Bayesian Accelerated Life Testing

In this paper a Bayesian approach for accelerated life testing will be considered. It will be assumed that the failure times at the different stress levels follow a Weibull distribution and exponential distribution, respectively. In accelerated life tests, the components are exposed to an environment that is more severe that the usual environment, such that the components will fail in a shorter than usual period of time. The failure information is then transformed through an accelerated model to predict the reliability under normal operating conditions. The power law model will be used. This accelerated life testing model is typically used when the accelerated stress is non-thermal. Inference for the model will be discussed, and results can be obtained by using Markov chain Monte Carlo (MCMC) methods. Keywords: Accelerated life testing; Bayesian inference; Exponential distribution; Weibull distribution. 1 Introduction In this paper we will consider a Bayesian approach to accelerated life testing for the power law model using the Weibull distribution and the exponential distribution, respectively, as the life distributions. Mazzuchi et al. (1997) considered a Bayesian approach for inference from accelerated life tests when the underlying life model is Weibull, using the power law. Their approach is based on the linear model framework by West et al. (1985). Singpurwalla et al. (1975) obtained least squares estimators of the parameters of the generalized Eyring model, where the life model is exponential. Chaloner & Larntz (1992) studied an experimental design for accelerated life tests where the life times were either lognormal distributions or Weibull distributions, using a Bayesian approach. Van Dorp & Mazzuchi (2005) developed a general Bayes inference model for accelerated life testing, where the failure times at a constant stress level were assumed to belong to a Weibull distribution, but the specification to a parametric time-transformation function is not required. They used prior information to indirectly define a multivariate prior distribution for the scale parameters at the different stress levels. Most modern products are designed to operate without failure for years, thus few units will fail in a test of practical length at normal use conditions. For such applications, ALTs are used in manufacturing industries to assess reliability, see Escobar & Meeker (2006) for further discussion. Erkanli & Soyer (2000) introduced a simulation-based design for accelerated life tests, where they considered an exponential life model with the power law as the time transformation function, using Monte Carlo approaches. This paper will extend on the work done by Erkanli & Soyer (2000), and focus on an objective Bayesian approach for the exponential model and a simulation based approach for the Weibull model. 2 The Model 2.1 Exponential Model We assume that life length is exponential with failure rate , denoted by ( ) with probability density function given by ( ) * + where and is the failure rate at the accelerated stress environment, Si. In this paper we will make use of the power law. The relationship between the failure rate and the stress level in the i th testing environment will then be
 , where and are the model parameters to be determined. This implies ( ) and the density is given by Proceedings 2nd ISI Regional Statistics Conference, 20-24 March 2017, Indonesia (Session CPS09)