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## Estimating Capability for Nonnormal Data

Statistical Thinking for Industrial Problem Solving

In this video, we show how to compute capability indices for nonnormal data using the Impurity data and the Distribution platform in JMP.

To start, we select Distribution from the Analyze menu.

We select Impurity for Y, Columns, and click OK.

The distribution appears to be right skewed. Before conducting the capability analysis, we check to see whether the underlying distribution is approximately normal.

We select Normal Quantile Plot from the red triangle for Impurity. There is a curve in the plot, indicating that the data don’t follow a normal distribution.

To identify the underlying distribution, we select Continuous Fit, then All, from the red triangle for Impurity.

This automatically fits and compares several continuous probability distributions. In this case, the lognormal distribution is selected as the best fit.

JMP reports parameter estimates for the lognormal distribution. To evaluate the fit of this distribution, we select Diagnostic Plot from the red triangle next to Fitted LogNormal.

This provides a lognormal probability plot. This is similar to a normal quantile plot but is based on the lognormal distribution. Because the data follow a straight line, we conclude that the lognormal distribution is a good fit.

Now, we estimate capability using the lognormal distribution.

To conduct the capability analysis, we select Capability Analysis from the red triangle for Impurity.

Our target is 3, and the upper spec is 7.  There isn’t a lower spec for this example, so we’ll leave this blank.

From the drop-down menu for the distribution, we select LogNormal.

We conduct a capability analysis based on the long-term estimate of the standard deviation. So we click OK to run the analysis.

Notice the label says Quantile Sigma instead of Long Term Sigma. JMP uses the percentiles, or quantiles, of the lognormal distribution to calculate the capability indices and estimate the percent out of spec.

There isn’t a lower spec, so Cp isn’t calculated.

The Cpk is 0.164, indicating that the process is off target.

An estimated 25.2% of the measurements will be above the upper spec limit. This means that approximately 25 out of 100 batches will fail to meet the upper spec for impurity.

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