Transformation Approaches for the Construction of Weibull Prediction Interval

10.1016/S0167-9473(02)00232-3Computational Statistics and Data Analysis433357-368CSDA

A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit

We propose a simple close-to-normal approximation to a Weibull random variable (r.v.) and consider the problem of estimation of upper prediction limit (UPL) that includes at least l out of m future observations from a Weibull distribution at each of r locations, based on the proposed approximation and the well-known Box-Cox normal approximation. A comparative study based on Monte Carlo simulations revealed that the normal approximation-based UPLs for Weibull distribution outperform those based on the existing generalized variable (GV) approach. The normal approximation-based UPLs have markedly larger coverage probabilities than GV approach, particularly for small unknown shape parameter where the distribution is highly skewed, and for small sample sizes which are commonly encountered in industrial applications. Results are illustrated with a real dataset for practitioners

Coverage Properties of Weibull Prediction Interval Procedures to Contain a Future Number of Failures

Prediction intervals are needed to quantify prediction uncertainty in, for example, warranty prediction and prediction of other kinds of field failures. Naïve prediction intervals (also known as intervals from the “plug-in method”) ignore the uncertainty in parameter estimates. Simulation-based calibration methods can be used to improve the accuracy of prediction interval coverage probabilities. This article investigates the finite-sample coverage probabilities for naive and calibrated prediction interval procedures for the number of future failures, based on the failure-time information obtained before a censoring time. We have designed and conducted a simulation experiment over combinations of factors with levels covering the ranges that are commonly encountered in practical applications. Our results indicate situations where the naïve prediction procedure performs poorly but where properly calibrated procedures do well. The simulation also uncovered exceptional cases, caused by the discreteness of the number of failures being predicted, where even the calibrated procedure can perform poorly

Modified weibull distributions in reliability engineering

Ph.DDOCTOR OF PHILOSOPH

A study of advanced control charts for complex time-between-events data

Ph.DDOCTOR OF PHILOSOPH