I-MR Charts

Individuals - Moving Range Charts

I-MR charts plot individual observations on one chart accompanied with another chart of the range of the individual observations - normally from each consecutive data point. This chart is used to plot CONTINUOUS types of data.

The Individuals (I) Chart plots each measurement (sometimes called an observation) as a separate data point. Each data point stands on its own and the means there is no rational subgrouping and the subgroup size = 1.

A typical Moving Range (MR) Chart uses a default value of 2, which means each data point plots the difference (range) between two consecutive data points as they come from the process in sequential order. Therefore there will be one less data point in the MR chart than the Individuals chart. However, this value can be adjusted in most statistical software programs.

I-MR charts should be in control according the control tests that you elect to use. There are many types of tests that can determine control and points within the control limits can also be out of control or special cause.

Example

The data set below was taken from 30 measurements were taken from the overall length of 30 different widgets.

The calculation for this chart uses the short-term estimate with un-biasing constant since it is most likely a sampling representing the short term performance of the process. Keep in mind there are several estimates for sigma (standard deviation) and each use should be agreed upon with the customer along with the reasoning for its selection.

I-MR charting data

The first data point in the RANGE chart since a moving range of 2 was selected = the absolute value (or the positive difference) of 5.77 - 4.57 = 1.20.

NOTE

One measurement per part, with no rational subgroups.

Parts are measured in order from which they came from the process.

There is one less "range" data point than parts measured.

Using MR-bar/d2 for estimate of sigma (short term estimate for standard deviation).

I-MR Chart

Both charts indicate a process that is stable and in control. This would suffice for the stability portion of an MSA.

If this were the new (AFTER) data from a process improvement and this performance is better and more desirable than the BEFORE performance, then these control limits could be set as the new process control limits.

If this were the previous (BEFORE) data of a process, and all the variation is explained by common cause inherent variation then it will take a fundamental change (hopefully an improvement) to change this performance.

The objective of the team is to eliminate (or explain) all special cause variation and make fundamental, unprecedented improvements to drive the existing level of common cause performance to a reduced variation and more precise performance around a target.

BEFORE / AFTER I-MR Chart

Below is an example of data compiled at the end of the IMPROVE phase from a time study before and after the improvements were implemented on an inspection process. The times were charted with each time representing its own group (subgroup size = 1). Time is an continuous data type that would you an SPC chart such as an I-MR.

You can see from the chart the times on average for the invidividual measurements went down to 9.79 minutes and the by examining the lower chart you can see the variation among the times also was reduced.

To statistically analyze whether the mean has changed you could use the 2 sample-t test or paired-t test (depending on the data and assuming the data is normally distributed).

I-MR before and after chart

To statistically check if the variation has changed from before you could use the F-Test for Equal Variances and a P-value < (1-CI) would indicate a significant change.

For example, if you are using a 95% level of confidence, then any P value < 0.05 would be statistically significant and you would reject the null hypothesis and conclude there is a difference.

VISUAL AID: Another visual guideline is to examine the confidence intervals shown in blue for the BEFORE (1) and AFTER (2) data.

IF the interval lines DO overlap then there is no statistical difference between the variation before and after.

IF the interval lines DO NOT overlap, there is a statistical significant difference between the variation before and after.

HINT:

The further the lines are away from overlapping the lower the P-value will be and more confidence you have in concluding there is a significant difference (seems obvious). If the edge of the lines were close to one another (such as the left edge of the top line and the right edge of the lower line in our example), then the P-value would be close to zero and the F-statistic would be about the same as the F-critical value.

Test for Equal Variances

RECALL: The goal of most Six Sigma projects is to improve the mean to a target (add accuracy) and reduce variation (add precision).

Levene's test can be used on non-normal sets of data to test for Equal Variances.

Now, if the new (AFTER) process is in control, then you can proceed assess the final process capability and come up with the new z-score or use a capability index.

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