Statistical Analysis Of Accelerated Life Test Under Mixed Distribution

Accelerated life test is a very important test method in the test of product reliability evaluation,and life information of products can be obtained as early as possible by testing.In practice,a product failure may be caused by various failure mechanisms,and the probability of various failure mechanisms is also different.The mixed distribution can better describe the complexity and the multicause of failure mechanism of such products,and its theoretical research is more practical.The accelerated life test under mixed distribution is mainly studied in this paper.The main contents are as follows:1.In selecting the acceleration model,the corresponding acceleration model is selected for the life characteristics of the mixed distribution.In this paper,the mean life of the mixed distribution is chosen as the life characteristic of the accelerated model,that is,the Arrhernius model is satisfied between the mean life?_i and the applied stress level S_i?i?28?,1,0?43?,k?.2.When the product has multiple failure mechanisms,the life distribution of the product is assumed to be a mixed distribution,and each sub distribution in the mixed distribution comes from different distribution families.In this paper,we choose the exponential distribution and weibull distribution as the sub distribution of the mixed distribution,that is,the life distribution of the product is the mixed exponential-weibull distribution,and the mixed weight in the mixed distribution is kept constant.Under the assumption of the accelerated life test,the statistical analysis of the constant stress accelerated life test and the step stress accelerated life test under the mixed distribution was carried out,and set up the basic model of the corresponding statistical analysis.When the test data is censored,the maximum likelihood estimation is used to estimate the unknown parameters in the model,and the optimal solution of the parameter estimation is obtained by the gradient descent method.Finally,the feasibility and effectiveness of the proposed method is verified by multiple numerical simulations.And the reliability function of the product under the normal stress level is obtained.3.After obtaining the estimated value of the parameters,we need to determine the value of?₀ and?₀ under the normal stress level.In order to determine the value of?₀ and?₀ under normal stress level,we also select characteristic life as the life characteristic of acceleration model.That is to say,the Arrhernius model is satisfied between the characteristic lifet_0iand the applied stress levelS_i?i?28?,1,0?43?,k?,and the two acceleration models can be combined to determine the value of?₀ and?₀.4.When generating random numbers of mixed distribution,constant stress accelerated life test generates random numbers by the mixed distribution.But the step stress accelerated life test generates random numbers by the remaining life distribution of mixed distribution,and the time conversion formula under different stress levels is needed to obtain the real life data under the corresponding stress level.Here,the data is converted by the cumulative failure hypothesis,and the real life data of the product at the stress level are obtained.