Statistical Inference Of Exponential Distribution Under The Condition Of Multiply Type-I Censoring

With the development of science and technology, the people attach more and moreimportance to the reliability of production. Because the life of the production is a stochasticphenomenon, it comes to a statistical inference problem that we try to determine thereliability indexes of the production. In order to make clear the life distribution of theproduction measured and solve the indexes of reliability and study the invalid mechanismof the production to give some pieces of advice about improving the reliability of theproduction,we ofen have to make the life experiment .The life experiment is separated intotwo kinds:complete life experiment and "cutting tail"experiment,but the later one is usedwidely. When we deal with the practical problem by the statistical methods, we oftenencounter the trouble about missing data. For example,during the experiment on the life ofproduction ,some data of experiment are missed or unobserved owing to the equipment ofexperiment and observation means or other difficulties. So we get "missing data". It is notworth and unable to make the experiment again as the result of the parts of missing data. It is a special and more difficult question how to analyse statistically about the existingdata after "missing data". So it is becoming a new and important field on the reliabilityanalysis how to research a scientific and effective statistical analysis to deal with theuncomplete data under the condition of missing data. Owing to study the sample after "missing data" primarily in the aspects of type –IIcensoring. The paper tries to use its basic theories and methods to study the statisticalinference for exponential distribution under type-I censoring. Under the condition of multiple type-I censoring , the trust that people infer the indexof reliability of production if only according to the information of the left data isinfluenced . So we can derive the Bayesian estimation for the average life θ after making IIuse of a priori information ,but it is difficult because the likelihood function of exponentialdistribution under multiple type-I censoring is too complex .For the simplicity ofcomputation, this paper tries to derive an approximation for the likelihood function. Thendiscusses the point estimation and interval estimation for the parameter of the sampledistribution.At last discusses the existance and uniqueness of MLE of the parameter underthe condition of the constant stress accelerated life testing...