Analysis for the Linear Failure-Rate Life-Testing Distribution

TLDR

Life‑testing distributions with polynomial hazard functions, particularly the linear hazard case h(t)=α+bt, are discussed as a framework for parameter estimation. The study derives maximum likelihood estimators and their asymptotic variance–covariance matrix for complete and censored samples, and uses Monte Carlo simulation to compute percentile points for hypothesis testing. Monte Carlo comparison shows that least squares estimators perform similarly to maximum likelihood estimators, slightly better when b/α² is small and worse when it is large.

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.