2015 **Abstract:** The purpose of this study is to suggest a new modification of the usual ranked set sampling (RSS) method, namely; neoteric ranked set sampling (NRSS) for estimating the population mean and variance. The performance of the empirical mean and variance estimators based on NRSS are compared with their counterparts in ranked set sampling and simple random sampling (SRS) via Monte Carlo simulation. Simulation results revealed that the NRSS estimators perform much better than their counterparts using RSS and SRS desi…

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“…It is to be worth mentioning that the bias in estimating ${\sigma}_{{\overline{Y}}_{\text{italicNRSS}}}^{2}$by using Equation is negligible and almost approaches to zero for all the cases (cf. Zamanzade and Al‐Omari). To further investigate in the present manuscript, for samples of size n = 3 and n = 5, a simulation study based on 100 000 iterations also revealed that the amount of bias in estimating ${\sigma}_{{\overline{Y}}_{\text{italicNRSS}}}^{2}$ by using Equation is almost zero for m ≥ 20 , which is usually the case in statistical process control.…”

confidence: 99%

“…It is to be worth mentioning that the bias in estimating ${\sigma}_{{\overline{Y}}_{\text{italicNRSS}}}^{2}$by using Equation is negligible and almost approaches to zero for all the cases (cf. Zamanzade and Al‐Omari). To further investigate in the present manuscript, for samples of size n = 3 and n = 5, a simulation study based on 100 000 iterations also revealed that the amount of bias in estimating ${\sigma}_{{\overline{Y}}_{\text{italicNRSS}}}^{2}$ by using Equation is almost zero for m ≥ 20 , which is usually the case in statistical process control.…”

confidence: 99%

“…The estimator of population mean with its variance under NRSS as defined in Zamanzade and Al‐Omari is given by $${\stackrel{true\xaf}{Y}}_{\mathit{\text{NRSS}}}=\frac{1}{\mathit{nm}}{\sum}_{j=1}^{m}{\sum}_{i=1}^{n}{Y}_{\left(p+\left(i-1\right)n\right)j}$$ $${\sigma}_{{\overline{Y}}_{\text{italicNRSS}}}^{2}=\frac{1}{{\mathrm{italicmn}}^{2}}{\sum}_{i=1}^{n}\mathrm{italicVar}\left({Y}_{\left(p+\left(i-1\right)n\right)}\right)+\frac{2}{m{n}^{2}}{\sum}_{i<l}^{n}\mathrm{italicCov}\left({Y}_{\left(p+\left(i-1\right)n\right)},{Y}_{\left(p+\left(l-1\right)n\right)}\right).$$ The estimator defined in Equation is an unbiased estimator of population mean when the underlying distribution is symmetric and it is more efficient as compared to the estimators of SRS and RSS (cf. Zamanzade and Al‐Omari). Keeping in view the supremacy of the NRSS in estimating the population mean, the control charts based on NRSS are proposed in the following section.…”

confidence: 99%

“…( ) (8) be the sample means of study and auxiliary variables in (NRSS). And now we can define regression estimators in (NRSS) as follows:…”

mentioning

confidence: 99%