Confidence Bands for the Reliability Function of a Two-Parameter Exponential Model

This paper considers the problem of constructing confidence bands for the reliability function of a two-parameter exponential distribution, which is widely used in reliability analysis. Both two-sided confidence bands and lower and upper one-sided confidence bands are considered with an exact confidence level. These confidence bands allow simultaneous inferences at the specified confidence level for all points on the reliability function. They also allow simultaneous inferences for all quantiles of the reliability function. The confidence bands are generated from an exact confidence set for the two parameters of the exponential distribution. Optimal minimum area confidence sets are derived for the two-sided case. These methodologies are applicable for a complete data set or a data set with type II censoring, and they are illustrated with some examples.