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Bayes analysis of accelerated life test design and the TFR model under the geometric distribution

Author: JinYing
Tutor: TangYinCai
School: Shanghai Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Geometric distribution optimal design TFR model Bayesian estimation
CLC: O213
Type: Master's thesis
Year: 2006
Downloads: 127
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Abstract


With the development of science technology and economy, accelerated life-testing(ALT) and the optimum design are recieved more and more care. The geometric distribution is one of the better known discrete probability distributions and has many useful applications. Its applications include in the fields of information engineering, electronics industry, theory of controls and economic, etc. Then the optimum design and analysis of ALT under geometric distribution are more useful in practice. In this dissertation, the problems are solved as follows :1. According to the local optimum design of single variable ALT, first it is discussed that how to set up accelerated equation. On the basis, an optimum test plan is explored by minimizing the asymptotic variance of the maximum likelihood estimates of the life. the optimal simple constant-and step-stress ALT with type-I censoring are given; the optimal simple constant -and step-stress ALT with type-II censoring are discussed.The plans are proved effective through the examples.2. The Bayes analysis of the geometry TFR model for ALT are solved. First the estimation of completed samples and censored samples in two step-stress test are studied, then the estimation of censored samples under restraint condition and under no restraint condition in n step-stress test are discussed. Those estimates are proved optimum by using the examples, moreover, it is proved that the estimation under restraint condition is more precise than the estimation of no restraint condition.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Application of statistical mathematics
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