A customer has asked for process capability on a particular process. The control charts, created with a sample size of n = 5, in place show that the centerline (XDB) is 0.50349 with a range of 0.00014. The specifications for this process are 0.50350 +/- 0.00020 mm. What should the customer be told about process capability?

Question

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The Answer is

\sigma=\frac{ ext { R-bar }}{\mathrm{d} 2}=\frac{0.00014}{2.326}=0.00006

6 \sigma=0.00036

C p=\frac{U S L-L S L}{6 \sigma}=\frac{0.50370-0.50330}{0.00036}=1.1

\mathrm{Cpk}=-\frac{Z(\min )}{3}=\frac{3.17}{3}=1.1

ext { where } Z(\min ) ext { is: }

Z(U S L)=\frac{\mathrm{USL}-\mathrm{XDB}}{\sigma}=\frac{0.50370-0.50349}{0.00006}=3.5

Z(L S L)=-\frac{X D B-L S L}{\sigma}=\frac{0.50349-0.50330}{0.00006}=3.17

ext { The process is centered and capable. }

A Customer Has Asked for Process Capability on a Particular