Statistical Analysis Based On Degradation Failure Model

This paper mainly focuses on the the degradation failure model in reliability statis-tics. It aims to model the degradation path with Wiener Process and analyze the results derived from the model. The model with a random degradation rate and the estimation method of its parameters are provided.The present research state of the degradation failure model and the definitions of Wiener process, as well as its main properties, are discussed in the fore two sections of Chapter 1. The work of the author is expounded in the last section of this chap-ter. Chapter 2 gives the degradation model based on the Wiener process under normal stress and the maximum likelihood estimate(MLE) of the parameters. Besides these, the advantage of estimating the parameters with compound data (i.e.both failure data and degradation data), comparing with the estimation with the failure data only under the rule with minimum mean square errors (MSE), is proved. Chapter 3 considers the degradation failure model and the MLE of the parameters of the model with constant degradation rate under the constant accelerated stress. Furthermore, the estimation of the probability density function of the product's life, of which the degradation rate is a constant, is calculated. Since the likelihood equations of the model, which has a random degradation rate, does not have analytical resolutions, the paper takes the posterior mean as the estimation of the parameters by the use of Win BUGS to do Gibbs sampling. At last the estimation of the probability density function of the product's life is given. In chapter 4 the degradation failure model and the estimation of the parameters under the step stress accelerated test are considered.The main work of this paper is to extend the applicable range of the degradation fail-ure model, which is modeled by the Wiener Process, through generalizing the degradation rate from a constant to a variable.