Bootstrapping estimators of P(Y&lt;X) in the gamma case

Constantine, Kenneth; Karson, Marvin J.; Tse, Siu‐Keung

doi:10.1080/00949658908811199

Cited by 12 publications

(3 citation statements)

References 13 publications

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“…Traditionally, the problem of the estimation of R, based on simple random sampling (SRS), is considered under various distributions of the stress X and the strength Y. For example, in the estimation of system reliability, normal (Downton, 1973), exponential (Beg, 1980), gamma (Constantine et al, 1986;Ismail et al, 1986), extreme value (Lin & Ke, 2013) and Weibull (Kundu & Gupta, 2006) distributions have been used as the distributions of X and Y. For more detailed information, we refer to Kotz et al (2003).…”

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 general, the problem of the estimation of is studied under SRS data. For example, Church and Harris (1970), Tong (1977), Constantine et al (1986) and Kundu and Gupta (2006) all discuss this problem when and are two independent normal, exponential, gamma and Weibull random variables; for more detailed information, see also Kotz et al (2003). Nevertheless, in recent years, several authors have considered the estimation of based ranked set sampling (RSS) using both parametric and non-parametric methods.…”

Section: Introductionmentioning

confidence: 99%

Estimation of using Modifications of Ranked Set Sampling for Weibull Distribution

Akgül¹,

Şenoğlu²

2017

Pak.j.stat.oper.res.

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In statistical literature, estimation of = (<) is a commonly-investigated problem, and consequently, there have been considerable number of studies dealing with its estimation of it under simple random sampling (SRS). However, in recent years, the ranked set sampling (RSS) method have been widely-used in the estimation of. In this study, we consider the estimation of when the distribution of the both stress and strength are Weibull under the modification of RSS, which are extreme ranked set sampling (ERSS), median ranked set sampling (MRSS) and percentile ranked set sampling (PRSS). We obtain the estimators of using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies under these modifications. Then the performances of proposed estimators are compared with the corresponding ML and MML estimators of using SRS via a Monte-Carlo simulation study.

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“…In literature, the estimation of strength reliability for the gamma model has been studied by Constantine & Karson [4]; Ismail, Jayaratnam & Panchapakesan [7]. Constantine, Karson & Tse [5] given a Bootstrap approach also in estimating strength reliability for gamma case. Shawky, Sayed & Nassar [11] have discussed confidence interval estimation of strength reliability using generalized gamma family.…”

Section: Introductionmentioning

confidence: 99%

Augmented Strength Reliability of Equipment Under Gamma Distribution

Chandra¹,

Sen²

2014

JSTA

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The strength-reliability of equipment is defined as the probability that the strength of the equipment exceeds its stress. Augmentation of strength-reliability of equipments gives better service protection and longevity. In this paper, the concept of Augmentation Strategy Plan (ASP) is introduced under three possible cases to increase the strength-reliability. Assume that strength and stress of equipment, both follow gamma distribution and strength reliability expressions for all three cases are derived. Possible combinations of parameters are tabulated, for desired level of strength-reliability. Also cost aspects of such augmented situations have been discussed.

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Bootstrapping estimators of P(Y<X) in the gamma case

Cited by 12 publications

References 13 publications

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

Estimation of using Modifications of Ranked Set Sampling for Weibull Distribution

Augmented Strength Reliability of Equipment Under Gamma Distribution

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