Bayesian Estimate of System Reliability

A Bayesian estimate of reliability for each component in the system of n-components, each exponentially distributed, is developed which utilizes the basic notion of loss in estimation theory. Here we assume that each component is independently dis­tributed. In reliability estimation, the loss associated with over­estimation is usually greater than the loss associated with under­estimation; and hence loss function can be a very useful tool. The prior distribution and loss function of reliability considered in this paper are flexible to be compatible with other situations in which reliability estimates are required. When the loss function is symmetric and no prior information is at hand, the resulting estimate is approximately the minimum variance unbiased estimate of reliability