[Hajo Schmidt]

Einstein once  said about assumption of nature laws:

– In most cases the nature says: „You are wrong „ (we assume the alternative hypothesis)

– In some cases the nature says: „Maybe you are right“ (we assume the null hypothesis)

– But the nature never says: „Yes, you are right“ (two things are equal)

By principle you can only state that something is not equal but you can never state that something is equal unless you know the entire population.

• This reply was modified 3 years ago by Hajo Schmidt.

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[Hajo Schmidt]

@rbutler, thanks for your statement. Myself I work in the german automotive industry where one’s requires at least 125 data points for the capability analysis. In many cases we have much higher sample sizes.
I made a simulation with normally distributed random data, sample size 30. See pic enclosed. I wonder that you can accept such a high 95%CI. The VDA norm (German Association of Automotive Industry) allows smaller sample sizes for the short term capability but then the target value has to be higher (i.e. 1,77 for sample size 30)

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[Hajo Schmidt]

@rbutler In fact you won’t find “>2000 data point” in the literature. It is my own advice because otherwise the number of data at the boarders becomes very low (0,00135 * 2000 = 2,7) and the percentile-value will be very sensitive to rare events.
In fact if you have fewer data points you have to extrapolate either by finding a suitable fit or by the mentioned graphical methode. By the way, in my training I often add the percentile-values 0,135% and 99,865% at the y-axle of the probability plot in Minitab. This makes the percentile-values visible to my colleages.

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[Hajo Schmidt]

Hi KKiru,

if you have a sufficient amount of data (appr. > 2000) you can calculate the capability directly from the data without any distribution or transformation using the “Quantile”-methode and calculating the 0,135%- and 99,865%-percentile values in Minitab.
In case of fever data you have to find an appropriate fit of the data (especially at the “boarders” of the distribution). Use the following Minitab function to find the best fit:
Stat > Quality Tools > Individual Distribution Identification

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