Cp/Cpk standard deviation - how many "sigmas?"?
What I don't understand is how to determine the width of a "sigma". Do I divide the x-axis into 6 "sigma" pieces? Or do I divide the area under the curve (whether it is a fat curve or a skinny curve) into six pieces, and then use the same size pieces to fill up the entire x-axis?
I don't understand, when calculating Cpk, how Cpk can ever be greater than 1. Cpk=(USL - M')/3*sigma
If there are always 3 "sigmas" between USL and M, USL - M' will always be less than 3 and then Cpk cannot be greater than 1. I know this is incorrect, because in industry Cpk should be at LEAST 1.33. All I can figure is that I need to divide the curve into more "pieces."
Thanks!
Answer:
I'm not a six-sigma guru by any stretch, but since no one else has answered, I'll try to help you out. I use probability and statistics in my work, and I do have a basic understanding of how it applies to process control.
Sigma (σ) denotes the standard deviation, a measure of the inherent variability or "scatteredness" of a particular characteristic of a population, which in your case is some measured value on a mass-manufactured part. If you don't know how to calculate σ, consult the first three links below. Conceptually speaking, the larger the value of σ, the more scatter there is. (Note: There is a difference between the actual σ of a population, and an estimate of σ based on a limited sample taken from it, but for now we’ll keep it simple by treating them as equivalent. Otherwise we’d have to start talking about confidence intervals, which at this point would probably be more confusing than enlightening.)
However, in and of itself, σ doesn't matter a whole lot. What matters is how large it is /relative/ to the specified upper and lower limits on the characteristic in question. As I understand it, the goal of "6σ" process control is to ensure that all six of the "sigmas" fit within the range between USL and LSL. If they don’t fit, it means that the process has too much inherent variability due to deficient manufacturing, or that the USL and LSL were specified too "tightly" by an overly optimistic designer, or both. Keep in mind that USL and LSL are essentially arbitrary (although /should/ be carefully selected with the actual 6σ in mind), while σ (and thus 6σ) are inherent properties of the manufacturing process.
So, as you can see, there are /not/ always 3 “sigmas” between the mean (M) and USL or LSL. Only if USL happens to be specified exactly at the M+3σ value for the process, and LSL at the M–3σ value, would your statement be true.
This explanation could go a lot further, but this much may be all that you needed, so I think I’ll stop here. If it still doesn’t make sense, feel free to email.
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