Semi-Parametric Method to Estimate the Time-to-Failure Distribution and its Percentiles for Simple Linear Degradation Model

Abstract

Most reliability studies obtained reliability information by using degradation measurements over time, which contains useful data about the product reliability. Parametric methods like the maximum likelihood (ML) estimator and the ordinary least square (OLS) estimator are used widely to estimate the time-to-failure distribution and its percentiles. In this article, we estimate the time-to-failure distribution and its percentiles by using a semi-parametric estimator that assumes the parametric function to have a half- normal distribution or an exponential distribution. The performance of the semi-parametric estimator is compared via simulation study with the ML and OLS estimators by using the mean square error and length of the 95% bootstrap confidence interval as the basis criteria of the comparison. An application to real data is given. In general, if there are assumptions on the random effect parameter, the ML estimator is the best; otherwise the kernel semi- parametric estimator with half-normal distribution is the best.Degradation model, semi-parametric estimator, maximum likelihood
estimator, ordinary least square estimator