Economic Design of a Joint X- and R -Control Chart

Jones, Lynn L.; Case, Kenneth E.

doi:10.1080/05695558108974551

Cited by 48 publications

(23 citation statements)

References 9 publications

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“…µ 0 Standard value for process mean σ 0 Standard value for process standard deviation δ Magnitude of shifts in the process mean, in multiples of σ 0 (δσ 0 ) κ Magnitude of increases in process standard deviation, in multiples of σ 0 (κσ 0 ) λ 1 Scale parameter of Weibull distribution (related to assignable cause (1)) λ 2 Scale parameter of Weibull distribution (related to assignable cause (2)…”

Section: Glossary Of Notationmentioning

confidence: 99%

“…Fixed cost of sampling a 2 Variable cost of sampling a 3 Expected cost required to locate and eliminate assignable causes (1) Profit per hour when the process is in control V 1 Profit per hour when the process mean is out of control V 2 Profit per hour when the process variance is out of control V 3 Profit per hour when both the process mean and variance are out of control I Expected net profit per hour L Expected loss cost per hour for the proposed model n j…”

Section: Glossary Of Notationmentioning

confidence: 99%

“…More recently, greater attention has been devoted to the joint economic design of X and R control charts (for example, Jones and Case [2], Saniga and Montgomery [3], Rahim [4] and Costa [5]). …”

Section: Introductionmentioning

confidence: 99%

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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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Section: Glossary Of Notationmentioning

confidence: 99%

Section: Glossary Of Notationmentioning

confidence: 99%

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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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“…Economic design of CUSUM charts was given by Chiu (1974). Jones and Case (1981) considered joint economic design of X and R charts. Extensive literature surveys on the topic of economic design is given in Montgomery (1980), Vance (1983), andCollani (1988).…”

Section: Introductionmentioning

confidence: 99%

Exact economic design of X¯ charts for general time in-control distributions

Surtihadi

Raghavachar

1994

International Journal of Production Research

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Economic design of control charts seeks to choose the parameters of control charts that will minimizethe cost. In an economic model, the time to the occurence of an assignable cause is usually assumed to follow an exponential distribution. In addition to this assumption, certain approximations are used in the optimization procedures. This paper extends the current economic design for X charts in two directions. First, economic design is considered for a general distribution for the time to the occurrence of an assignable cause. The method is specialized to several distributions such as Weibull, lognormal, folded-normal, folded-logistic, and gamma. Second, an exact method to obtain the optimal design parameters is developed. Using Duncan's examples, the optimal designs obtained by exact method are compared for different distributions. These are also compared with the approximate optimal designs given by Duncan. This comparison shows that the optimality of the design for X charts is insensitive to the distributional assumption ofthe time to the occurrence of an assignablecause for small valuesof the sampling interval.

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“…Since Duncan's pioneering work [1], many studies have been developed to serve different purposes for the economic model of control charts. From the viewpoint of the production run, Gibra [2], Ladany and Bedi [3], Jones and Chase [4], Saniga [5] have considered the economic statistical model of the x control chart for the infinite-length horizon; Crowder [6], Del Castillo and Montgomery [7] have considered models of the control chart for short run cases. However, the feedback model stating from out-of-control state was not considered explicitly.…”

Section: Introductionmentioning

confidence: 99%