# Short Run IX-MR Chart Example

Assess process control for short production runs between different part numbers.

# Short Run IX-MR Charts

Short run individual X and moving range (IX-MR) charts combine short run data sets to analyze process capabilities in limited production runs. Review the following example—an excerpt from Innovative Control Charting1—to get a sense of how a short run IX-MR chart works.

Figure 1. Three fire extinguishing bottles, each with different burst pressure requirements.

## Case Description

A certain manufacturer of aerospace fire extinguishing bottles performs destructive testing on each batch of bottles. The test involves pressurizing the bottle until it bursts. Burst pressure is the key characteristic. Each bottle’s burst requirements are different. Also, since each bottle type can be made of different materials with different wall thickness, burst pressure variability changes with each bottle type. For these reasons, a short run IX-MR chart is selected to monitor all data from the burst test. All target values were obtained from past control charts.

Table 1. Target values and minimum specification limit for all three bottle types.

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## Sampling Strategy

Since burst testing is destructive, only one bottle from each lot is tested—typically the first piece. However, results from all burst tests are recorded on the same control chart. Tests are immediately performed as first-piece bottles become available. One test stand supports the entire manufacturing operation. Bottle types can change for each test.

## Data Collection Sheet

Table 2. Burst test data including plot point calculations for the short run IX-MR chart.

Note: The MR and coded MR values found in Table 2 are calculated using previous data points from the same bottle type. For example, the coded MR value of 0.49 in subgroup 16 is the result of taking the absolute difference between the coded IX values in subgroups 13 and 16: |1.06 — 1.55| = 0.49.

## Short Run IX-MR Chart

Figure 2. Bottle burst test data short run IX-MR control chart.

## Chart Interpretation

Short run MR chart: Because there are no non-random patterns or points outside control limits, the variability in burst pressure is consistent across all three bottle types.
Short run IX chart: The individual plot points appear to be stable with no non-random patterns occurring.

## Recommendation

Because both charts are in control, the target values (obtained from past control charts) are still appropriate for the current data. Continue maintaining the control chart with no changes in target values.

## Estimating the Process Average

Estimates of the process average should be calculated separately for each characteristic or part on the short run IX and MR chart. In this case, estimates of the process average should be calculated separately for each bottle type. This is illustrated with bottle type A in Calculation 1.

Calculation 1. Estimate of average burst pressure for bottle type A.

## Estimating Sigma

Estimates of sigma are also calculated separately for each characteristic or location represented on short run IX-MR charts. In this case, estimates of the standard deviation should be calculated for each bottle type. The calculation of MR for bottle type A is found in Calculation 2.

Calculation 2. Calculation of the average moving range for bottle type A (to be used in estimating its standard deviation).

Calculation 3. Estimate of the process standard deviation for bottle type A.

Note: To ensure reliable estimates, k needs to be at least 20. For bottle type A, k is only 9. Therefore, the estimates here and in Table 3 are used for illustration purposes only.

## Calculating Process Capability and Performance Ratios

Recall that the minimum specification for bottle type A burst pressure is 1070. Because there is only a single minimum burst specification, Cp and Cpk upper are not calculated.

Calculation 4. Cpk lower calculation for bottle type A burst pressure.

## Short Run IX-MR Chart Advantages

• Graphically illustrates the variation of multiple product or process characteristics on the same chart.
• Can chart process parameters that have changing target values. Characteristics from different parts with different means, different standard deviations, and different units of measure can be analyzed on the same chart.
• Pinpoints the characteristics that are in need of the most attention.
• Separates variation due to the process from variation that is product specific.

## Short Run IX-MR Chart Disadvantages

• The MR chart is dependent upon consecutive IX chart plot points.
• IX, MR, and estimates of sigma must be calculated separately for each characteristic on the chart.

• The case study shown here displayed three bottle types. In the actual situation, there were 22 different bottle types being monitored on the same short run IX-MR chart.
• Process capability and performance calculations for the remaining bottle types are shown in Table 3.

Table 3. Additional summary statistics and process capability and performance ratios for remaining bottle types.

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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