An adaptive exponentially weighted moving average chart for the mean with variable sampling intervals

PurposeThis study aims to focus on proposing a new memory-type chart called progressive mean exponentially weighted moving average (PMEWMA) control chart. This memory-type chart is an improvement on the existing progressive mean control chart, to detect small and moderate shifts in a process.Design/methodology/approachThe PMEWMA control chart is developed by using a cumulative average of the exponentially weighted moving average scheme known as the progressive approach. This scheme is designed based on the assumption that data follow a normal distribution. In addition, the authors investigate the robustness of the proposed chart to the normality assumption.FindingsThe variance and the mean of the scheme are computed, and the mean is found to be an unbiased estimator of the population mean. The proposed chart's performance is compared with the existing charts in the literature by using the average run-length as the performance measure. Application examples from the petroleum and bottling industry are also presented for practical considerations. The comparison shows that the PMEWMA chart is quicker in detecting small shifts in the process than the other memory-type charts covered in this study. The authors also notice that the PMEWMA chart is affected by higher kurtosis and skewness.Originality/valueA new memory-type scheme is developed in this research, which is efficient in detecting small and medium shifts of a process mean.

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On designing a robust double exponentially weighted moving average control chart for process monitoring

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217744614 ◽

2018 ◽

Vol 40 (15) ◽

pp. 4253-4265 ◽

Cited By ~ 5

Author(s):

Ishaq Adeyanju Raji ◽

Nasir Abbas ◽

Muhammad Riaz

Keyword(s):

Moving Average ◽

Real Life ◽

Exponentially Weighted Moving Average ◽

Data Set ◽

Parameter Estimations ◽

Real Life Data ◽

Monitoring Process ◽

The Mean ◽

Weighted Moving Average ◽

Exponentially Weighted

A double exponentially weighted moving average chart has been proven more efficient for monitoring process mean in comparison to the classical exponentially weighted moving average chart. We, in this article, made a careful investigation on how well this scheme performs with the presence of disturbances in the process under consideration. This investigation was motivated in exploring the scheme with some robust statistic, as the mean estimator performs woefully. We also evaluated the effects of parameter estimation on the phase II assuming the parameters are unknown. Adopting a 20% trimmed mean of trimeans (robust) reveals the effect of parameter estimations. We substantiated these claims by applying the scheme on a real-life data set. The findings of the study pronounced the trimean estimator to be the best of all the five estimators used, including the mean.

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

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539308003052 ◽

2008 ◽

Vol 15 (03) ◽

pp. 217-245 ◽

Cited By ~ 26

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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