An adaptive chart for monitoring the process mean and variance

Costa, Antônio Fernando Branco; Magalhães, Maysa S. De

doi:10.1002/qre.842

Cited by 58 publications

(23 citation statements)

References 37 publications

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“…In SPC for variables, the main task of a control chart is to detect process shifts in mean and variance. To date, the combination of a Shewhart " X chart and an R chart (or an S chart) is still widely adopted despite the fact that computing systems are available in most of today's manufacturing industries (Costa and De Magalha˜es 2007). This is obviously attributable to the simplicity of these combinations for understanding, implementation and design.…”

Section: Introductionmentioning

confidence: 99%

The X control chart for monitoring process shifts in mean and variance

Yang

Lee

et al. 2012

International Journal of Production Research

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Control charts are widely used in statistical process control (SPC) to monitor the quality of products or production processes. When dealing with a variable (e.g., the diameter of a shaft, the hardness of a component surface), it is necessary to monitor both its mean and variability (Montgomery 2009[Montgomery, D.C., 2009. Introduction to statistical quality control. New York: John Wiley & Sons.]). This article studies and compares the overall performances of the X chart and the 3-CUSUM chart for this purpose. The latter is a combined scheme incorporating three individual CUSUM charts and is considered as the most effective scheme for detecting mean shift and/or standard deviation shift in current SPC literature. The results of the performance studies reveal two interesting findings: (1) the best sample size n for an " X chart is always n ¼ 1, in other words, the simplest X chart (i.e., the " X chart with n ¼ 1) is the most effective "X chart for detecting and/or ; (2) the simplest X chart often outperforms the 3-CUSUM chart from an overall viewpoint unless the latter is redesigned by a difficult optimisation procedure. However, even the optimal 3-CUSUM chart is only slightly more effective than the X chart unless the process shift domain is quite small. Since the X chart is very simple to understand, implement and design, it may be more suitable in many SPC applications, in which both the mean and variance of a variable need to be monitored.

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Section: Introductionmentioning

confidence: 99%

The X control chart for monitoring process shifts in mean and variance

Yang

Lee

et al. 2012

International Journal of Production Research

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“…Costa (1998) and Costa (1999) introduced the variable parameters (VP) procedure, where the sampling interval, sample size and width of the limits, are all varied so that the VP chart is more powerful than the VSI, VSS and VSSI schemes. Moreover, Costa and De Magalhães (2006) presented an adaptive chart for monitoring the mean and variance.…”

Section: Introductionmentioning

confidence: 99%

The variable sampling interval run sumX‾control chart

Chew

Khoo

Teh

et al. 2015

Computers & Industrial Engineering

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“…References [1][2][3][4][5][6][7][8][9][10][11][12] ). The variable parameter feature is extended to CUSUM control charts (e.g.…”

Section: Introductionmentioning

confidence: 99%

The variable sampling rate X̄ control charts for monitoring autocorrelated processes

Lin

Chou

2008

Quality & Reliability Eng

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Recent studies demonstrated that the adaptive X control charts are more efficient than fixed parameters (FP) X control chart from statistical and economic criteria.The usual assumption for designing a control chart is that the observations from the process are independent. However, for many processes, such as chemical processes, consecutive measurements are often highly correlated, especially when the interval between samples is small. In the present paper, the observations are modeled as an AR(1) process plus a random error, and the properties of the variable sampling rate (VSR) X charts are evaluated and studied under this model. Based on the study, the VSR X chart is faster than the FP, variable sampling interval and variable sample size X control charts in detecting mean shifts. However, when the level of autocorrelation is high or the process mean shift is large, the advantage of the VSR X chart is reduced.

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An adaptive chart for monitoring the process mean and variance

Cited by 58 publications

References 37 publications

The X control chart for monitoring process shifts in mean and variance

The X control chart for monitoring process shifts in mean and variance

The variable sampling interval run sumX‾control chart

The variable sampling rate X̄ control charts for monitoring autocorrelated processes

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