Generalized Inference For Two-parameter Weibull Distribution

The Weibull distribution is one of the most widely used lifetime distributions in reliability and survival analysis This parametric model is usually used to estimate important life characteristics of a product,such as the average life of the product,reliability or probability of failure at a specific time,and to determine warranty time Because of the value of the shape and scale parameters,it is a versatile simple distribution that specializes to other types of distributions These characteristics of the Weibull distribution have made it a useful and important distributional model in reliability and survival,analysisIn this dissertation,However,our review of literature showed that there is no systematic approach to find pivotal quantities,and applications of Monte Carlo procedures for other important problems such as interval estimation of a Weibull mean,comparing two Weibull means and stress-strength reliability are not clear/Therefore it is of importance to find an effective inference method for the problems of Weibull(b,c)distribution.In Chapter 2,we provide generalized inference based on Fiducial method for the one-sample problems In particular,we provide generalized variable approaches for constructing confidence intervals for a Weibull distribution.The statistical properties of the proposed generalized inference and other available methods are evaluated using Monte Carlo simulation.In Chapter 3,we consider some two-sample problems we use the connect of a generalized pivot statistic a generalized confidence interval due to Weerhandi,solve that a generalized confidence intervals is constructed for the reliability of series connection and parallel connection composed of components with two-parameter Weibull distributions Based on type II Censored data of the components Furthermore The generalized confidence interval can be obtained by numerical method and the computations are simple and strightforward,We can obtain the coverage probability of the generalized confidence interval.Our evaluation studies indicate that the proposed generalized variable approach for estimating a Weibull mean is satisfactory even for small samples whereas the available asymptotic method is not satisfactory even for large samples Furthermore,the proposed approach produced satisfactory results(in terms of coverage probabilities of confidence intervals)for other problems.Simulation study shows that the coverage probability of the generalized lower confidence limit is very excellent and steady.