Process capability calculations can be critical to a manufacturing process, when correctly applied.
Having spent a fair amount of time working with mass-produced parts that may number in the hundreds of thousands per year, process capability analysis methods have been a presence in my engineering tasks in several of the positions that I have held over the years.
One of the analyses commonly made was for a number known as Cpk. This is defined as follows:
Cpk = min (USL- μ/3 σ),( μ-LSL/3 σ)
USL – upper specification limit
LSL – lower specification limit
σ – standard deviation
μ – average
Estimates what the process is capable of producing, considering that the process mean may not be centered between the specification limits.
The absolute minimum that Cpk can be is 1.00, which reflects that the process under analysis produces a measurement that fits exactly within the measurement’s tolerances. This leaves no room for process drift. For an existing process, a figure of 1.33 is more typical.
Some years back, I was in a meeting where a person unfamiliar with proper use of Cpk calculations and the purposes behind them stated that a production run of approximately 40 assemblies had a Cpk figure for one or another performance characteristics of less than 1.00, which of course means that the process is not sound.
All of these assemblies were tested, with the measurement in question always coming within the specified tolerance.
The production sampling rate for these assemblies was 100%, yet calculations demonstrated they should not be within tolerance. It took a bit of explaining to make the point that Cpk figures are intended to estimate process capability where the sampling rate is considerably less than 100%, say 30 parts chosen at random out of 100,000 total parts for the manufacturing run.
Because the sampling rate of the process in question is 100%, Cpk calculations would be meaningless.
In fact, it would be worse than meaningless as the potential exists to reject qualified hardware as well as to find cause to modify an existing process that is producing satisfactory parts.
In this instance, the engineers carried the day and the process was left alone.
Norman T. Neher, P.E.
Analytical Engineering Services, Inc.
Elko New Market, MN
www.aesmn.org