A double exponentially weigiited moving average control procedure with variable sampling intervals

Recent studies have shown that enhancing the common T 2 control chart by using variable sample sizes (VSS) and variable sample intervals (VSI) sampling policies with a double warning line scheme (DWL) yields improvements in shift detection times over either pure VSI or VSS schemes in detecting almost all shifts in the process mean. In this paper, we look at this problem from an economical perspective, certainly at least as an important criterion as shift detection time if one considers what occurs in the industry today. Our method is to first construct a cost model to find the economic statistical design (ESD) of the DWL T 2 control chart using the general model of Lorenzen and Vance (Technometrics 1986; 28:3-11). Subsequently, we find the values of the chart parameters which minimize the cost model using a genetic algorithm optimization method. Cost comparisons of Fixed ratio sampling, VSI, VSS, VSIVSS with DWL, and multivariate exponentially weighted moving average (MEWMA) charts are made, which indicate the economic efficacy of using either VSIVSS with DWL or MEWMA charts in practice if cost minimization is of interest to the control chart user.

Section: Introductionmentioning

confidence: 99%

Economic statistical design of a T² control chart with double warning lines

Faraz

Saniga

2011

“…Many different schemes of the EWMA chart have been developed in an effort to increase its sensitivity to detect small shifts in a process. Shamma et al and Shamma and Shamma introduced a double EWMA (DEWMA) chart for normally distributed data. Zhang et al used the DEWMA chart for monitoring Poisson data (PDEWMA), and Riaz and Abbasi proposed a nonparametric DEWMA (NPDEWMA) chart for monitoring the location parameter that has an unknown distributional behavior.…”

Section: Introductionmentioning

confidence: 99%

A double exponentially weighted moving average control chart for monitoring COM‐Poisson attributes

Alevizakos

Koukouvinos

2019

The Conway‐Maxwell‐Poisson (COM‐Poisson) distribution is a two‐parameter generalization of the Poisson distribution, which can be used for overdispersed or underdispersed count data and also contains the geometric and Bernoulli distributions as special cases. This article presents a double exponentially weighted moving average control chart with steady‐state control limits to monitor COM‐Poisson attributes (regarded as CMP‐DEWMA chart). The performance of the proposed control chart has been evaluated in terms of the average, the median, and the standard deviation of the run‐length distribution. The CMP‐DEWMA control chart is studied not only to detect shifts in each parameter individually but also in both parameters simultaneously. The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the CMP‐DEWMA chart is more effective than the EWMA chart at detecting downward shifts of the process mean. Finally, a real data set is presented to demonstrate the application of the proposed chart.

“…The idea of using variable sampling rate originated from the ‘skip‐lot sampling plan’ suggested by Dodge . Reynolds et al presented the VSI cumulative sum charts while Shamma et al proposed the double Exponentially Weighted Moving Average (EWMA) control procedure with VSI. Reynolds et al studied the VSI

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chart when correlation is present while Lee and Bai proposed the VSI

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chart with runs rules.…”

Section: Introductionmentioning

confidence: 99%

The Run Sum Hotelling's χ² Control Chart with Variable Sampling Intervals

Chew

Khoo

Teh

et al. 2016

Control charts are widely used for process monitoring and quality control in manufacturing industries. Implementing variable sampling interval (VSI) control schemes on control charts rather than traditional fixed sampling interval procedure can significantly improve the control chart's efficiency. In this paper, the VSI run sum (RS) Hotelling's χ2 chart is proposed. The optimal scores and parameters of the proposed chart are determined using an optimization technique to minimize the following: (i) out‐of‐control average time to signal (ATS); (ii) adjusted ATS (AATS), when the exact shift size can be specified; (iii) expected ATS; or (iv) expected AATS, when the exact shift size cannot be specified. The Markov chain method is used to evaluate the zero‐state ATS and expected ATS, and steady‐state AATS and expected AATS of the proposed chart. The results show that the VSI RS Hotelling's χ2 chart significantly outperforms the standard RS Hotelling's χ2 chart and the former also performs well compared with other competing charts. By adding more scoring regions, the efficiency of the VSI RS Hotelling's χ2 chart can be further enhanced. An illustrative example using data from a manufacturing process is presented to demonstrate the application of the VSI RS Hotelling's χ2 chart. The application of the proposed chart in a quality improvement program can be extended to management and service industries. Copyright © 2016 John Wiley & Sons, Ltd.