Spanking Process Capability Study
Notice! This will probably go down as the most brilliant literature ever written on this site and in a few years, it'll be common place for everyone to be demanding that their spankers process have a CpK value of at least 1.67! Actually....I'm very aware that this will most likely be considered the most pointless and boring post ever made on here.... I also just realized I should have used Cp Upper but it's fine, it wont matter for the sake of this example.....
Find out if your spanking ability is not capable, potentially capable, adequate, proficient, or six sigma status with the following information!
Cp and Cpk (process capability indices) are used to measure the ability of a process to consistently satisfy certain requirements. In terms of using them in the context of spanking, the spanker might notice considerable variations between the results they get with different implements (their aim may be off which would certainly account for some.) In the example I provided below, the spanker uses three different implements on a total of 20 targets - which are listed as spankees.
For the sake of the example, lets say that the spanker was measuring their capacity to consistently strike within a certain proximity - this would be our nominal.
The spanker is permitted to strike a small distance above or below of those limits, that is the number that gives us the +tolerance and -tolerance. The Upper Specification Limit is the total of the nominal plus the +tolerance. Likewise the Lower Specification Limit is the total of the nominal and the -tolerance.
Cp is an index which measures POTENTIAL process capability. It is calculated using the following formula: USL - LSL / 6s (where 6s means 6 standard deviations which is the square root of the sample variance).
CpK is an index which measures the ACTUAL process capability. It is calculated using the following formula: Cpk = min(USL - μ, μ - LSL) / (3σ) (whichever is lower). It's also important to remember that CpK is NEVER greater than Cp, at best it is equal to Cp.
If CpK is below 0, its an indication that the process mean has fallen outside of the specification limits (notice this occurred to the CpK value when she used the belt - and in all fairness, I made those +/-tolerances extremely tight. If this happened under other cirucmstances, it would indicate a huge problem with the process.
Also, before Cp and CpK can be sufficiently measured, you will need to:
- have a large enough sample size
- verify the data is normally distributed
- make sure your process is stable (this is done with control charts which I will get to in another entry)
In most cases:
- a CpK of 1.33 is acceptable
- a CpK of 1.67 is desirable
- a CpK of 2.00 means the specification width is twice the process spread. Since the process spread is always six standard deviations wide, then the specification width has to be 12 standard deviations. The distance between the process mean to either specification limit is six standard deviations which means that it is a six sigma process.
- a CpK of 1.00 is never good enough but it measn that the process is potentially capable.
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