Abstract
In this paper, we consider the estimation of stress-strength reliability  under the type-II right censored data when the distributions of both the stress and the strength are Weibull. First, we discuss the estimation of  based on simple random sampling (SRS). Then, we use the effective and the efficient alternative of SRS which is known to be the ranked set sampling (RSS) to estimate . In the estimation procedure of , we use two different approaches they are i) maximum likelihood (ML) which requires an iterative method and ii) modified maximum likelihood (MML) which has an explicit form. Monte-Carlo simulation study is performed to identify the efficient sampling method (i.e., SRS or RSS) and the efficient estimation method (i.e., ML or MML). Finally, strength and wind speed data sets are analyzed to illustrate the proposed methods in practice.
Highlights
In the literature, considerable attention has been raised to estimate the stress-strength reliability R = P(X < Y)
When the number of cycles increase, i.e. rx = ry = 5, and the scale parameters are differ each other, i.e. σ1 = 1, σ2 = 2 and σ1 = 1, σ2 = 3, the maximum likelihood (ML) estimator of R is more efficient than the corresponding maximum likelihood (MML) estimator, see the column corresponding to RE4
Simulation results show that the most efficient estimator of R is the ML estimator based on ranked set sampling (RSS) as expected
Summary
In many life-testing and reliability studies, complete information may not always be obtained on failure times of experimental units This type of data is called as censored data. Most of the works concerning with the estimation of R have been done under the assumption of censored SRS data In this context, Krishnanmoorthy and Lin (2010) considered the interval estimation of the stress-strength reliability involving two independent Weibull distribution under complete and censored data. In contrast to SRS, there has been few studies concerning with the censored RSS data in the literature, for example, Yu and Tam (2002) considered the estimation of the population mean and standard deviation based on left censored RSS data with fixed censoring times in the context of ML and Kaplan-Meier (KM) methodologies He and Naharaja (2012) developed the Fisher information matrix in censored samples from Downton’s bivariate exponential distribution based on RSS.
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