Where et are the deviations from the process mean at time t and are iid as normal with mean = 0 and variance = process variation.
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But how can we predict how it will behave? For variables data free of autocorrelation, a stable process can be described by the following Shewhart-Deming model: Or another way to put it, a stable process will behave in a predictable manner. Stability is to ensure we have predictability. Use of empirical percentiles requires VERY large sample sizes. Transformation don’t always work and can be somewhat confusing to customers. The distribution-based analysis is somewhat easier and “cleaner”, but it does not provide both Cpk and Ppk metrics. None of these methods is better than the other. Minitab doesn’t offer a tool for this, likely because most users simply will not have the needed sample sizes (1000? 10,000?) If your sample sizes are large enough, you theoretically could use empirical (nonparametric) percentiles to caclulate the capability indices. Just click on the option in the main Nonnormal Capability Analysis dialog box.ĥ. The output for this transformation does show a transformed data probability plot. Minitab Release 14 now provides a Johnson transformation that seems to do a better job of normalizing data, though the form of the transformation is messier than that of the Box-Cox transformation. Make sure you store the Box-Cox transformed data and run it through the Normality test tool, just to be sure the new tranformed data are truly normal.Ĥ. WARNING – I wish the Box-Cox transformation tool also offered a probablity plot of the transformed data so the user could assess the new fit. Then enter the lambda you chose into the capability analysis using the Options button. Others prefer to use a “nice” lambda that is still inside the confidence interval such as 0.5 (square root), 2, -1 (ln), …. Some use the value listed next to “Est” – this is the best value. Find a lambda value that is inside the red confidence interval lines. Use the Box-Cox transformation to try to normalize your data. Minitab Release 14 now provides a distribution identification tool and provides capability analysis for large number of other distributions (13 I think) in addition to the Weibull.ģ. Use the Weibull Capability Sixpack to check the probability plot, check the control chart, and then assess capablity. Try to find another distribution that fits your data. If using a mean chart, you could increase your sub-group sample size so that the means are “driven” to normality (via the central limit theorem).Ģ. If you data are not normally distributed then you have several choices:ġ. You also need to assess the stability of the process. That is why I tend to prefer the normal probability plot. If the p-value for the AD test is greater than 0.05, then you can also assume normality, BUT keep in mind that for very large sample sizes the AD test can get picky about normality and tend to say even fairly normally distributed data are not normal. If the data points fall roughly on a straight line, you can assume the data are normal. For most situations this is likely easiest and more intuitive done using a probablity plot (Stat > Basic Statistics > Normality test), but you can also use the Anderson-Darling normality test. It is critial that you assess the normality of the data. Dieter brought up a very important point.
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