Is this a poor process? – How Gage R&R impacts Process Capability

A non-technical explanation of the impact of gage variation on process capability.

To get the most out of this article you should:

  • Understand a histogram
  • Understand Specification Limits
  • Understand the concept of Process Capability

Is this a poor process?

Let’s say we run a machine and produce 100 parts. Then, we measure each part and draw up a histogram as shown on the right. The bottom scale represents the measured sizes, and the height of the bars represents how the many of the 100 parts there were at each size.Process-Capability-Chart-Cp-1-33-3

For further information we add the Upper and Lower Specification Limits, ie the Tolerance Limits shown in red. Now we have a visual assessment of the process capability.
Note: I should point out here that in a real situation we would calculate the process capability by using a tolerance interval which would take into account the confidence interval on the standard deviation.

Let’s define a good process as a process that produces all parts within the specification limits, and a poor process as one that can’t help but produce some parts outside of specification

Now, answer this question:
Is this a poor process?
A Yes
B No
C I don’t know

 

It depends on the gage

This is a bit of a trick question, but I think that the answer to this question is C – I don’t know, and here’s why:
The individual values we see on the chart are based on 2 numbers

  1. The true size of the part if we had an absolutely perfect measuring gauge – let’s call this the True Value
  2. The amount of error that our measuring system introduced – let’s call this the Measurement Error

So, we can say that:
Measured Value = True Value + Measurement Error

So, unless we are using a gage with zero measurement error, some of the variation on our original histogram must be due to measurement error – but how much?

Well, we can answer this question by using a gage R&R study. A gage R&R study will allow us to get an estimate of the error introduced due to repeatability (one operator doing multiple measurements) and reproducibility (difference between operators), and any interaction between the two.
But, before looking at gage R&R studies we should confirm why we are doing it by reviewing some process capability examples.

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Click the buttons above to change the Gage

Conclusion

In fact, the process capability chart shown at the top of the page is same as the process as shown above, but measured with a “Very Poor” Gage.
In other words, this is a process that really is relatively good
The process is “good”, or capable, and it’s probably more cost effective to improve the measurement system – by reducing measurement variation – than it is to start other major process improvement efforts.

 

Notes

  1. Original “True Value” Process based on 1,000 normally distributed data points Cp = 1.33
  2. “Very Poor” Gauge based variance derived from 0.35 SNR as defined in Reference (6)
  3. 1,000 normally distributed data points generated as simulated gauge variation
  4. Process measured using “Very Poor” Gauge Cp = 0.58
  5. Process Capability Charts generated in Minitab v. 16
  6. Reference: Design and Analysis of gauge R&R Studies
    ISBN 0-89871-588-1
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