Estimation of Process Parameters to Determine the Optimum Diagnosis Interval for Control of Defective Items

Dasgupta, Tirthankar; Mandal, Abhyuday

doi:10.1198/004017008000000118

Cited by 13 publications

(12 citation statements)

References 21 publications

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“…The geometric distribution behaves similarly to the exponential distribution, but it is typically used for the discrete case in which the duration is measured by the number of units produced before the shift. Following previous articles (Nayebpour and Woodall, 1993;Nandi and Sreehari, 1997;Jiang and Tsui, 2000;Borges et al, 2001;Ho et al, 2007;Trindade et al, 2007;Dasgupta and Mandal, 2008;Ding and Gong, 2008), this study relies on a geometric distribution with parameter , 0 < < 1, to describe the random time shift from State I to State II (out-of-control).…”

Section: Probabilistic Modelmentioning

confidence: 98%

See 1 more Smart Citation

On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

Bessegato

Quinino²,

Duczmal³

et al. 2012

Communications in Statistics - Theory and Methods

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On-line process control consists of inspecting a single item for every m (integer and m ≥ 2) produced items. Based on the results of the inspection, it is decided whether the process is in-control (the fraction of conforming items is p 1 ; State I) or outof-control (the fraction of conforming items is p 2 < p 1 ; State II). If the inspected item is non conforming, it is determined that the process is out-of-control, and the production process is stopped for an adjustment; otherwise, production continues. As most designs of on-line process control assume a long-run production, this study can be viewed as an extension because it is concerned with short-run production and the decision regarding the process is subject to misclassification errors. The probabilistic model of the control system employs properties of an ergodic Markov chain to obtain the expression of the average cost of the system per unit produced, which can be minimised as a function of the sampling interval, m. The procedure is illustrated by a numerical example.

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Section: Probabilistic Modelmentioning

confidence: 98%

“…The procedure of on-line control used to monitor a process has been studied by many authors, such as Nayebpour and Woodall (1993), Gong and Tang (1997), Borges et al (2001), Wang and Yue (2001), Dasgupta (2003), Trindade et al (2007), Dasgupta and Mandal (2008), and Quinino et al (2010).…”

mentioning

confidence: 99%

On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

Bessegato

Quinino²,

Duczmal³

et al. 2012

Communications in Statistics - Theory and Methods

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show abstract

“…The geometric distribution behaves similarly to the exponential distribution but it is typically used for the discrete case in which the duration is measured by the number of units produced before the shift. Following the previous articles (Nayebpour and Woodall 1993, Nandi and Seehari 1999, Jiang and Tsui 2001, Borges et al 2001, Trindade et al 2007, Dasgupta 2008, Ding and Gong 2008, this study relies on a geometric distribution with parameter π to describe the random time shift from State I to State II.…”

Section: Probabilistic Modelmentioning

confidence: 99%

“…In this situation, minimizing costs of process control is the emphasis and not a potential loss due to the variability of products. The economical approach was the subject of some recent articles, including those of Al-Orainia andRahim (2002, 2003), Costa and Rahim (2001), Dasgupta (2003), Wu et al (2004), Wang (2007), Govindaraju (2007), Ho et al (2007) and Dasgupta and Mandal (2008).…”

Section: Introductionmentioning

confidence: 98%

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

Quinino

2010

Engineering Optimization

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The procedure for online process control by attributes consists of inspecting a single item at every m produced items. It is decided on the basis of the inspection result whether the process is in-control (the conforming fraction is stable) or out-of-control (the conforming fraction is decreased, for example). Most articles about online process control have cited the stoppage of the production process for an adjustment when the inspected item is non-conforming (then the production is restarted in-control, here denominated as corrective adjustment). Moreover, the articles related to this subject do not present semi-economical designs (which may yield high quantities of non-conforming items), as they do not include a policy of preventive adjustments (in such case no item is inspected), which can be more economical, mainly if the inspected item can be misclassified. In this article, the possibility of preventive or corrective adjustments in the process is decided at every m produced item. If a preventive adjustment is decided upon, then no item is inspected. On the contrary, the m-th item is inspected; if it conforms, the production goes on, otherwise, an adjustment takes place and the process restarts in-control. This approach is economically feasible for some practical situations and the parameters of the proposed procedure are determined minimizing an average cost function subject to some statistical restrictions (for example, to assure a minimal levelfixed in advance-of conforming items in the production process). Numerical examples illustrate the proposal.

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“…In the present context, we consider that items are produced one at a time (interested readers may see Trindade, Ho, and da Costa Quinino 2007;Dasgupta and Mandal 2008;Ho and Trindade 2009;Bessegato et al 2012, etc.). The geometric distribution is typically used for this discrete case in which the duration is measured by the number of units produced before the shift.…”

Section: Problem Descriptionmentioning

confidence: 99%

Economic modelling for statistical process control subject to a general quality deterioration

Li¹,

Xie

2015

International Journal of Production Research

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The applications of control chart have traditionally focused on the detection of step shifts in process mean. However, changes are usually gradual, not as perfect step shifts. The common consideration of a shift as a step function does not always adequately describe what actually happens in practice. Hence, there is a need for more realistic assumptions to be incorporated. This paper employs a Markov chain approach and provides a way to quantitatively measure the economic performance of control charts in the presence of a more general quality deterioration mechanism. The finite production run is considered in the model as it has become a very important production mode at present and the process failure mechanism is described by geometric distribution. The chart properties, particularly on the issues of the quality deterioration mechanism, are investigated. The findings provide critical insights on the use of step shift assumption when designing control charts.

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Estimation of Process Parameters to Determine the Optimum Diagnosis Interval for Control of Defective Items

Cited by 13 publications

References 21 publications

On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

Economic modelling for statistical process control subject to a general quality deterioration

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