Date of Award
Master of Science (MS)
Mathematics and Statistics
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.
Shah, Naresh, "Bayesian Estimate of System Reliability" (1970). All Graduate Plan B and other Reports. 1141.