An Exact Lower Confidence Bound for the Reliability of a Series System Where Each Component has an Exponential Time to Failure Distribution

Consider a complex system consisting of several components in series. The system as a whole is either impossible or too expensive to test. The only data available are the times to failure of the components when tested individually. Based on these data an exact lower confidence bound for the reliability of the system is obtained. Initially, the method is developed for the case when the components are independent. Later the method has been extended to the case when the components are dependent and have multivariate exponential time to failure distribution. The sampling method considered is type II censoring of r out of n with or without replacement. An asymptotically smallest confidence interval has also been developed.