Conservative Likelihood Inference for Type I Censored Samples from the Log-Location-Scale Distributions

A new method, theoretically justified, is proposed to overcome difficulties in analysing reliability data coming from Type I censored samples. The article shows that, by means of Monte Carlo simulations, it is possible to obtain quasi-exact likelihood estimator properties and conservative confidence intervals for log-location-scale distributions. In the case of the exponential distribution, comparisons with the exact estimator properties show that the Monte Carlo approach allows to calculate the properties with very good accuracy. Finally, for the exponential distribution it is demonstrated that, if the number of failures can only be different from zero, confidence intervals based on the asymptotic properties of the likelihood estimators may give statistically meaningless results in the case of small sample size (3–10) and low probability of failure (.05–.20).