centerline and ucl lcl for the x bar and s charts

In the production of a precision mechanical component, a critical dimension is measured every hour, and at that time we take a sample of n=5 units. From 30 initial samples we find that x-bar = 200 and S-bar = 0.5,

What are the centerline and UCL, LCL for the x-bar and S charts?

Observing the charts we conclude that the process is in a state of statistical control. If the part specifications are 199 ± 2, what are:


Two remedies to the low Cpk have been suggested:

– Center the process at the target – i.e. X-bar-bar = 199

– Reduce the standard deviation to half of its original value through better tooling maintenance.

Which will achieve a higher Cpk?

Shfting xBarbar,
Sifting S,
they will both achieve the same Cpk, or
Neither change will improve Cpk


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