Question

If a process was a 5 sigma process and the specifications for the product are .5” +/-.00001”, and the mean of the process has shifted 1.25 SD above the desired mean, what is the current Cpk? Is the process producing any out of tolerance products at this point, if so, what proportion?

Answer 1

Cp = Cpk = process mean is on traget or process is centred.
              Cpk = min (Cpl, Cpu)
Cpk considers process centering. Cpk is a ratio of the distance measured between the process mean and the closest specification limit to half of the total process spread.
Therefore, Cp against specific limits, then
Cpl = (mean – LSL)/3s
Cpu = (USL – mean)/3s
Cpk = 0: The process mean falls on one of the specification limits, therefore, 50% of the process output falls beyond the specification limits.
Cpk < -1: The process mean is completely out of the specification limits, therefore, 100% of the process output is out of specification limits.

Cpk=min((USl?mean) / (3× std.Deviation) ,(mean?LSL) / (3× std.Deviation) )

Upper Specification Limit(USL)= 5.00001
Lower Specification Limit(LSL)= 4.99999
Process Standard Deviation= 5k
Process Mean= 1.25k

So,cpk= - 0.25