Why the process capability index is a better way to assess equipment.

Determining the true capability of process equipment can be a daunting task to the average process engineer. No industry standard requires the equipment manufacturer to report their equipment/process capability in a specific manner. Hence, it has become a game of statistical gamesmanship.

The usual drivers – smaller parts, denser boards, more precise material deposits – require OEMs to offer increased process capabilities while maintaining high yield. How we assess the true capability of assembly equipment is the subject of discussion here.

One common OEM practice is to express machine capability as +X, where X is a number chosen by the machine supplier (example: +20 µm) without taking the specification (requirements) into consideration. In reality, the true machine capability should be expressed as a comparison of output of an in “control” process with the specification limits by using statistical measure such as “capability indices,” Cp and Cpk.

Consider: You are presented with two stencil printers: printer A and printer B. Printer A has a reported accuracy of +10 µm, and printer B has a reported accuracy of +25 µm. Which one would you choose and why? The answer may appear simple: printer A, with +10 µm accuracy. If so, you might be making a poor decision without having additional information, such as process capability. In other words, equipment accuracy and repeatability present only part of the story regarding equipment capability.

What is a process engineer to do? We suggest using a sound statistical approach to understand the process capabilities of equipment before making purchases. As mentioned, the best way to express the ability of equipment to perform according to the product’s design is to use process capability indices (Cp, Cpk, etc.). Many process engineers are becoming aware, particularly through 6-Sigma types of programs, of the capability of some of these statistical tools in determining process capabilities and to subsequently improve them.

A simple process capability index (Cp, Cpk, etc.), as many of us know, is calculated as a ratio of the tolerance of some feature (print tolerance, X-axis accuracy, placement force, etc.) to the variability of the process (typically measured as a function of standard deviation). At this point I should mention the process capability that most of us calculate is not the “true process capability,” but rather an estimate. It is beyond the scope of this discussion to go into a detailed discussion of true Cp and Cpk vs. estimated Cp and Cpk. Instead, I recommend readers refer to the references at the end of this article. Briefly, the difference between “true Cpk” and “estimated Cpk” is true Cpk uses population parameters µ and s, (µ refers to the mean of the population and s refers to the standard deviation of the population), and estimated Cpk uses and  (where  refers to sample average and  refers to sample standard deviation).

We rarely, if ever, have the population parameters (e.g., µ and s) to obtain true Cpk; instead, we typically have the estimates of those population parameters: the sample average, , and the sample standard deviation, s. With that in mind, we can use the following formulas to estimate Cp and Cpk.

where
LSL = lower specification limit
USL = upper specification limit.

Cp is known as the “inherent process capability” index and Cpk is known as the “actual process capability” index. The reason for Cpk being referred to as the actual process capability index is that it, unlike Cp, bases its calculations on two parameters: the average of the process, , and the variability in the process, s. On the other hand, Cp does not use information about the centering of the process. Therefore, to get a true understanding of whether the process is actually producing parts outside of specification limits, Cpk should be used. A Cpk of 2 is associated with a process capable of performing at a 6-Sigma level.

Getting back to our example of printers A and B, consider the hypothetical data generated from the two printers with respect to Y-axis offset. The data set and process capability indices are shown in Table 1. Although all the data points for printer A are within +10 µm, it has a Cpk value of 0.45 compared to printer B, which has a Cpk of 3.45 This result tells us Printer A, with its accuracy of +10 µm, is not very capable.


This effect is further demonstrated in Figure 1. Printer A, even though printing within the pad, may cross over at any time. This constitutes a poor process. Still not convinced? Consider Figure 2 (I get an unanimous agreement when I present this to my SPC class). Which pilot would you rather fly your plane? I rest my case!


Rita Mohanty, Ph.D., is director advanced development at Speedline Technologies (speedlinetech.com); rmohanty@speedlinetech.com.

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