Economic-Statistical Design of<i>X̄</i>and R or<i>X̄</i>and S Charts

McWilliams, Thomas P.; Saniga, Erwin M.; Davis, Darwin J.

doi:10.1080/00224065.2001.11980070

Cited by 38 publications

(18 citation statements)

References 12 publications

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“…Third, nonlinear programming must be employed to find these designs although there are published algorithms that allow these to be calculated for N X and R charts (see, e.g., McWilliams et al 2001). Our first analysis was to run regression models of the design parameters (g, k, and h for the N X chart and g, k, h and n for the CUSUM chart) and ARL 0 and ARL 1 for both charts.…”

Section: Analysis Of Resultsmentioning

confidence: 99%

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

Saniga

Davis

Faraz

et al. 2015

Frontiers in Statistical Quality Control 11

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In this paper we investigate the characteristics of economic control chart designs for both Shewhart ( N X ) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of these charts, where design is defined as finding the values of sample size, intersample interval and control limit (Shewhart chart) or control parameters (k and h) for the CUSUM chart. Here, we run a large number of experiments consisting of many configurations of the parameters and describe and model the results in terms of the actual economic designs.

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Section: Analysis Of Resultsmentioning

confidence: 99%

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

Saniga

Davis

Faraz

et al. 2015

Frontiers in Statistical Quality Control 11

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show abstract

“…Nevertheless, the developed methodology should provide the basis for further investigation of an economic model for simultaneous control of process mean and process variance and for a comparison of the performances of the X-R control procedure with the X-S 2 control procedure under non-Markovian shock models. A recent article on economic-statistical design of X and R or X and S 2 by McWilliams and Saniga [17] can be used as a good reference.…”

Section: Discussionmentioning

confidence: 99%

An economic model for \font\twelveit=cmti10 scaled 1600$\overline{\kern‐0.85ex\hbox{\twelveit X}}$\nopagenumbers\end and R charts with time‐varying parameters

Ohta

Kimura

Rahim

2002

Quality & Reliability Eng

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SUMMARYThis paper proposes an economic model for the selection of time-varying control chart parameters for monitoring on-line the mean and variance of a normally distributed quality characteristic. The process is subject to two independent assignable causes. One cause changes the process mean and the other changes the process variance. The occurrence times of these assignable causes are described by Weibull distributions having increasing failure rates. The paper combines two existing models: (I) the model of Ohta and Rahim (IIE Transactions 1997; 29:481-486) for a dynamic economic design of X control charts, where a single assignable cause occurs according to a Weibull distribution and all design parameters are time varying; (II) the model of Costa and Rahim (QRE International 2000; 16:143-156) for the joint economic design of X and R control charts where two assignable causes occur independently according to Weibull distribution, with variable sampling intervals. The advantages of the proposed model over traditional X and R control charts with fixed parameters are presented.

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“…In the 'Control' phase of Six Sigma, nonlinear optimization techniques have been applied to optimize the design of control charts, including economic design, economic-statistical design and robust design, design of sampling schemes and control plans, etc. Examples of these applications can be found in Tagaras 30 , Crowder 31 , Rahim 32 , Chung 33 , McWilliams et al 34 and Rohleder and Silver 35 , to name a few. In addition, a brief introduction of meta-heuristics, which is a class of effective solution techniques for solving various mathematical programming and combinatorial optimization problems, can also be included into the training of Six Sigma BBs.…”

Section: A New Six Sigma Bb Training Roadmapmentioning

confidence: 97%

Fortification of Six Sigma: expanding the DMAIC toolset

Tang

Goh

Lam

et al. 2007

Quality & Reliability Eng

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Six Sigma as a quality improvement framework cannot remain static if it is to sustain its value for businesses beyond the first waves of applications. This paper explores the possibilities of enhancing the usefulness and effectiveness of Six Sigma by the integration of established Operations Research/Management Science (OR/MS) techniques. In this paper, we elucidate the needs for OR/MS techniques to enhance Six Sigma deployment in operational and transactional environments and propose a new training roadmap for core Six Sigma professionals (Six Sigma Black Belts) which incorporates these techniques. A matrix relating the components of the proposed training curriculum to the actual deliverables during implementation for a hybrid of operational and transactional environments is also presented. A practical case study is also presented to demonstrate the usefulness of the OR/MS tools in a typical transactional environment.

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Economic-Statistical Design ofX̄and R orX̄and S Charts

Cited by 38 publications

References 12 publications

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

Characteristics of Economically Designed CUSUM and $$\bar{X}$$ Control Charts

An economic model for \font\twelveit=cmti10 scaled 1600$\overline{\kern‐0.85ex\hbox{\twelveit X}}$\nopagenumbers\end and R charts with time‐varying parameters

Fortification of Six Sigma: expanding the DMAIC toolset

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