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Early in my career, a wise old mentor told me, "Steve, never argue about what can be measured." As an engineer by trade and German by lineage, he knew a little about precision craftsmanship. This advice has stuck with me, and in the quest for continuous improvement it has translated into "How can we get better if we don’t know where we are now?" followed by "How can we know where we are now without metrics?"
I will try to follow my KISS philosophy and stay away from all the scary math as much as possible, so let’s begin by reviewing the fundamentals of statistical process control (SPC). It is important to note at this point that not every process is a good candidate for statistical control, and that in these instances alternate process control methods may be required. The laws of physics dictate that although every single process has variation, once a process is stable, that variation follows a repeatable pattern that is called a normal distribution. That means that only some of the product (any process output) will be exactly the same as the process average (mean). It also means that the rest of the product will either be less or greater than the average, and will occur in decreasing frequency the further away from the mean the data stray. If you were to draw this product data set in graphical form, it would take the shape of a bell, which is why a normal distribution is also called a bell-shaped curve. Another thing that is known about a normal distribution is that the relationship of the product that falls on either side of the mean is predictable. In other words, the data can be divided into groups based on the distance (deviation) from the mean. The term standard deviation is used to describe these groups.
Every product has an optimum value, and because every process has variation, it also has a tolerance. This is defined as specification limits, with both an upper and lower spec limit (USL, LSL) surrounding the optimum value. Simply stated, when a product or process is outside of either of these spec limits, bad product is produced. How well the process variation is centered and contained within these spec limits is called process capability. The relationship of this variation to the mean and spec limits is the process capability, or Cpk. The less variation in a process, and the closer the variation is to the mean, the higher the Cpk number. With all the statistical tools available, the formula is not important for this purpose, but what is important is recognizing what this number means. It is generally accepted that a Cpk of less than 1.33 would indicate a process that is not capable of consistently meeting customer requirements, and a Cpk of 2.0 would represent a six sigma level. The sigma level represents how many standard deviations, or sigmas, it takes to reach the spec limits on either side of the mean. In other words, in a three sigma process it takes three sigmas to reach the LSL and three sigmas to reach the USL.
Editor's Note: This article originally appeared in the March 2015 issue of The PCB Magazine.