7) The upper and lower specification limits for a component are 3.98 and 4.02 in

Question

7) The upper and lower specification limits for a component are 3.98 and 4.02 inches, respectively. The process standard deviation is .004, and the process average is 4.005 inches. Is this process capable of achieving four-sigma performance (the four-sigma performance target value is 1.33)? A) CPk 1.25, CP 1.67, Four sigma performance can be met with regards to variability but work must be done on the process to improve centering in order to achieve four sigma process performance B) CPk is 1.5 and CP is 1.75; four sigma can be met for variability and centering.

Explanation / Answer

Here the correct answer is A, CPk =1.25 and CP= 1.67

Lets solve this:

Given,

Upper specification limit (UCL)= 3.98

Lower specification limit (LCL)= 4.02

standard deviation (?) = 0.004

process average = 4.005

4 ? performance target = 1.33

Cpk= minimum of [ (process average-Lower specification limit)/3?, (Upper specification limit - process average)/3? ]

Cpk=  minimum of [(4.005-3.98)/3*0.004, (4.02-4.005)/ 3*0.004]

Cpk=  minimum of (2.08, 1.25)= 1.25

Process capability ratio= Cp= LCL-UCL/6?

Cp= 4.02-3.98/6*0.004

Cp= 0.04/0.024 = 1.67

A process capability ratio of 1.67 tells that four-sigma performance can be met with regard to variability but work must be done on the process to improve centering in order to achieve four-sigma process performance. Currently it is not able to meet the specs.

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