Analysis for the Linear Failure-Rate Life-Testing Distribution

Abstract

Some general comments are made concerning life-testing distributions with polynomial hazard functions, and some least squares type estimators are suggested as a possible method of parameter estimation. The linear hazard function case (h(t) = α + bt ) is considered in some detail. The maximum likelihood estimators of the parameters and reliability are studied for both complete and censored sampling, and the asymptotic variance covariance matrix is derived. In the linear case the simple least squares type estimators were compared to the maximum likelihood estimators by Monte Carlo simulation, and they were found to be fairly comparable to the maximllm likelihood estimators, being somewhat, better for small b/α2 and poorer for large b/α2. Percentage points were also determined by Monte Carlo simulation to mske possible tests of hypotheses for the parameters.