Estimation of stress-strength reliability using record ranked set sampling scheme from the exponential distribution

Abstract

In this paper, point and interval estimation of stress-strength reliability based on upper record ranked set sampling (RRSS) from one-parameter exponential distribution are considered. Maximum likelihood estimator (MLE) as well as the uniformly minimum variance unbiased estimator (UMVUE) of stress-strength parameter are derived and their performance are studied. Also, some confidence intervals for stress-strength parameter based on upper RRSS are constructed and then compared on the basis of a simulation study. Finally, a data set has been analyzed for illustrative purposes.

Estimation of P(Y X) using record values from the generalized inverted exponential distribution

“…Similarly, through combining the prior density (14) and the likelihood function (7). The posterior density of  is given by The Bayes estimator of R using SELF under URV cannot be computed analytically, therefore the Lindley's approximation is applied in the following subsection.…”

Interval Estimation of the Stress-Strength Reliability for Lower Record Data Based on One-parameter Exponential Distribution Using Median Ranked Set Sampling and Record Ranked Set Sampling

“…Next, Salehi and Ahmadi (2014) proposed the RRSS. Salehi and Ahmadi (2015) considered the CI of 𝑅 based on RRSS from the exponential distribution using the pivotal quantity, approximate CI, and parametric bootstrap CI (percentile CI and bootstrap-t CI) and found that the percentile CI and exact CI had finer performance than the other CIs. Sadeghpour et al (2020) used lower RRSS to estimate 𝑅 for the generalized exponential distribution using a pivotal quantity, approximate CI, and parametric bootstrap CI (percentile CI and bootstrap-t CI), and it was found that the exact CI had better performance than the other CIs.…”

Comparison of two sampling schemes in estimating the stress-strength reliability under the proportional reversed hazard rate model

“…For the upper case, we useF instead of F whereF = 1 − F . Salehi and Ahmadi [26] considered the estimation of stress-strength reliability based on RRSS for the exponential distribution. With collaboration of Dey [27], they also compared the RRSS scheme with ordinary records in estimating the unknown parameter of PHR model.…”