Quality Quiz from Professor Cleary
"B" is correct.
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Many people make the mistake of assuming that the Cpk number can be translated into a percentage of capability, but this is not true. Expressing the meaning of Cpk is a linguistic challenge, but it demands statistical accuracy.
Consider the following data for a capability study.
USL = 29
LSL = 5
Calculations of Cpk:
If Cpk is equal to 1.0, it would be accurate to say that the process is capable of producing at least 99.73% good parts. The percentage is determined to be 99.73 because by calculating plus and minus three sigmas, one captures 99.73% of the area under the normal distribution. (Remember: Z min is divided by three.)
What about that vague “at least,” though? If Z usl and Z lsl were both 3, then Z min would be 3 and the Cpk would be 1. On the other hand, if the Z usl is 3 and Z lsl is 5, the Cpk would still be 1, but the process would be capable of producing greater than 99.73% good parts. The lower spec limit will be 5 standard deviations from the mean, producing more than 99.73% good parts.
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