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Abstract
Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.
Highlights
To ensure the sustainability and the improvements of the quality of the products over time and to assess the effectiveness of a manufacturing process, Statistical Process Control (SPC) techniques are introduced by a physicist, Dr Walter Andrew Shewhart, to accomplish the objective [1]
The conforming run length (CRL) value is the number of the samples that have been captured before the first test statistic lies outside the control limit or since the last test statistic that lies outside the control limits
We extend the work of Abdul Haq et al [9] and propose a Synthetic exponentially weighted moving average (EWMA) median chart based on ranked set sampling (RSS) scheme for a quicker discovery of small to large mean shifts
Summary
To ensure the sustainability and the improvements of the quality of the products over time and to assess the effectiveness of a manufacturing process, Statistical Process Control (SPC) techniques are introduced by a physicist, Dr Walter Andrew Shewhart, to accomplish the objective [1]. Dell and Clutter [6] verified that the estimator of the population mean based on RSS is still dominate the SRS mean estimator except ranking is worse than random ordering Based on these evidence, some researchers have implemented the use of RSS scheme in control chart; for instance, Salazar and Sinha [7] implemented the scheme into the classical Shewhart control chart to examine the process mean; Muttlak and Al-Sabah [8] had proposed a new control chart based on perfect and imperfect RSS schemes to boost up the sensitivity of a control chart. We extend the work of Abdul Haq et al [9] and propose a Synthetic EWMA median chart based on RSS scheme for a quicker discovery of small to large mean shifts. The proposed chart is further compared with the existing charts such as EWMA median chart based on RSS scheme in terms of MRL to study the superiority of the chart
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