Bilateral Censored Exponential Distribution Of The Statistical Analysis

For the life test, the current discussion are mainly concentrated in type-Ⅰcensoring and type-Ⅱcebsoring, but the discussion on doubly Censored data are less. Complete sample case and the type-Ⅰcensoring and type-Ⅱcebsoring are special circumstances of doubly censoring. This paper discuss systematically the estimateon of parameters of exponential distribution based on doubly type-Ⅰcensoring and doubly type-Ⅱcebsoring. I also introduce the doubly censoring into the constant stress accelerated life test,These results can be further extended to other kinds of accelerated life tests such as step-stress accelerated life test.The first part of this paper introduce the mathematical definition of doubly censoring and symbols used in the latter chapters . introduced two basic assumptions of the constant stress accelerate-d life test.The second part derive the MLE (2.3) of failure rate, Bayesian estimation (2.12) and (2.13), interval estimation(2.4) of average life Under doubly type-ⅡCensoring. It also derive the MLE (2.15) of reliability ,Bayesian estimation (2.16) and (2.17), moment estimation(2.19) Under doubly type-ⅠCensoring.The third part introduce the doubly Censoring into constant stress life test. I derive the maximum likelihood estimate (3.3) (3.4) and linear estimation (3.7) (3.10)of parameters in the accelerating equation under both doubly type-Ⅰcensoring and doubly type-Ⅱcensoring .I derived the Bayesian estimation (3.16) based on constrained failure rate method and (3.27) based on accelerated factor method.Part four does a lot of random simulation. Matlab program are attached for readers' reference. Except the interval estimation of the second chapter of and the mle estimation of the third chapter, other results of this paper have been simulated. I calculate the relative mean square error. Since the relative mean square error are calculated in the area of 10^-2 , it confirmed the results above is feasible.