A Control Chart Based on Sample Median for the Detection of a Permanent Shift in the Process Mean

Abstract

The monitoring of the process average is usually done with the control chart for the means (a.k.a. the X¯ chart). However, the sample average, X¯, is sensitive to outliers which are observations whose values are larger or smaller than the majority of the other observations. The median statistic, on the other hand, is robust to outliers. The occurrence of outliers could be due to either the presence of assignable causes or common causes. Suppose that from past experiences, the occurrence of outliers in a certain process which happen occasionally is usually associated with the presence of common causes and that assignable causes will lead to permanent shifts in the process. Under such situations, using a median chart is more suitable because the chart's limits are less influenced by outliers so that unnecessary revision of the limits can be avoided. For these situations, occasional outliers (due to common causes) occurring in a subgroup will lead to an underestimated or overestimated sample average, hence producing more frequent false out-of-control signals for the X¯ chart. If our major concern is the detection of assignable causes which lead to permanent shifts in the process and not occasional outliers that cause temporary shifts, the use of a sample median chart is justified. Another reason which justifies the use of a sample median chart is because it is an easy to plot chart, especially for odd sample sizes.

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