Statistical Inference And Applications For Accelerated Life Test With GP Model For Weibull Distribution

In statistical analysis of reliability,accelerated life test(ALT)is the most common and important method to evaluate the life of electronic products.Such experiment transforms the reliability information obtained beyond the normal stress level by using an acceleration model with certain failure rules.Furthermore,it can obtain reliability information of components at a given stress level.In this paper,on the basis of summarizing the existing research,the geometric process theory is introduced for the first time to design a constant stress accelerated life test.Weibull-constant stress acceleration model is established based on three different censoring types.In this model,the monotonicity of the hazard function is determined by the shape parameter,describing the whole life cycle of products.Scale parameters are important variables reflecting life characteristics and are the focus of inference.Geometric process theory,based on the idea of degraded system,is quite perfect in the field of reliability maintenance.Its ratio coefficient can well describe a series of failure time data with trend.When studying the lifetime of products,the maximum likelihood equation is constructed and the approximate solution is obtained by Newton iteration method.Asymptotic confidence interval in GP is derived on the asymptotic normality and invariance of the estimator.There are only very slight differences comparing bootstrap interval and asymptotic confidence interval.It is proved that the model proposed in this paper is correct and effective from the perspective of parameter estimation results.Secondly,Monte-Carlo numerical simulation evaluates the finite sample properties of the estimator.The results show that the estimated value fits well with the real value,and the accuracy of this method is high.After that,hypothesis testing further proves that the random numbers of numerical simulation meet the geometric process theory.At this point,the rationality of the model is proved by numerical calculation.Then the paper introduces two classical acceleration models and expounds the relationship between them and geometric process theory through mathematical derivation.This proves that the geometric process model is simple and efficient from a theoretical point of view.Finally,the paper demonstrates that the geometric process theory accords with the traditional acceleration model.The performance of the geometric process model is compared with that of the traditional accelerated failure-time regression model by numerical examples.The results show that it is reasonable to introduce the geometric process theory into the acceleration test,and its performance seems to be better than the traditional acceleration model.At the end of this paper,the empirical analysis of a certain type of electronic products are discussed under three different schemes.The estimated value of shape parameter is very close to the experience value of practical engineering application.Moreover,the estimation of scale parameters is slightly different from that of traditional accelerated test.