EWMA control charts with variable sample sizes and variable sampling intervals

Reynolds, Marion R.; Arnold, Jesse C.

doi:10.1080/07408170108936850

Cited by 89 publications

(55 citation statements)

References 29 publications

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“…When the process is in control (p 0 = 0.01), the VSSI CUSUM chart produces ATS 0 = 127 568, AIR = 0.0856 (25) This value of ATS 0 corresponds to a value of 370 for the in-control ANSS (average number of samples to signal) preferred by Reynolds and Arnold 9 .…”

Section: Study Two: Comparison With the Cusum Charts In An Examplementioning

confidence: 99%

“…(8) Calculate the out-of-control ATS (the formulae are given in Appendix B). (9) If the calculated ATS is smaller than the current ATS min , replace the latter by the former, and the current parameter values of n 1 , n 2 , w 1 , w 2 , h 1 , h 2 , UCL 1 and UCL 2 are stored as the temporary optimal design. (10) At the end of the entire search, the optimal design of the VSSI chart that results in the minimum ATS can be identified.…”

Section: Optimization Design Of the Adaptive Np Chartsmentioning

confidence: 99%

“…Costa proposed the joint VSSIX & R charts 7 and theX chart adapting n, h and k all together 8 . Reynolds and Arnold 9 presented the VSSI EWMA and CUSUM charts for variables.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

Luo

2004

Quality & Reliability Eng

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Recent research has shown that the adaptive control charts are quicker than the traditional static charts in detecting process shifts. This paper develops the algorithm for the optimization designs of the adaptive np control charts for monitoring the process fraction non-conforming p. It includes the variable sample size chart, the variable sampling interval chart, and the variable sample size and sampling interval chart. The performance of the adaptive np charts is measured by the average time to signal under the steady-state mode, which allows the shift in p to occur at any time, even during the sampling inspection. By studying the performance of the adaptive np charts systematically, it is found that they do improve effectiveness significantly, especially for detecting small or moderate process shifts.

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Section: Study Two: Comparison With the Cusum Charts In An Examplementioning

confidence: 99%

Section: Optimization Design Of the Adaptive Np Chartsmentioning

confidence: 99%

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Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

Luo

2004

Quality & Reliability Eng

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“…We note that general expressions for the first moments of the time to signal, number of observations to signal, and number of samples to signal are given in Reynolds and Arnold 36 for the case in which the control statistic is a stationary Markov process. These expressions could be extended to adaptive CUSUM or EWMA charts.…”

Section: Discussionmentioning

confidence: 99%

Design issues for adaptive control charts

Jensen

Bryce

Reynolds

2008

Quality & Reliability Eng

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Adaptive control charts allow the components of the quality-monitoring scheme to vary in order to obtain improved performance over non-adaptive control charts. Research has centered on components such as the sample size, time between samples, warning limits, and control limits and has recommended a variety of schemes, many of which are optimal in some sense. In practice, there are many other adaptive schemes that are near optimal, which will still yield considerable improvement over non-adaptive control charts. In addition, the impact of parameter estimation on adaptive control chart performance must be taken into consideration. Based on the simulation results shown here, adaptive control charts should only be used for mature processes, where a sufficient amount of Phase I data have been obtained to ensure that the estimated control limits are accurate. When evaluating control chart performance, we consider initial state performance measures for simplicity and note that the conclusions obtained here apply to steady-state performance measures. The evaluation of performance measures is easily handled by the Markov chain approach detailed in the Appendix.

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“…The Shewhart type control charts are regarded as threshold control charts while non-Shewhart control charts (e.g., CUSUM and EWMA charts) are regarded as deviation control charts. There are different approaches which have been used to improve the efficiency of the control charts in detecting changes in the process parameters: for example, Battaglia (1993) used a regression based approach, Chun (2000) used a nonparametric control charting approach, Muttlak and Al-Sabah (2001) used a ranked sampling approach, Reynolds and Arnold (2001) used a variable sample size approach, Jones et al (2004) used a CUSUM approach, Knoth (2005) used an EWMA approach, Chen and Huang (2005) used a synthetic control charting approach, He and Grigoryan (2006) used a double sampling approach, Muhammad and Riaz (2006) used a probability weighted moments based approach, Riaz and Saghir (2007) used a gini mean difference based approach, and Riaz (2008a,b) used an auxiliary information based approach.…”

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confidence: 99%

A process variability control chart

Riaz

Does

2008

Comput Stat

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In this study a Shewhart type control chart namely the V t chart, is proposed for improved monitoring of the process variability of a quality characteristic of interest Y . The proposed control chart is based on the ratio type estimator of the variance using a single auxiliary variable X . It is assumed that (Y, X ) follows a bivariate normal distribution. The design structure of the V t chart is developed for Phase-I quality control and its comparison is made with those of the S 2 chart (a well-known Shewhart control chart) and the V r chart (a Shewhart type control chart proposed by Riaz (Comput Stat, 2008a) used for the same purpose. It is observed that the proposed V t chart outperforms the S 2 and V r charts, in terms of discriminatory power, for detecting moderate to large shifts in the process variability. It is observed that the performance of the V t chart keeps improving with an increase in ρ yx , where ρ yx is the correlation between Y and X .

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EWMA control charts with variable sample sizes and variable sampling intervals

Cited by 89 publications

References 29 publications

Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

Optimal Design of the Adaptive Sample Size and Sampling Interval np Control Chart

Design issues for adaptive control charts

A process variability control chart

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