Estimation of σ for Individuals Charts

Braun, W. John; Park, Dongryeon

doi:10.1080/00224065.2008.11917738

Cited by 18 publications

(11 citation statements)

References 25 publications

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“…Control charts based on these standard estimates perform reasonably well under the usual assumptions that observations come from a normal distribution but are known to be inefficient when the assumption of normality is violated. Many authors have reported in their studies that because of non‐normality, the estimation of σ is affected more than the estimation of μ (see the works by Burr, and Braun and Park). Researchers have investigated different estimates of σ with the aim of improving the efficiency and robustness of control charts' performance (see the works by Cryer and Ryan, Cruthis and Rigdon, Derman and Ross, and Chen).…”

Section: Introductionmentioning

confidence: 99%

On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes

Abbasi

Miller

2011

Quality & Reliability Eng

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Control charts are an important statistical process control tool used to monitor changes in process location and variability. This study addresses issues regarding the proper choice of control chart for efficient monitoring of process variability. The choice of the best estimator to be used for variability charts has not been made clear in literature. We have analyzed the performance of eight control chart structures, based on different estimates of process standard deviation. The performance of control charts is investigated under the existence and violation of ideal assumptions of normality. Control chart constants and factors required for computing probability limits, considering normal and different non‐normal parent distributions, are provided for all variability charts. This study aims at providing guidance to quality practitioners in choosing the appropriate variability control chart for normal and non‐normal processes. Copyright © 2011 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes

Abbasi

Miller

2011

Quality & Reliability Eng

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“…Also, the screening of outliers to help improve the performance of other estimators is something that can be analyzed with both MTCC and TCC. For instance, Braun and Park (2008), when dealing with independent individual observations on Phase I, evaluated the reduction in the mean squared error of several "outlier-robust" estimators of , by doing a previous screening activity with an x-chart constructed with Boyles's 1997 estimator for , the median absolute deviation. MTCC and TCC have the advantage, over Boyles's method, that no parameters have to be estimated for the screening activity, and they are suitable for normal, and nonnormal distributions, TCC when symmetry can be assumed, and MTCC when it cannot.…”

Section: Discussionmentioning

confidence: 99%

Modified Tukey's Control Chart

Tercero-Gómez¹,

Ramirez-Galindo²,

Cordero-Franco³

et al. 2012

Communications in Statistics - Simulation and Computation

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Phase I of control analysis requires large amount of data to fit a distribution and estimate the corresponding parameters of the process under study. However, when only individual observations are available, and no a priori knowledge exists, the presence of outliers can bias the analysis. A relatively recent and successful approach to address this situation is Tukey's Control Chart (TCC), a charting method that applies the Box Plot technique to estimate the control limits. This procedure has proven to be effective for symmetric distributions. However, when skewness is present the average run length performance diminishes significantly. This article proposes a modified version of TCC to consider skewness with minimum assumptions on the underlying distribution of observations. Using theoretical results and Monte Carlo simulation, the modified TCC is tested over several distributions proving a better representation of skewed populations, even in cases when only a limited number of observations are available.

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“…Sim and Wong used estimated probability limits to study R chart properties when observations follow exponential, Laplace, and logistic distributions. Braun and Park investigated a large number of standard deviations when sample size was 300 to show the effect of outliers and bimodality on the performance of EWMA charts. Abbasi et al evaluated performance of a wide range of possible phase I dispersion charts such as R , S , and MD for non‐normal process distributions.…”

Section: Introductionmentioning

confidence: 99%

EWMA Control Chart Performance with Estimated Parameters under Non-normality

Noorossana

Fathizadan

Nayebpour

2015

Qual. Reliab. Engng. Int.

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Exponentially weighted moving average (EWMA) control charts can be designed to detect shifts in the underlying process parameters quickly while enjoying robustness to non‐normality. Past studies have shown that performance of various EWMA control charts can be adversely affected when parameters are estimated or observations do not follow a normal distribution. To the best of our knowledge, simultaneous effect of parameter estimation and non‐normality has not been studied so far. In this paper, a Markov chain approach is used to model and evaluate performance of EWMA control charts when parameter estimation is subject to non‐normality using skewed and heavy‐tailed symmetric distributions. Using standard deviation of the run length (SDRL), average run length (ARL), and percentiles of run lengths for various phase I sample sizes, we show that larger phase I sample sizes do not necessarily lead to a better performance for non‐normal observations. Copyright © 2015 John Wiley & Sons, Ltd.

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Estimation of σ for Individuals Charts

Cited by 18 publications

References 25 publications

On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes

On Proper Choice of Variability Control Chart for Normal and Non‐normal Processes

Modified Tukey's Control Chart

EWMA Control Chart Performance with Estimated Parameters under Non-normality

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