I-MR-R/S (Between/Within) Chartoverview how to example data see also
I-MR-R/S (Between/Within) ChartStat > Control Charts > Variables Charts for Subgroups > I-MR-R/S (Between/Within)
I-MR-R/S (Between/Within) Chart produces a three-way control chart using both between-subgroup and within-subgroup variations. An I-MR-R/S chart consists of:
When collecting data in subgroups, random error may not be the only source of variation. For example, if you sample five parts in close succession every hour, the only differences should be due to random error. Over time, the process could shift or drift, so the next sample of five parts may be different from the previous sample. Under these conditions, the overall process variation is due to both between-sample variation and random error.
Variation within each sample also contributes to overall process variation. Suppose you sample one part every hour, and measure five locations across the part. While the parts can vary hour to hour, the measurements taken at the five locations can also be consistently different in all parts. Perhaps one location almost always produces the largest measurement, or is consistently smaller. This variation due to location is not accounted for, and the within-sample standard deviation no longer estimates random error, but actually estimates both random error and the location effect. This results in a standard deviation that is too large, causing control limits that are too wide, with most points on the control chart placed very close to the centerline. This process appears to be too good, and it probably is.
You can solve this problem by using I-MR-R/S (Between/Within) to create three separate evaluations of process variation:
Individuals chart: charts the means from each sample on an individuals control chart, rather than on an Xbar chart. This chart uses a moving range between consecutive means to determine the control limits. Since the distribution of the sample means is related to the random error, using a moving range to estimate the standard deviation of the distribution of sample means is similar to estimating just the random error component. This eliminates the within-sample component of variation in the control limits.
Moving range chart: charts the subgroup means using a moving range to remove the within-sample variation. Use this chart, along with the Individuals chart, to track both process location and process variation, using the between-sample component of variation.
R chart or S chart: charts process variation using the within-sample component of variation. Whether Minitab displays an R chart or an S chart depends on the size of the subgroups (see I-MR-R/S Chart - Options - Estimate).
Thus, the combination of the three charts provides a method of assessing the stability of process location, the between-sample component of variation, and the within-sample component of variation.
For more information, see Control Charts Overview and Variables Control Charts for Subgroups Overview.
All observations for a chart are in one column: Choose if data are in one or more columns, then enter the columns.
Subgroup sizes: Enter a number or a column of subscripts. If the subgroups are not equal, each control limit is not a single straight line but varies with the subgroup size.
Observations for a subgroup are in one row of columns: Choose if subgroups are arranged in rows across several columns, then enter the columns.