Multiple-criteria optimal design of X¯ control charts

Mackin, Patrick D.; Montgomery, Douglas C.

doi:10.1080/07408179608966293

Cited by 21 publications

(6 citation statements)

References 13 publications

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“…Del Castillo et al [4] reported an interactive multicriteria nonlinear optimization algorithm to design the X chart. Their model does not need to specify the cost of false alarms and running out of control.…”

Section: The Solution Algorithmmentioning

confidence: 99%

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Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Safaei

Kazemzadeh

Niaki

2011

Int J Adv Manuf Technol

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Shewhart charts are the most popular control charts that can be used to monitor variable quality characteristics in a production process. In this paper, a multi-objective model of the economic statistical design of the X-bar control chart is first proposed by incorporating the Taguchi loss function and the intangible external costs. The model minimizes the mean hourly loss cost while minimizing out-of-control average run length and maintaining reasonable in-control average run length. A multiobjective evolutionary algorithm, namely NSGA-II, is then developed and used to obtain the Pareto optimal solution of the model. Some sensitivity analyses are next performed to investigate the effect of parameter estimation on the chart performances. Finally, a comparison study with a traditional economic design model reveals that the proposed multiple objective design of the X-bar control chart offers a better approach and more practical outcomes for the practitioners.

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Section: The Solution Algorithmmentioning

confidence: 99%

“…Optimally determining the parameters of the X chart via the economic approach have been widely studied in the literature (see, e.g., [3][4][5][6][7][8]). Weiler [9] was the first one who attempted to design a control chart based on an economic criterion.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Safaei

Kazemzadeh

Niaki

2011

Int J Adv Manuf Technol

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“…To deal with this issue, Castillo et al (1996) proposed a multicriteria optimal design of X control chart through an interactive multicriteria decision making (MCDM) algorithm by using a linear value function to approximate the customers' decision preference. The model involves three criteria (i.e., the expected number of false alarms, the average time to signal, and the sampling cost per cycle) and two statistical constraints (an upper bound on false alarm and a lower bound on power).…”

Section: Introductionmentioning

confidence: 99%

A new approach for multicriteria design of an X control chart

Kapur

Chen

2009

2009 8th International Conference on Reliability, Maintainability and Safety

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This paper proposes to design an X control chart through a data envelopment analysis (DEA) based multicriteria branch and bound algorithm. The proposed multicriteria model avoids the difficulty of estimating costs associated with false alarm and operation under out-of-control status, and reduces the need for the decision maker to specify the statistical bounds on two types of errors and to provide preference information during the control chart design process. Through appropriate branching and bounding procedures, the DEA-based multicriteria branch and bound algorithm can quickly target the solution region where Pareto optimal solutions exist. Instead of involving the decision makers during the whole design process, few Pareto optimal solutions with useful trade off information can be presented to decision makers.

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“…Approaches like Saniga's, with the exception that multiple objectives concerning costs and error probabilities, were also considered by Del Castillo et al and Celano and Ficher . Del Castillo et al developed a multiobjective approach to minimize sampling costs, average time to signal, and expected number of false alarms for an

\overset{X}{true}

chart.…”

Section: Introductionmentioning

confidence: 99%

\overset{X}{true}

chart. Later, Celano and Ficher proposed a multiobjective approach to the design of an

\overset{X}{true}

chart where the type I and type II error probabilities as well as cost as determined by Duncan's model is minimized.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to bar and S² Charts

Faraz

Saniga

2012

Quality & Reliability Eng

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Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, a statistical criterion, an economic criterion, or a joint economic statistical criterion. Each method has its strengths and weaknesses. One weakness of the methods of design listed is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this article, we explore multiobjective models as an alternative for the methods listed. These provide a set of optimal solutions rather than a single optimal solution and thus allow the user to tailor their solution to the temporal imperative of a specific industrial situation. We present a solution to a well-known industrial problem and compare optimal multiobjective designs with economic designs, statistical designs, economic statistical designs, and heuristic designs.

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Multiple-criteria optimal design of X¯ control charts

Cited by 21 publications

References 13 publications

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

A new approach for multicriteria design of an X control chart

Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to bar and S² Charts

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Multiple-criteria optimal design of X¯ control charts

Cited by 21 publications

References 13 publications

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

A new approach for multicriteria design of an X control chart

Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to bar and S2 Charts

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Product

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Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an Application to bar and S² Charts