A synthetic control chart for monitoring the process mean and variance

2006 ◽  
Vol 12 (1) ◽  
pp. 81-88 ◽  
Author(s):  
A.F.B. Costa ◽  
M.A. Rahim
Keyword(s):  
Control Chart ◽  
Synthetic Control ◽  
Process Mean ◽  
Mean And Variance

Monitoring the process mean and variance using a synthetic control chart with two-stage testing

2009 ◽  
Vol 47 (18) ◽  
pp. 5067-5086 ◽  
Author(s):  
Antonio F. B. Costa ◽  
Maysa S. de Magalhães ◽  
Eugenio K. Epprecht
Keyword(s):  
Control Chart ◽  
Synthetic Control ◽  
Process Mean ◽  
Two Stage ◽  
Mean And Variance

MONITORING AUTOCORRELATED PROCESS MEAN AND VARIANCE USING A GWMA CHART BASED ON RESIDUALS

2008 ◽  
Vol 25 (06) ◽  
pp. 781-792 ◽  
Author(s):  
SHEY-HUEI SHEU ◽  
SHIN-LI LU
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Autoregressive Process ◽  
Process Mean ◽  
Process Variability ◽  
Autocorrelated Process ◽  
Ewma Control Chart ◽  
Mean And Variance ◽  
Run Lengths

This investigation elucidates the feasibility of monitoring a process for which observational data are largely autocorrelated. Special causes typically affect not only the process mean but also the process variance. The EWMA control chart has recently been developed and adopted to detect small shifts in the process mean and/or variance. This work extends the EWMA control chart, called the generally weighted moving average (GWMA) control chart, to monitor a process in which the observations can be regarded as a first-order autoregressive process with a random error. The EWMA and GWMA control charts of residuals used to monitor process variability and to monitor simultaneously the process mean and variance are considered to evaluate how average run lengths (ARLs) differ in each case.

A SYNTHETIC CONTROL CHART FOR MONITORING THE PROCESS MEAN OF SKEWED POPULATIONS BASED ON THE WEIGHTED VARIANCE METHOD

2008 ◽  
Vol 15 (03) ◽  
pp. 217-245 ◽  
Author(s):  
MICHAEL B. C. KHOO ◽  
ZHANG WU ◽  
ABDU M. A. ATTA
Keyword(s):  
Control Chart ◽  
Moving Average ◽  
Synthetic Control ◽  
Exponentially Weighted Moving Average ◽  
Process Mean ◽  
Variance Method ◽  
The Mean ◽  
Synthetic Chart ◽  
Weighted Moving Average ◽  
Exponentially Weighted

A synthetic control chart for detecting shifts in the process mean integrates the Shewhart [Formula: see text] chart and the conforming run length chart. It is known to outperform the Shewhart [Formula: see text] chart for all magnitudes of shifts and is also superior to the exponentially weighted moving average chart and the joint [Formula: see text]-exponentially weighted moving average charts for shifts of greater than 0.8σ in the mean. A synthetic chart for the mean assumes that the underlying process follows a normal distribution. In many real situations, the normality assumption may not hold. This paper proposes a synthetic control chart to monitor the process mean of skewed populations. The proposed synthetic chart uses a method based on a weighted variance approach of setting up the control limits of the [Formula: see text] sub-chart for skewed populations when process parameters are known and unknown. For symmetric populations, however, the limits of the new [Formula: see text] sub-chart are equivalent to that of the existing [Formula: see text] sub-chart which assumes a normal underlying distribution. The proposed synthetic chart based on the weighted variance method is compared by Monte Carlo simulation with many existing control charts for skewed populations when the underlying populations are Weibull, lognormal, gamma and normal and it is generally shown to give the most favourable results in terms of false alarm and mean shift detection rates.

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