,but:

[0086] y i =μ+σx i +ε i (8)

[0087] In the formula, μ represents the intercept of the linearized model, σ represents the slope of the linearized model, and ε i represents the fitting residual for the i-th sampling;

[0088] For periodic sampling data, the larger the sample size of a single sampling, the higher the credibility. Therefore, weighted least squares can be used for parameter estimation, and the weight value is:

[0089]

[0090] In the formula, ω i represents the weight of the i-th sampling, t i represents the time of the i-th sampling inspection, n i represents the sample size of the ith random inspection, and k represents the total number of random inspections;

[0091] The least squares estimates of the parameters μ and σ are:

[0092]

[0093] In the formula, Represents x i The mean of Represents y i The mean of They represent the estimated values ​​of parameters μ and σ respectively, and ρ represents the correlation coefficient;

[0094] In step S4, the position parameter interval γ can be calculated according to the above method. i Next ρ i , and solve the zero-time failure probability p under each set of parameters 0i ,Right now:

[0095]

[0096] In the formula, γ i Indicates the currently selected position parameter, m i ,η i They are the shape parameter and scale parameter of the Weibull distribution corresponding to the currently selected location parameter;

[0097] Define the indicator φ ij is the correlation coefficient ρ i and the failure probability p at time zero 0i The ratio of the difference between the mean estimate at time zero and the correlation coefficient is larger, and the closer to the mean point, the larger the indicator is:

[0098]

[0099] In the formula, ρ i represents the correlation coefficient, p 0i represents the probability of failure at time zero, represents the estimated value of the mean probability of failure at time zero;

[0100] Select φ i The largest parameter is used as the life distribution parameter to deduce the storage life of the product:

[0101]

[0102] In the formula, They represent the location parameter, scale parameter and shape parameter of the i-th group of Weibull distribution, φ i represents the index under the i-th group of position parameters, Represents the best estimates of the location parameter, scale parameter, and shape parameter of the Weibull distribution;

[0103] After determining the optimal parameter combination, recalculate the errors of each data point in step 2 to determine the data points to be eliminated. If the data points to be eliminated twice are consistent, the algorithm is valid; otherwise, re-screen the error points.

[0104] The discrete parameter algorithm adopts a discrete weighted least squares regression parameter estimation method.

[0105] The following are specific application examples of the present invention:

[0106] The control cabin of a certain type of product has multi-stage success and failure data during its service life (including factory acceptance data, regular inspection data, usage data and maintenance data). The natural storage life assessment result of the control cabin of this type of product is given by using a storage life assessment method based on the fusion of multi-stage success and failure data during the service period.

[0107] The multi-stage success and failure data of the control cabin of this type of product during its service life include:

[0108] Table 1 Product control cabin factory acceptance data

[0109]

[0110]

[0111] Table 2 Product control cabin regular inspection data

[0112] Storage time (year) Total number of samples Number of failures Failure rate 15 18 9 0.50 14 78 32 0.41 13 119 62 0.52 12 54 37 0.69 9 50 10 0.20

[0113] Table 3 Product control cabin user usage data

[0114]

[0115]

[0116] Table 4 Product control cabin return repair data

[0117] Storage life Number of samples tested Number of failures Failure rate 14 42 4 0.095 15 38 1 0.026 12 60 2 0.033 15 8 1 0.125 13 150 2 0.013 13 66 3 0.045 15 6 1 0.167

[0118] Since there are many factory inspection batches and there are differences between batches, other types of data are roughly the same. It is assumed that the failure rate of each factory inspection data follows a specific distribution, and the zero-time prior distribution is fitted. The other data are merged and processed to fit the life distribution. The fitted life distribution is evaluated according to the zero-time distribution, so as to select the optimal distribution type and optimal distribution parameters. According to the factory data of the product control cabin, it can be known that the control cabin has the possibility of failure when it leaves the factory. Assuming that the failure probability at the factory follows the β distribution, the fitting parameters based on the factory data are a=0.02, b=1, and the mean failure probability at zero time is estimated to be E(p0)≈0.0196. Since the scheduled inspection data and the usage data are reduced in time, the time scale can be increased by 0.5 years to improve the accuracy. The fused failure data is as follows:

[0119] Table 5 Fusion results of product control cabin inspection data and usage data

[0120] Serial number time Number of samples Number of failures Failure rate 1 0.5 29 1 0.03 2 1.5 41 5 0.12 3 2.5 14 5 0.36 4 3.5 49 2 0.0408 5 4.5 26 3 0.1154 6 5.5 38 13 0.3421 7 6.5 59 12 0.2034 8 7.5 22 6 0.2727 9 8.5 18 7 0.3889 10 9.5 90 20 0.2222 11 10.5 28 9 0.32 12 11.5 19 7 0.3684 13 12.5 123 39 0.3171 14 13.5 335 67 0.2000 15 14.5 120 36 0.3000 16 15.5 70 12 0.1714

[0121] Next, we make adjustments for the Weibull distribution and lognormal distribution, respectively, establish a three-parameter distribution model that takes into account the influence of initial values, and select the optimal distribution type and distribution parameters based on the evaluation results.

[0122] For the three-parameter Weibull distribution, the initial parameters are selected from the MLE estimation results. The data points are screened by calculating the fitting error, and the remaining data are processed to preserve the order. The results are as follows:

[0123] Table 6 Weibull distribution parameter estimation results after abnormal data screening and order preservation

[0124]

[0125]

[0126] For the three-parameter lognormal distribution, the initial parameters are selected from the MLE estimation results. The data points are screened by calculating the fitting error, and the remaining data are processed to preserve the order. The results are as follows:

[0127] Table 7 Estimation results of lognormal distribution parameters after abnormal data screening and order preservation

[0128] Positional parameters Shape parameters Size parameters Zero time probability 0 4.479 2.772 0.000 0.1 4.427 2.689 0.006 0.2 4.345 2.550 0.010 0.3 4.254 2.387 0.011 0.4 4.165 2.218 0.011 0.5 4.085 2.052 0.010 0.6 4.017 1.894 0.008 0.7 3.960 1.745 0.007 0.8 3.915 1.607 0.005 0.9 3.881 1.480 0.004 1 3.857 1.364 0.002

[0129] The weighted sum of the vertical distance samples from the fitting data points to the fitting curve is used as the evaluation index, that is:

[0130]

[0131] Among them, w i is the sample size weight, p i is the failure data of the corresponding point, is the fitting failure data at the corresponding moment. The following comparison results can be obtained:

[0132] Table 8 Product control cabin evaluation result error

[0133]

[0134] Therefore, according to the WME index, it can be judged that the log-normal distribution based on the discrete parameter method is most effective in evaluating multi-stage storage life data. At this time, the reliable life corresponding to the reliability of 0.8 is 9.11 years.

[0135] The present invention mainly establishes a method based on multi-stage success-failure data information, according to which the product storage life and storage reliability assessment method is used to improve the accuracy of product storage life assessment, integrates various existing success-failure data such as factory verification data, regular sampling data, user usage data and return to factory repair data to accurately assess the life, solves the difficult problems in the prior art such as the inability to directly assess the storage life, and provides a point estimate or confidence limit estimate result of the storage life.

[0136] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A product storage life assessment method based on multi-stage success / failure data, characterized in that: It uses a discrete parameter algorithm to evaluate the storage life of products based on the product's multi-stage success-failure natural storage test data. The specific evaluation process includes the following steps: S1: Fitting and mean estimation of zero-time failure probability distribution. Based on prior information and factory data, the zero-time failure probability distribution is fitted using the β distribution, and its probability density function is: In the formula, p0 represents the failure probability of the sample, a, b represent the parameters in the distribution model; And calculate its expected mean estimate, namely: In the formula, E(p0) represents the expectation of p0, a and b represent the parameters in the distribution model; S2: Outlier screening and order-keeping processing of fused data: merge regular inspection data, user usage data and return maintenance data, set error threshold to eliminate outliers, and perform order-keeping processing; S3: Discretize the location parameters and perform Weibull parameter estimation; determine the interval range of the location parameters, divide the intervals equally, and the median of the intervals is γ1,γ2,…,γ n , perform corresponding translation processing on the data, that is, the new failure time t ij =t i +γ j ; Based on the two-parameter Weibull distribution, the sample weighted least squares regression method is used for parameter estimation, and the weights are: In the formula, ω i represents the weight of the i-th sampling, t i represents the time of the i-th sampling inspection, n i represents the sample size of the ith random inspection, and k represents the total number of random inspections; S4: Life parameter selection and abnormal point consistency judgment; calculation of zero-time failure probability p for each parameter combination 0i , define the index η ij , which means that the larger the correlation coefficient is and the closer it is to the estimated point of the distribution mean at time zero, the larger the index is and the better the parameter fitting effect is; the parameter that maximizes the index is selected as the model parameter of the product storage life distribution function.

2. A product storage life assessment method based on multi-stage success / failure data according to claim 1, characterized in that: In step S1, the beta distribution parameters can be estimated based on prior information and discrete parameter methods; after estimating the parameters a and b, the expected mean of the zero-time failure probability can be estimated by the beta distribution properties or the Bootstrap resampling method. Used to evaluate subsequent parameter estimates. In the formula, μ represents the expectation of β distribution, σ 2 represents the variance of the beta distribution, and a and b represent the parameters in the beta distribution.

3. A product storage life assessment method based on multi-stage success / failure data according to claim 2, characterized in that: The Bootstrap resampling includes the following steps: S11: Perform multiple sampling based on the estimated parameter distribution and randomly select some samples to get the average value S12: Take the expectation of the mean sample as the point estimate of the probability of failure at time zero 4. A product storage life assessment method based on multi-stage success / failure data according to claim 2, characterized in that: In step S2, the order preservation process is to put the periodic sampling data and the user usage data together. The merged data may have an "inverted" phenomenon, and the order preservation algorithm can be used for adjustment. The order preservation algorithm is: if the adjacent samples in the sample f i ,…,f i+l Reverse order, and record the order-preserving failure frequency value of the sample as f i * , then it satisfies: Where n i represents the sample size of the i-th random inspection; Calculate the corresponding sample order-preserving failure number In the formula, represents the order-preserving failure frequency value of the i-th sampling, n i represents the sample size of the i-th random inspection.

5. The product storage life assessment method based on multi-stage success / failure data according to claim 2, characterized in that: In step S3, the process of fitting the two-parameter Weibull distribution is as follows: S31: Linearizing the two-parameter Weibull distribution function yields: Where, t ij represents the sampling time after translation, p i represents the failure probability of the product at the i-th random inspection, η, m represent the scale parameter and shape parameter in the Weibull distribution respectively; Let y i = lnt i ' j ,x i = lnln(1 - p i ) -1 ,μ = lnη,σ = β -1 ,then: y i =μ+σx i +e i (8) In the formula, μ represents the intercept of the linearized model, σ represents the slope of the linearized model, and ε i represents the fitting residual for the i-th sampling; For periodic sampling data, the larger the sample size of a single sampling, the higher the credibility. Therefore, weighted least squares can be used for parameter estimation, and the weight value is: In the formula, ω i represents the weight of the i-th sampling, t i represents the time of the i-th sampling inspection, n i represents the sample size of the ith random inspection, and k represents the total number of random inspections; The least squares estimates of the parameters μ and σ are: In the formula, Represents x i The mean of Represents y i The mean of They represent the estimated values ​​of parameters μ and σ respectively, and ρ represents the correlation coefficient.

6. A product storage life assessment method based on multi-stage success / failure data according to claim 5, characterized in that: In step S4, the position parameter interval γ can be calculated according to the above method. i Next ρ i , and solve the zero-time failure probability p under each set of parameters 0i ,Right now: In the formula, γ i Indicates the currently selected position parameter, m i ,η i They are the shape parameter and scale parameter of the Weibull distribution corresponding to the currently selected location parameter; Define the indicator φ ij is the correlation coefficient ρ i and the probability of failure at time zero p 0i The ratio of the difference between the mean estimate at time zero and the correlation coefficient is larger, and the closer to the mean point, the larger the indicator is: In the formula, ρ i represents the correlation coefficient, p 0i represents the probability of failure at time zero, represents the estimated value of the mean probability of failure at time zero; Select φ i The largest parameter is used as the life distribution parameter to deduce the storage life of the product: In the formula, They represent the location parameter, scale parameter and shape parameter of the i-th group of Weibull distribution, φ i represents the index under the i-th group of position parameters, Represents the best estimates of the location parameter, scale parameter, and shape parameter of the Weibull distribution; After determining the optimal parameter combination, recalculate the errors of each data point in step 2 to determine the data points to be eliminated. If the data points to be eliminated twice are consistent, the algorithm is valid; otherwise, re-screen the error points.

7. A product storage life assessment method based on multi-stage success / failure data according to claim 1, characterized in that: The discrete parameter algorithm adopts a discrete weighted least squares regression parameter estimation method.

8. The product storage life assessment method based on multi-stage success / failure data according to claim 1, characterized in that: In step S1, to improve estimation efficiency, b is set to 1.

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