Competing risk models in reliability systems, a gamma distribution model with bayesian analysis approach

Abstract

Abstract. In this paper our effort is to introduce the basic notions that constitute a competing risks models in reliability analysis using Bayesian analysis approach with Gamma distribution as our model and presenting their analytic methods. The Gamma distribution is widely used in reliability analysis and it is known as an natural extension of the exponential distribution. The cases are limited to the models with independent causes of failure, only the scale parameter is a random variable, and uniform prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.