New ranked set sampling for estimating the population mean and variance

Zamanzade, Ehsan

doi:10.15672/hjms.20159213166

Cited by 35 publications

(29 citation statements)

References 18 publications

(33 reference statements)

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“…It is to be worth mentioning that the bias in estimating

σ_{{\overset{Y}{true}}_{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

σ_{{\overset{Y}{true}}_{italicNRSS}}^{2}

by using Equation is almost zero for m ≥ 20, which is usually the case in statistical process control.…”

Section: Designing Univariate Control Charts Based On Nrssmentioning

confidence: 99%

“…The estimator of population mean with its variance under NRSS as defined in Zamanzade and Al‐Omari is given by

{\overset{true¯}{Y}}_{NRSS} = \frac{1}{nm} \sum_{j = 1}^{m} \sum_{i = 1}^{n} Y_{([], p + ((), i - 1) n) j}

σ_{{\overset{Y}{true}}_{italicNRSS}}^{2} = \frac{1}{{italicmn}^{2}} \sum_{i = 1}^{n} italicVar ((), Y_{([], p + ((), i - 1) n)}) + \frac{2}{m n^{2}} \sum_{i < l}^{n} italicCov ((),, Y_{([], p + ((), i - 1) n)}, Y_{([], p + ((), l - 1) n)}) .

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.…”

Section: Neoteric Ranked Set Sampling (Nrss)mentioning

confidence: 99%

“…Contrary to RSS, instead of dividing the selected n 2 sampling unit into n sets, all the selected units are ranked into a single set in NRSS sampling design recently introduced by Zamanzade and Al-Omari. 29 Similar to RSS, here it is also assumed that ranking of the units is easier and less expensive as compared to obtaining their precise values. After ranking the units equally spaced units are selected for actual measurements.…”

Section: Neoteric Ranked Set Sampling (Nrss)mentioning

confidence: 99%

“…Recently, Zamanzade and Al‐Omari have suggested neoteric ranked set sampling (NRSS) for estimation of the population mean and variance which outweighs the conventional ranked set sampling procedure and its modifications such as MRSS and ERSS. Moreover, Zamanzade and Al‐Omari have shown that NRSS performance is superior irrespective of the underlying distribution of the variable of the interest being symmetric or asymmetric. The usefulness of NRSS in designing of the control charts for mean and range of bivariate asymmetric distributions is studied by Koyuncu and Karagoz and Karagoz and Koyuncu .…”

Section: Introductionmentioning

confidence: 99%

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A new approach to design efficient univariate control charts to monitor the process mean

Nawaz

Raza

Han

2018

Quality & Reliability Eng

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Designing of efficient control charts for monitoring manufacturing processes and identifying assignable cause of variations is of constant interest in statistical process control. The present study incorporates neoteric ranked set sampling to design more efficient Shewhart, cumulative sum, and exponentially weighted moving average control charts for monitoring the mean of normal process. Using Monte Carlo simulations, the performance of the proposed charts is evaluated and compared with competing control charts on the basis of average run length and standard deviation of the run length for detection of shift of a specific magnitude. The extra quadratic loss is used to assess the overall performance of the control charts to detect shifts of various magnitudes. To further support the findings, a simulation study is carried out which revealed the supremacy of the proposed control charts over the existing charts. A real data set from a combined cycle power plant is used to demonstrate the application of the proposed control charts.

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“…It is to be worth mentioning that the bias in estimating

σ_{{\overset{Y}{true}}_{italicNRSS}}^{2}

σ_{{\overset{Y}{true}}_{italicNRSS}}^{2}

by using Equation is almost zero for m ≥ 20, which is usually the case in statistical process control.…”

Section: Designing Univariate Control Charts Based On Nrssmentioning

confidence: 99%

“…The estimator of population mean with its variance under NRSS as defined in Zamanzade and Al‐Omari is given by

{\overset{true¯}{Y}}_{NRSS} = \frac{1}{nm} \sum_{j = 1}^{m} \sum_{i = 1}^{n} Y_{([], p + ((), i - 1) n) j}

σ_{{\overset{Y}{true}}_{italicNRSS}}^{2} = \frac{1}{{italicmn}^{2}} \sum_{i = 1}^{n} italicVar ((), Y_{([], p + ((), i - 1) n)}) + \frac{2}{m n^{2}} \sum_{i < l}^{n} italicCov ((),, Y_{([], p + ((), i - 1) n)}, Y_{([], p + ((), l - 1) n)}) .

Section: Neoteric Ranked Set Sampling (Nrss)mentioning

confidence: 99%

Section: Neoteric Ranked Set Sampling (Nrss)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new approach to design efficient univariate control charts to monitor the process mean

Nawaz

Raza

Han

2018

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…( ) (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%

Regression Estimators in Ranked Set, Median Ranked Set and Neoteric Ranked Set Sampling

Koyuncu

2018

Pak.j.stat.oper.res.

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This paper proposes new regression estimators in median ranked set and neoteric ranked set sampling using one and two auxiliary variables. The proposed estimators have large gain in presicion compared to the classical ranked set sampling (RSS) design. A simulation study is designed to see the performance of suggested estimators. A real data set example is also used. In this data set, we have examined a rare endemic annual plant species which is grown in Turkey. We have found that suggested estimators are highly efficient that existing estimators.

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Efficient monitoring of coefficient of variation with an application to chemical reactor process

Mahmood

2020

Quality & Reliability Eng

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Control chart is a useful tool to monitor the performance of the industrial or production processes. Control charts are mostly adopted to detect unfavorable variations in process location (mean) and dispersion (standard deviation) parameters. In the literature, many control charts are designed for the monitoring of process variability under the assumption that the process mean is constant over time and the standard deviation is independent of the mean. However, for many real‐life processes, the standard deviation may be proportional to mean, and hence it is more appropriate to monitor the process coefficient of variation (CV). In this study, we are proposing a design structure of the Shewhart type CV control chart under neoteric ranked set sampling with an aim to improve the detection ability of the usual CV chart. A comprehensive simulation study is conducted to evaluate the performance of the proposed CV[NRSS] chart in terms of ARL, MDRL, and SDRL measures. Moreover, the comparison of CV[NRSS] chart is made with the existing competitive charts, based on simple random sampling, ranked set sampling (RSS), median RSS, and extreme RSS schemes. The results revealed that the proposed chart has better detection ability as compared to all existing competitive charts. Finally, a real‐life example is presented to illustrate the working of the newly proposed CV chart.

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New ranked set sampling for estimating the population mean and variance

Cited by 35 publications

References 18 publications

A new approach to design efficient univariate control charts to monitor the process mean

A new approach to design efficient univariate control charts to monitor the process mean

Regression Estimators in Ranked Set, Median Ranked Set and Neoteric Ranked Set Sampling

Efficient monitoring of coefficient of variation with an application to chemical reactor process

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