# Group IX-MR Charts

Group individual X and moving range (IX-MR) charts display several parameters, characteristics, or process streams on one chart, enabling you to assess relative uniformity or consistency across multiple data streams. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a group IX-MR chart works.

Figure 1. Arc width key characteristic shown with three measurement locations and upper and lower specifications.

## Case Description

The arc shown in Figure 1 is a sheet metal stamping. It serves as a guide for a tractor throttle control. For the throttle assembly to function correctly, the arc width must be uniform and within specification. If the width is too large, the assembly binds, if it is too small, the assembly will not lock into position. To monitor arc width uniformity, measurements are taken at three locations, a, b, and c. The quality department wants to use a chart that will examine all three locations simultaneously.

## Sampling Strategy

Because the same characteristic is being measured at three different locations on the part and there is an interest in evaluating them all on one chart, a group IX-MR chart is used.

## Data Collection Sheet

Table 1. Group IX-MR chart data collection sheet. MAX and MIN plot points are shown in bold.

## Plot Point Calculations

### The Group IX Chart

No calculations are required for the group IX. The MAX and MIN plot points are picked from the individual measurements. For example, in group 1, the largest (MAX) arc width is 0.6813 at location a. The smallest (MIN) width is 0.6790 at location b.

### The Group MR Chart

The moving range is calculated by taking the absolute difference between individual measurements at the same location from two consecutive groups. For example, location a in group 2 is 0.6813 and location a in group 3 is 0.6811, so the moving range between the two groups is 0.0002. The moving range at location a between groups 1 and 2 is 0.0000 because the arc width is 0.6813 in both groups for the a location. The same calculations are performed for locations b and c.

Note: There is no moving range for group 1 because no previous measurements exist.

### Group IX-MR Chart Plot Points

Table 2. Group IX-MR chart plot point summary.

### Group IX-MR Chart

Figure 2. Group IX-MR chart for arc widths.

## Chart Interpretation

Group moving range chart: Location b appears in the MAX position six out of eight times. This suggests that location b has the largest standard deviation of all three locations. Location a appears in the MIN position in five of the eight groups. This suggests that the variability at location a may be less than the other two locations.
Note: The centerline (MR = 0.00036) is the average of all the ranges from the data sheet, not just the average of the MAX and MIN ranges.

Group individual X Chart: Location a dominates the MAX position. This means that the arc width at location a is consistently wider than locations b or c. Locations b and c are both found in the MIN position. Even though location c is MIN more often, the raw data show that the individual values for locations b and c are very similar.

The distance between the MAX and MIN lines on the IX chart—0.0023 at plot point 1 and 0.0021 at plot point 9—are indicators of the amount of taper across the arc.
Note: The centerline (IX = 0.67997) is the average of all the individual measurements from all nine groups.

## Recommendations

• The consistently larger thickness at location a should be reduced to make the location less prone to binding.
• The variability at location b might be decreased by modifying the tooling to make the arc more rigid at location b when stamping.
This example is typical of what is found in many products that have within-piece variation problems. The group chart helps to detect and highlight those consistently high and low values.

## Estimating the Process Average

Process average estimates should be performed separately for each characteristic or location on the group chart.

Calculation 1. Estimate of the process average for location a.

## Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location on the group chart. Continuing with location a, see Calculation 2.

Calculation 2. Estimate of the process standard deviation for location a.
Note: To ensure reliable estimates, k needs to be at least 20. In this example, k is nine. Therefore, the estimates found here are used only for illustration purposes.

Calculating Process Capability and Performance Ratios
Calculations 3 through 5 show the process capability and performance calculations for location a.

Calculation 3. Cp for location a.

Calculation 4. Cpk upper for location a.

Calculation 5. Cpk lower for location a.

• Graphically illustrates the variation of multiple product or process characteristics simultaneously and relative to each other
• Quickly pinpoints the characteristics that are most in need of attention

• Not as sensitive to changes in the process average as the group Xbar-R chart
• No visibility of the characteristics that fall between the MAX and MIN plot points
• Cannot detect certain out-of-control conditions because the group charts shown here have no control limits

Table 3. Process capability and performance calculations for locations b and c.

When you use SPC software from InfinityQS, consuming the information provided by group IX-MR charts becomes faster and easier than ever. See how this type of analysis is surfaced in InfinityQS solutions.

FOOTNOTE:
1 Wise, Stephen A. and Douglas C. Fair. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment. Milwaukee, WI: ASQ Quality Press.

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