The Prediction Study Based On CSALT

With the advent of the digitalization of information and the era of mechanization,the similar products of different producers,especially smart phones,tablet computers and other high-tech products,the competition between products with high elimination rate is gradually heating up,people's requirements for product quality are getting higher and higher.Therefore,research on the reliability of products has also received extensive attention.At present,many smart products are being updated faster and faster,and people need a clear understanding of the lifespan of their products.In this era,the traditional life test has been cannot keep up with the pace of the times,so the accelerated life test is often used to evaluate the reliability characteristics of reliable life products.For manufacturers,you need to understand the reliability of the product,but also need to understand the service life under normal conditions.This has played an important role in the development of warranty and maintenance plans.As a result,research on accelerated life testing,especially forecasting,has received increasing attention.Firstly,in the case of the product accelerated by the Gamma distribution under the constant accelerated life test of the complete sample,in the case of point estimation,the maximum likelihood estimate for the unknown parameter exists under certain conditions,And an alternative estimate of the parameters is proposed.Through the simulation calculation,the deviation and the mean square error of the parameter estimation values calculated by the two estimation methods are compared,and the maximum likelihood estimation and the alternative estimation are compared.The alternative estimation is considered to be superior to the maximum likelihood estimation.In terms of interval estimation,based on the maximum likelihood estimation,the Fisher information matrix of unknown parameters is calculated,and the Wald confidence interval of unknown parameters is constructed.At the same time,based on the alternative estimation and Cornish-Fisher expansion,the approximate interval estimation of the shape parameters is constructed,and then the generalized confidence interval of other parameters of the acceleration model and the prediction interval of product life under the normal stress level are inferred.The simulation calculation is carried out,and the generalized confidence interval proposed above is better than the Wald interval.Finally,the proposed method is illustrated by practical examples.Secondly,in this paper,in view of the exponential distribution of product life,in the constant accelerated life test of type II censor,the statistics and generalized pivot quantity of product failure time under normal stress level are studied.According to the approximate distribution of the statistic and the generalized pivot quantity,the approximate prediction interval and the generalized prediction interval are respectively given.At the same time,the two prediction intervals are compared by simulation calculation,and the generalized prediction interval is obtained in the case of small samples using the approximate prediction interval in the case of large samples.In the research of constant acceleration life test of type I censor,the statistics of product failure time under normal stress level are constructed.Based on the approximate distribution of the statistic,the approximate prediction interval of failure time is inferred and calculated by simulation.The interval coverage and the average interval length show that the method is simple and feasible even in the case of small samples.The research on the above two types of censoring is explained by practical examples.Finally,when the product life is subject to the Weibull distribution,this paper studies the product failure time prediction problem under the normal stress level of the constant accelerated life test based on the type II censor.Based on the previous studies,this paper gives the function containing the shape parameters,and inversely solves the estimated values of the shape parameters according to the characteristics of the distribution of the function and the unknown parameters.At the same time,according to the estimated value of the shape parameters,the generalized pivot quantity of the acceleration model coefficient is constructed.Then,according to the estimated value of the shape parameter and the generalized pivot quantity,the generalized pivot quantity of the product failure time under normal stress level is inferred and the prediction interval is constructed.Also,through simulation calculations,it is concluded that the generalized prediction method used in this paper is still very good even in the case of finite samples.Finally,the proposed method is illustrated by practical examples.