Reliability inference and sample-size determination under double censoring for some two-parameter models

Assuming that some extreme sample values have been censored or discarded, a reliability analysis of several two-parameter models, as the exponential, Pareto and power-function laws, is presented. Explicit expressions for the distribution, density and moments of the natural generalized pivot of the true reliability are deduced. Its asymptotic normality is also shown. Reliability point estimates are derived by selecting summary features of the pivotal quantity. Reliability confidence limits, which are shown to provide exact coverage probabilities, are readily found by solving simple nonlinear equations. Quite accurate approximate limits are given in closed forms. In addition, a procedure for determining confidence intervals of shortest length is proposed. Reliability tests, which are carried out using generalized pp-values, satisfy the conventional repeated-sampling property. Minimum sample sizes and decision rules of optimal reliability demonstration plans, which accept good (bad) products with a certain high (low) probability, are obtained via iterative methods. A numerical example is included for illustrative purposes.