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A simple and effective X¯ chart for process monitoring

A simple and effective X¯ chart for process monitoring Purpose – The purpose of this paper is to introduce a new design of the X¯ chart to catch smaller shifts in the process average as well as to maintain the simplicity like the Shewhart X¯ chart so that it may be applied at shopfloor level. Design/methodology/approach – In this paper, a new X¯ chart with two strategies is proposed which can overcome the limitations of Shewhart, CUSUM and EWMA charts. The Shewhart chart uses only two control limits to arrive at a decision to accept the Null Hypothesis ( H 0 ) or Alternative Hypothesis ( H 1 ), but in the new X¯ chart, two more limits at “K” times sample standard deviation on both sides from center line have been introduced. These limits are termed warning limits. The first strategy is based on chi‐square distribution (CSQ), while the second strategy is based on the average of sample means (ASM). Findings – The proposed X¯ chart with “strategy ASM” shows lower average run length (ARL) values than ARLs of variable parameter (VP) X¯ chart for most of the cases. The VP chart shows little better performance than the new chart; but at large sample sizes ( n ) of 12 and 16. The VSS X¯ chart also shows lower ARLs but at very large sample size, which should not be used because, as far as possible, samples should be taken from a lot produced under identical conditions. The inherent feature of the new chart is its simplicity, so that it can be used without difficulty at shopfloor level as it uses only a fixed sample size and fixed sampling interval but it is very difficult to set the various chart parameters in VP and VSS X¯ charts. Research limitations/implications – A lot of effort has been expended to develop the new strategies for monitoring the process mean. Various assumptions and factors affecting the performance of the X¯ chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and performance of the proposed chart may be studied. Originality/value – The research findings could be applied to various manufacturing and service industries as it is more effective than the Shewhart chart and simpler than the VP, VSS and CUSUM charts. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Quality & Reliability Management Emerald Publishing

A simple and effective X¯ chart for process monitoring

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Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0265-671X
DOI
10.1108/02656710810873907
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to introduce a new design of the X¯ chart to catch smaller shifts in the process average as well as to maintain the simplicity like the Shewhart X¯ chart so that it may be applied at shopfloor level. Design/methodology/approach – In this paper, a new X¯ chart with two strategies is proposed which can overcome the limitations of Shewhart, CUSUM and EWMA charts. The Shewhart chart uses only two control limits to arrive at a decision to accept the Null Hypothesis ( H 0 ) or Alternative Hypothesis ( H 1 ), but in the new X¯ chart, two more limits at “K” times sample standard deviation on both sides from center line have been introduced. These limits are termed warning limits. The first strategy is based on chi‐square distribution (CSQ), while the second strategy is based on the average of sample means (ASM). Findings – The proposed X¯ chart with “strategy ASM” shows lower average run length (ARL) values than ARLs of variable parameter (VP) X¯ chart for most of the cases. The VP chart shows little better performance than the new chart; but at large sample sizes ( n ) of 12 and 16. The VSS X¯ chart also shows lower ARLs but at very large sample size, which should not be used because, as far as possible, samples should be taken from a lot produced under identical conditions. The inherent feature of the new chart is its simplicity, so that it can be used without difficulty at shopfloor level as it uses only a fixed sample size and fixed sampling interval but it is very difficult to set the various chart parameters in VP and VSS X¯ charts. Research limitations/implications – A lot of effort has been expended to develop the new strategies for monitoring the process mean. Various assumptions and factors affecting the performance of the X¯ chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and performance of the proposed chart may be studied. Originality/value – The research findings could be applied to various manufacturing and service industries as it is more effective than the Shewhart chart and simpler than the VP, VSS and CUSUM charts.

Journal

International Journal of Quality & Reliability ManagementEmerald Publishing

Published: May 23, 2008

Keywords: Charts; Production processes; System monitoring

References