On the Statistical Design of Geometric Control Charts

Zhang, Lingyun; Govindaraju, K.; Lai, C. D.

doi:10.1080/16843703.2004.11673075

Cited by 31 publications

(15 citation statements)

References 9 publications

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“…This undesirable phenomenon means that the ARL does not meet its target value 1/α. Zhang et al (2004) present some criteria to achieve the near maximal and the near unbiased ARL design for CCC-1 charts.…”

Section: Discussionmentioning

confidence: 99%

“…Two approaches arose more or less simultaneously to approach this conundrum: Chen and Cheng's (2010) and Chen's (2009) proposals, which are discussed in the following section. (2000) and Zhang et al (2004), Chen and Cheng (2010) proposed a new approach for setting control limits for CCC-r charts on the basis of an ARL-unbiased when r ࣙ 2 (Method I). To determine the modified control limits for a CCC-r chart, it is assumed that p 0 is known, or it can be estimated from historical data when the process is in the state of statistical control (Phase I).…”

Section: Theoretical Basis Of Ccc-r Chartsmentioning

confidence: 99%

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A comparative study of two proposed CCC-rcharts for high quality processes and their application to an injection molding process

Joekes

Smrekar

Righetti

2016

Quality Engineering

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KEYWORDSaverage run length (ARL); car parts plant; CCC-r control charts; high-quality processes; negative binomial distribution ABSTRACT High-quality industrial processes, characterized by a low fraction of non-conforming items, require paying special attention to the statistical control methods employed since traditional Shewhart's control charts are no longer suitable. In this article, CCC-r charts are considered based on the cumulative count of conforming items inspected until r non-conforming items are observed. However, even though these charts have shown to be useful for high-quality processes, they are characterized by a biased average run length (ARL). In order to help engineers interested in this control methodology to select the best option, a computational study of statistical validation was performed to compare the two most outstanding procedures for the cases r = 2, 3, and 4. The performance was evaluated based on the ARL under control. The application of the CCC-r chart to a real process is shown with data from an automobile parts plant. Finally, analysis and discussion of the results are presented.

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Section: Discussionmentioning

confidence: 99%

Section: Theoretical Basis Of Ccc-r Chartsmentioning

confidence: 99%

A comparative study of two proposed CCC-rcharts for high quality processes and their application to an injection molding process

Joekes

Smrekar

Righetti

2016

Quality Engineering

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“…Because of the skewness of this distribution, Bourke 2 suggests to use probability limits, while Quesenberry 3 proposes a 'normalizing' transformation. Zhang et al 4 showed that the choice of probability limits does not necessarily lead to the most effective chart design, also see Schwertman 5 .…”

Section: Introductionmentioning

confidence: 98%

Group inspection of dependent binary processes

Weiß

2008

Quality & Reliability Eng

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We consider serially dependent binary processes, how they occur in several fields of practice. If such a process cannot be monitored continuously, because of process speed for instance, then one can analyze connected segments instead, where two successive segments have a sufficiently large time-lag. Nevertheless, the serial dependence has to be considered at least within the segments, i.e. the distribution of the segment sums is not binomial anymore. We propose the Markov binomial distribution to approximate the true distribution of the segment sums. Based on this distribution, we develop a Markov np chart and a Markov exponentially weighted moving average (EWMA) chart. We show how average run lengths (ARLs) can be computed exactly for both types of chart. Based on such ARL computations, we derive recommendations for chart design and investigate the out-of-control performance. A real-data example illustrates the application of these charts in practice.

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“…This is based on the idea of an unbiased hypothesis test. Other literature concerned with ARL-unbiased designs includes Acosta-Mejia et al (1999), Jones and Champ (2002), Zhang and Chen (2002), Tang and Cheong (2004), and Zhang et al (2004).…”

Section: Introductionmentioning

confidence: 99%

Design of exponential control charts using a sequential sampling scheme

Zhang¹,

Xie

Goh

2006

IIE Transactions

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Control charts for monitoring the time between events can be applied in various areas. In this study, we focus on the exponential control chart and consider the phase II problem (when process parameters are known) as well as the phase I problem (when process parameters are unknown). An exponential chart designed with the conventional approach has the disadvantage that the Average Run Length (ARL) value may increase when the process deviates from the nominal state. An ARL-unbiased design approach is therefore proposed for both phase II and phase I exponential charts. A sequential sampling scheme is adopted for the phase I exponential chart. The proposed ARL-unbiased design approach has several advantages over the conventional one, as it provides a self-starting feature and can significantly improve the ARL performance. Specific guidelines are suggested regarding the time to stop updating the estimates of parameters and control limits based on the actual false alarm rate. The phase I exponential chart can be calibrated to a constant in-control ARL value for each successive event accumulated to date. Simulated and real data examples are given to demonstrate the use and efficiency of the proposed design approach.

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On the Statistical Design of Geometric Control Charts

Cited by 31 publications

References 9 publications

A comparative study of two proposed CCC-rcharts for high quality processes and their application to an injection molding process

A comparative study of two proposed CCC-rcharts for high quality processes and their application to an injection molding process

Group inspection of dependent binary processes

Design of exponential control charts using a sequential sampling scheme

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