In Accelerated Life Testing (ALT), a product is subjected to higher stress levels to induce failures more quickly than the normal condition. Statistical models are then fitted to the ALT data to develop life-stress relationship and the results obtained are then extrapolated to estimate the characteristic of lifetime distribution at normal operating condition. Though there is considerable amount of literature available on ALT involving competing risks of failure, the literature on Bayesian approach of analysis of ALT data involving competing risks is sparse. The Bayesian approach of analysis is particularly well suited to the small sample data usually generated by an ALT.

In the first part of the thesis, a Bayesian framework for ALT will be developed involving multiple stresses. The model will be developed incorporating independent competing risks of failure. Bunea and Mazzuchi (Journal of Statistical Planning and Inference, 2006) have developed the Bayesian framework in the competing risk set up assuming the failure time due to a specific risk follows exponential distribution. In this research, first the Bayesian analysis will be performed under the assumption that the time to failure due to a specific risk follows Weibull distribution. Bayesian analysis proceeds by selecting normal distributions as the prior distribution of the model parameters. Standard Markov Chain Monte Carlo Methods (MCMC) like Metropolis-Hastings algorithm with a suitable proposal density and Gibbs sampling will be applied appropriately to infer about the posterior distribution of the model parameters.

Next, the Bayesian inference framework will be developed assuming the time to failure due to a specific risk follows log-normal distribution. Later, the inference scheme will be extended to the case when the time to failure due to some risks will be assumed to follow Weibull distribution, while for the rest of the risks, it will be assumed to follow log-normal distribution. This would lead to the problem of Bayesian Model selection when the failure time distribution of a component can have either the Weibull distribution or log-normal distribution. The appropriate model will be chosen by calculating Intrinsic Bayes Factor (IBF) following Berger and Pericchi (Journal of American Statistical Association, 1996). The IBF is the geometric mean of the Bayes Factor calculated over all possible training samples. For calculating the Bayes Factor, the methodology presented by Carlin and Chib (Journal of Royal Statistical Society, Series B,1995) will be utilised.

In the final part of the thesis, construction of optimal Bayesian designs will be taken up for planning accelerated life tests with multiple stresses. Zhang and Meeker (Technometrics, 2006) have discussed Bayesian methods for planning accelerated life tests with single stress in the presence of one failure mode. The methods will be extended to the competing risk set up involving multiple stresses.