A consultant has been brought in to a manufacturing plant to help apply Six Sigm

Question

A consultant has been brought in to a manufacturing plant to help apply Six Sigma principles. Her first task is to work on the production of rubber balls. The upper and lower spec limits are 21 and 19 cm, respectively. The consultant takes ten samples of size five and computes the sample standard deviation to be .7 cm and the sample mean to be 19.89 cm. Compute Cpk for the process. Give the consultant advice on what to do with the process based on your findings.

Cpk = 0.424, process is not capable

Cpk = 0.848, process is not capable

Cpk = 2.24, process is capable

Cpk = 0.424, process is capable

which is the correct answer?

Cpk = 0.424, process is not capable

Cpk = 0.848, process is not capable

Cpk = 2.24, process is capable

Cpk = 0.424, process is capable

which is the correct answer?

Explanation / Answer

Cpk is process capability index which is equal to minimum of Cpl, and Cpu where Cpl = (mean - LSL)/3sigma and

Cpu = (USL - mean)/3sigma

Ideally Cpk =1.33 as in the present case it is very low therefore it may be stated that the case is that of crunched nearest the door edge so my preference is first choice Cpk = .424, process is not capable.

USL 21 LSL 19 Mean 19.89 S.D. 0.7 Cpl 0.42381 Cpu 0.528571 Cpk 0.42381

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