Estimation algorithms for Weibull parameters and percentiles

Abstract

This study concerns the use of Weibull distribution in statistical component reliability. Recently, estimation of confidence intervals and confidence lower bounds for Weibull parameters and percentiles in small samples has received increasing attention in the literature. In expensive or long experiments, it is crucial to keep the sample size to a minimum, however, the estimates become less reliable as the sample size decreases. Therefore, it has become a necessity to perform a comparative study of estimation algorithms for small sample sizes and code them in an efficient manner. In this study, uncensored reliability data have been considered; algorithms have been developed for goodness-of-fit tests, point and confidence interval estimation for parameters and percentiles by the maximum likelihood and weighted least squares methods based on simulation. The algorithms have been generated in the standard C++ language and integrated under a computer interface. Similar studies in the literature were performed only for a limited number of failure probabilities, confidence levels and sample sizes with low simulation run numbers; the user has to use coefficients and formulae obtained from the simulations to produce the estimates. In contrast, the algorithms developed in this study allow the user to perform simulations with any run number, failure probability, confidence level and sample size, and calculate the estimates in a reasonable amount of time. The simulation error can be kept at low levels by specifying large simulation run numbers. Also, the application of the interface has been illustrated on failure times of DC motors.