Weibull accelerated life testing with unreported early failures

Situations arise in life testing where early failures go unreported, e.g. a technician believes an early failure is “his fault” or “premature” and must not be recorded. Consequently, the reported data come from a truncated distribution and the number of unreported early failures is unknown. Inferences are developed for a Weibull accelerated life-testing model in which transformed scale and shape parameters are expressed as linear combinations of functions of the environment (stress). Coefficients of these combinations are estimated by maximum likelihood methods which allow point, interval, and confidence bound estimates to be computed for such quantities of interest for a given stress level as the shape parameter, the scale parameter, a selected quantile, the reliability at a particular time, and the number of unreported early failures. The methodology allows lifetimes to be reported as exact, right censored, or interval-valued, and to be subject optionally to testing protocols which establish thresholds below which lifetimes go unreported. A broad spectrum of applicability is anticipated by virtue of the substantial generality accommodated in both stress modeling and data type