Continuous or discrete data?

Or why should we avoid discrete data? Why is failure rate not a good indicator?

I already mentioned this problem in two previous issues of the Newsletter (Six Sigma methodical mistakes and Statistics lifehacks). For me, it is a central limitation factor. If we understand the underlying logic, we concentrate our efforts and creativity on finding the proper continuous variable(s).

The first reason is the required sample size. With around a 50-piece sample, we could reach a pretty good overview (between the averages 0.65 times Standard Deviation can be detected) for continuous data if the distribution is normal,

If we have a 10% failure rate and want to detect a (rather big!) 5% difference, we need a 300-piece sample. If the difference is only 1% to be detected, we need to do more than a 9000-piece sample.

For the pilot/test, it is economically not viable.

As you can see, we need 1 or 2 magnitudes more data if we want to conclude.

The second reason is the “quality” of the measurement system. Most of the time, this problem is overlooked. For Gage R&R (continuous), the acceptance criterion is that only less than 1% of the Variance (square of Standard Deviation) comes from the measurement system. On the other hand, for discrete variables (Attribute Gage R&R), we accept the measurement system if the kappa-value is over 0.9. Roughly speaking, 10% of the observers made a wrong decision. Additionally, even with a perfect match (at a 15-piece sample), the lower value of the confidence interval is just a little over 80%.

Even when we use the required quantity data, our measurement data will not be reliable.

Shall we use continuous data?

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