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**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 C_{p} isn’t calculated.

The C_{pk} 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.