Are Your Capability Indices Too Low for Your Process?

My prior blog post was about the incorrect calculation of Cp, Cpk, Pp, Ppk that results in unusually high capability indices given the customer perceptions of your product quality (e.g. the capability indices are > 1.0 but customer complaints for the same or equivalent property or failure mode are frequent).

This post is about the opposite problem - estimates of process capability that are too low. The most common cause (pun intended) of artificially low (small) capability indices is the selection of incorrect limits as the specification limits.

Recall: Cp = (USL-LSL)/6sigma.

"How can that be - how could we choose the wrong limits?" you ask. Simply put, your release limits for purposes of dispositioning product may not be the true customer tolerance limits. Given that nearly all of our product testing is performed on a small sample of a production lot, judgement about the quality of that lot is based on the decision limit for the sample. However, the Decision Limit (DL) of a sample is NOT the Individual Specification Limit (ISL).

Let's take an example from in-process QC testing: Say we typically perform a QC test on three "individual" samples on every 3rd output of production. We apply the "Spec Limits" of 18 - 36 units to each individual. Each individual (sample) must pass this specification (i.e. n=1, c=0 sampling plan); otherwise, the "Lot" of 3 outputs produced since the last known good test result are placed on Quality Hold.

Question: Are these the specification limits (18-36) you are using to calculate your adhesion process capability? If so, you may be under-estimating your Cp, Cpk, Pp and Ppk. Why? Because Decision Limits are not Specification Limits. The true specification limits may be wider, resulting in a larger Cp, Cpk. Fortunately, the ISL (Indivdual Specification Limit) can be calculated from knowledge of the process variation, decision limit, and 'k' factor.