Estimation of Reliability for Exponential Distributions Using Ranked Set Sampling with Unequal Samples

Dong, Xianjun; Zhang, Liangyong; Li, Fengqin

doi:10.1080/16843703.2013.11673417

Cited by 23 publications

(8 citation statements)

References 1 publication

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“…In practical terms, using RSS is more reasonable than SRS when the sampling units are difficult or expensive to measure, but these units can be ranked easily and cheaply with respect to variable of interest, see Takahasi and Wakimoto (1968), Dell and Clutter (1972), and Chen et al (2004) for more detailed information. In the context of estimation of R, Mukhuti (2008a, 2008b), Muttlak et al (2010) and Dong et al (2013) derived the estimator of the system reliability R using RSS data. In addition to these studies, the usage of RSS is very applicable to different areas, such as quality control, reliability analysis and environmental statistics, see Salazar (1997), Ghitany (2005) and Patil et al (1993) for more detailed information.…”

Section: Introductionmentioning

confidence: 99%

Estimation of P(X < Y) using ranked set sampling for the Weibull distribution

Akgül

Şenoğlu

2016

Quality Technology & Quantitative Management

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This paper deals with making inferences regarding system reliability R = P(X < Y ) when the distribution of the stress X and the strength Y are independent Weibull. In the literature, estimators based on simple random sampling (SRS) are widely used in estimating R. However, in recent years, ranked set sampling (RSS) has become popular in performing statistical inference. We, therefore, obtain the estimators of R based on RSS using maximum likelihood (ML) and modified maximum likelihood (MML) methodologies. The performances of the proposed estimators are compared with their counterparts based on SRS using Monte Carlo simulation. The simulation results show that the proposed estimators are more preferable than the estimators based on SRS in terms of efficiency. In addition, under the assumption of imperfect ranking the efficiencies of the ML and the MML estimators of R, based on RSS, are compared and the ML estimator of R is found to be more efficient. Finally, a real data-set is analysed to demonstrate the implementation of the proposed estimators at the end of the paper.

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Section: Introductionmentioning

confidence: 99%

Estimation of P(X < Y) using ranked set sampling for the Weibull distribution

Akgül

Şenoğlu

2016

Quality Technology & Quantitative Management

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“…In the statistical literature, estimation of R has been examined by a quite number of authors under various distributions of X and Y based on simple random sampling (SRS) data. However, in recent years, the ranked set sampling (RSS) method, originated by McIntyre [16], was used for estimating R, since it is plausible and efficient alternative of SRS [9,18,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Interval Estimation of the System Reliability for Weibull Distribution based on Ranked Set Sampling Data

Akgül¹,

Şenoğlu²,

Acıtaş³

2018

HJMS

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Inference for the system reliability R is one of the most popular problems in the areas of engineering, statistics, biostatistics and etc. Therefore, there exist considerable numbers of studies concerning this problem. Traditionally, simple random sampling (SRS) is used for estimating the system reliability. However, in recent years, ranked set sampling (RSS), cost effective and efficient alternative of SRS, is used to estimate the system reliability. In this study, we consider the interval estimation of R when both the stress and the strength are independent Weibull random variables based on RSS. We first obtain the asymptotic confidence interval (ACI) of R by using the maximum likelihood (ML) methodology. The bootstrap confidence interval (BCI) of R is also constructed as an alternative to ACI. An extensive Monte-Carlo simulation study is conducted to compare the performances of ACI and BCI of R for different settings. Finally, a real data set is analyzed to demonstrate the implementation of the proposed methods.

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“…RSS is very feasible to different areas such as for environmental studies, see Yu and Lam (1997), Barnett (1999) and Bocci et al (2010). There are lots of studies in literature for estimating the system reliability based on RSS data, see Mukhuti (2008a, 2008b), Muttlak et al (2010), Dong et al (2013), Mahdizadeh and Zamanzade (2016, 2018a, 2018b and Şenoğlu (2017, 2018).…”

Section: Introductionmentioning

confidence: 99%

Estimation of Stress-Strength Reliability For Weibull Distribution Based on Type-II Right Censored Ranked Set Sampling Data

Akgül¹,

Şenoğlu²

2018

Pak.j.stat.oper.res.

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In this paper, we consider the estimation of stress-strength reliability Â 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 Â 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.

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Estimation of Reliability for Exponential Distributions Using Ranked Set Sampling with Unequal Samples

Cited by 23 publications

References 1 publication

Estimation of P(X < Y) using ranked set sampling for the Weibull distribution

Estimation of P(X < Y) using ranked set sampling for the Weibull distribution

Interval Estimation of the System Reliability for Weibull Distribution based on Ranked Set Sampling Data

Estimation of Stress-Strength Reliability For Weibull Distribution Based on Type-II Right Censored Ranked Set Sampling Data

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