# Designing control chart for non-normal variables

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#### CJLee

I understand that the fundamental assumption in the development of X_bar and R control charts is that the underlying distribution of the quality characteristic is normal. However, in reality, many measured data do not follow normal distribution. So, for these nonnormal cases, how can I design control chart to control process variability?

#### Steve Prevette

##### Deming Disciple
Super Moderator
Re: designing control chart for nonnormal variables

I understand that the fundamental assumption in the development of X_bar and R control charts is that the underlying distribution of the quality characteristic is normal. However, in reality, many measured data do not follow normal distribution. So, for these nonnormal cases, how can I design control chart to control process variability?

Dr. Shewhart did show in his original development work that the SPC setup works equally well for non-normal data as normal. This is due to the Tchebychev Inequality (see other posts here on the Cove about that subject).

It is true that the formulae to convert from Range to Sigma are based upon the normal distribution. If that does bother you, you could shift to doing Sigma charts instead of Range charts, using the statistical formula for the standard deviation (easy to evaluate with modern spreadsheets, versus the calculational tools available prior to computers).

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#### pagnonig

I agree with Steve.

In my opinion, Shewhart's assumption about Tchebychev Inequality works very well for the I-MR chart when underlying data is not normally distributed.

For XbarR charts, I understand that despite of the underlying distribution the central limit theorem says that both Xbar and R are normally distributed. Then all the control limits calculations according to this distribution follows.

The normal distribution of the population should be necessary in case of process capability indexes calculation.

Do you agree?

Giuseppe

#### bobdoering

Trusted Information Resource
If you have a non-normal distribution based on only tool wear, then you have the continuous uniform distribution Tchebychev's inequality will support the probabilities, the Central Limit Theorem does not apply, because tool wear is not an independent variable. No worries, the details for dealing with that distribution are documented in

Statistical process control for precision machining Part 1 & 2