Optimal designs for inspection times of interval-censored data

Abstract

We treat optimal equidistant and optimal non-equidistant inspection times for interval-censored data with exponential distribution.We provide in particular a recursive formula for calculating the optimal non-equidistant inspection times which is similar to a formula for optimal spacing of quantiles for asymptotically best linear estimates based on order statistics. This formula provides an upper bound for the standardized Fisher information which is reached for the optimal non-equidistant inspection times if the number of inspections is converging to infinity. The same upper bound is also shown for the optimal equidistant inspection times. Since optimal equidistant inspection times are easier to calculate and easier to handle in practice, we study the efficiency of optimal equidistant inspection times with respect to optimal nonequidistant inspection times. Moreover, since the optimal inspection times are only locally optimal, we provide also some results concerning maximin efficient designs.