Selecting an appropriate distribution is an essential first step in conducting a capability analyses. If the chosen distribution does not fits the data well, then the capability estimates will be inaccurate.
Most often, it is best to use engineering and historical knowledge of your process to identify a distribution that fits your process data. For example, does the data follow a symmetric distribution? What distribution has worked in the past for similar situations?
Sometimes it can be difficult to determine the best distribution based on the probability plot and goodness-of-fit measures. Use the Table of Percentiles from Individual Distribution Identification for several selected distributions to see how your conclusions change depending on the distribution chosen.
If several distributions provide an adequate fit to the data and similar conclusions, then it probably does not matter which distribution you choose. Conversely, if your conclusions differ depending on the distribution chosen, you may want to report the most conservative conclusion or collect more information.
Use Individual Distribution Identification prior to performing a capability analysis to determine which distribution or transformation is most appropriate for your data.
For example, an engineer collects data on the extent of warping in ceramic tiles. The data distribution is unknown, so she performs Individual Distribution Identification on the data to compare goodness-of-fit between the exponential distribution and the normal distribution after a Johnson transformation.