A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Abstract

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 John Wiley & Sons, Ltd.

A review of ranked set sampling and modified methods in designing control charts

“…These units are allocated at random to $$( {m + 1} )/2$$ sets each of size m units. The units of each set are ranked with respect to the study variable or by expert knowledge based on an inexpensive method 81 . After ranking the units of each set, the i th and $$( {m - i + 1} ){\rm{th}}$$ ranked units from the i th set are picked, where $$i = 1,2, \ldots ,m/2$$ for even m , and $$i = 1,2, \ldots ,( {m + 1} )/2$$ for odd m .…”

“…designed a new EWMA control chart to monitor the mean and variance of a process based on perfect and imperfect ODRSS schemes. Haq et al 81 . proposed the EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator obtained under PRSS and imperfect PRSS schemes.…”

“…The units of each set are ranked with respect to the study variable or by expert knowledge based on an inexpensive method. 81 After ranking the units of each set, the 𝑖th and (𝑚 − 𝑖 + 1)th ranked units from the 𝑖th set are picked, where 𝑖 = 1, 2, … , 𝑚∕2 for even 𝑚, and 𝑖 = 1, 2, … , (𝑚 + 1)∕2 for odd 𝑚. This is a full cycle of the PRSS for the sample size 𝑚.…”

“…Haq et al 142 designed a new EWMA control chart to monitor the mean and variance of a process based on perfect and imperfect ODRSS schemes. Haq et al 81 proposed the EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator obtained under PRSS and imperfect PRSS schemes. In another work, they designed the EWMA control charts for efficiently monitoring the process mean based on perfect and imperfect MxRSS schemes.…”

On Dual Use of Auxiliary Information for Efficient Monitoring

“…Abujiya et al enhanced the performance of EWMA and CUSUM charts by proposing their structures based on MRSS, median double RSS, and double median RSS schemes. Haq et al proposed EWMA and maximum EWMA control charts based on the best linear unbiased estimators obtained under ordered double RSS and ordered imperfect double RSS schemes. Haq et al proposed a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator obtained under paired RSS scheme.…”