The Quality Blog

What is CP(k)? Many people ask this question. I have a simple explanation which possible will help. Cp(k) is the capability of a process on the side of the process distribution closest to the risk (specification) Risk in this case is going outside the specification which presumably has dire circumstances or a bad effects.

The best way to describe this is by utilizing an example everyone can relate to. Lets talk about a road. The width of 1 lane will represent the blueprint specifications high and low. The width of the specification is set by the design engineer while preparing the design. This represents one half af the ratio required to calculate Cp(k). The other half is related to the variation of the car and its’ driver. No car can drive straight down the road without some variation. This variation is made up of the things we typically look at when constructing a Fishbone Diagram (Ishikawa). Man, Method, Machine, Material, Measurement, and Mother Earth(environment). These common cause variables determine the standard deviation that is calculated in order to construct the distribution.

Cp(k) then becomes the ratio of the distance from the center of where the car has been travelling in real time divided by half of the width of the bell curve (3 sigma or 3 standard deviations) This ratio is simply analysed by evaluation whether it is greater than 1 or not. Less than 1 means the car is going over the edge of the road on one side and if closer to the other side of the lane, crossing into oncoming traffic. The k factor is only expressed on the side that has the greatest risk…. 1.33 ie 4 sigma capable, which provides for some (1/3 more) margin of safety. 1.67 has a greater margin etc…

In order to do a good job, Cp(k) must have a sample size large enough to determine a behavior of the system (car and driver etc…). Too few and one can surmise that the process is capable when in fact we have only observed the car driving down one block. Applying what we see on one block does not provide for a comfortable extrapolation to a trip across the country. This is important as Cp(k) is best used when sample sizes are greater than 30 where the amount of sample error is reduced to an acceptable amount when considering the cost of measuring many more. Fewer than 30 and we are making a judgment that a driver and car are capable of driving across the country without leaving the lane by only observing how well they did while driving the relatively short distance of one block. A whole lot or risk there in my opinion.