INTERVAL ESTIMATION FOR A TWO-PARAMETER WEIBULL DISTRIBUTION BASED ON TYPE-2 CENSORED DATA

Abstract

In most occasions, when performing life testing experiments, the main interest is to examine the lifespan of a specimen. For example, the time an aircraft wing takes until it fails from metal fatigue, or the survival time of a patient after a kidney transplant. In practice, such life data is usually censored because one does not have sufficient resources in terms of money and time. Type-2 censoring is one of the most popular censoring schemes used in reliability and life testing experiments. Weibull distribution is the most preferred distribution to fit censored life data because it is versatile and able to take on characteristics of other types of statistical distributions based on the value of the shape parameter. The maximum likelihood method is applicable for obtaining ML estimates (MLEs) for parameters of the 2-parameter Weibull distribution. Once the parameter point estimates have been obtained, construction of confidence intervals and confidence regions can be performed. In previous research works, construction of approximate confidence intervals based on Wald method under type-2 censoring scheme has been done. However, these confidence intervals may not be accurate for small sample sizes. The profile-likelihood method can be used to construct approximate confidence intervals for the parameters of interest when the sample size is small. In this study, the approximate profile-likelihood confidence intervals and likelihood confidence region are constructed for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. The study employed both simulated and real data sets. Subroutines for construction of profile- likelihood intervals were developed in 𝑅 program (version 3.5.1). Approximate profile-likelihood confidence interval results were then compared with the Wald confidence intervals using confidence lengths and coverage probabilities. Most of the coverage probability results for the parameters associated with the Wald method were relatively unstable because they were below the nominal coverage probability (0.95). On the other hand, most of the coverage probabilities associated with the profile-likelihood method were relatively close to the nominal coverage probability (0.95). The Profile-likelihood method outperformed Wald method because the confidence lengths obtained using profile-likelihood technique were narrower as compared to those associated with Wald method. Finally, Profile-likelihood interval estimates obtained in this study using small type-2 censored data can be used to make better inferences in life-testing experiments by using an effective small sample size.