In: Operations Management
When is Cpk = Cpu = Cpl = Cp?
Cpk = Cpu = Cpl = Cp when the mean 
 is centered between Upper Specification Limit USL and Lower
Specification limit LSL
Cp = 
When Mean is centered between USL and LSL, USL - 
 = 
 - LSL
Cpu = 
USL = 3
* Cpu + 
Cpl = 
LSL = 
 - 3
* Cpl
Cpk = min (
,
)
As seen from above, when USL - 
 = 
 - LSL, Cpu = Cpl = Cpk
Similarly, Cp = 
 = 
 = 
However, Cpu = Cpl, Cp = 
 = Cpu
Hence, Cp = Cpu
Thus, Cpk = Cpu = Cpl = Cp
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