Two-parameter Exponential Distribution Reliability

Two-parameter exponential distribution is an important distribution in reliability engineering. It is studied because it is useful in theory and in practice. In this dissertation, two-parameter exponential distribution is discussed and problems are solved as follows:1.Under Type- II doubly censored, We give Bayesian estimation of parameters and index of reliability from two-parameter exponential distribution. We give a numerical example to simulate and the result indicates that the method in this paper is feasible.2. The two-parameter exponential distribution is proposed to be the underlying model, and prediction bounds for future observations are obtained using Bayesian approach. Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type II doubly censored samples. A numerical example is given to illustrate the procedures, and prediction intervals are investigated via Monte Carlo method, and the accuracy of prediction intervals is shown.3. The statistical analysis of reliability growth tests under two-parameterexponential distribution. A point estimate and lower confidence bound of reliability of current period were given. The effect of simulation suggested that the method is simple, so it is convenience in reliability engineering.4. JM model—a famous model for software reliability was improved. A necessary and sufficient condition has been given for existence of the maximum likelihood estimation of the parameters in the modified JM model Based on the article of Chen Jiading. The lower limit of reliability and it's computational method were derived of the new model. In the end, numerical simulation was given, the method of the paper is simple and is convenience in reliability engineering.