This paper considers a competing risk model for a one-shot device testing analysis under an accelerated life test setting. Due to the consideration of competing risks, the joint posterior distribution becomes quite complicated. The Metropolis-Hastings sampling method is used for the estimation of the posterior means of the variables of interest. A simulation study is carried out to assess the Bayesian approach with different priors, and also to compare it with the EM algorithm for maximum likelihood estimation. Finally, an example from a tumorigenicity experiment is presented.