Based on the given process limit values, the following formula can be used to calculate the Cp value:
Cp=(Upper Limit - Lower Limit)/6s
When the process target is 0, the upper and lower limits are the same, so the above formula is rewritten as follows:
Cp=Upper Limit/3s
Cpk determines that there are 3 sets of standard deviations between the process average and the value closest to the specified limit. groups of standard deviations. The Cpk value is utilized in a normal or non-normal distribution, which is valuable because it can determine the value of ppm that is not within the specified limits due to lack of accuracy and stability of the mounting equipment.
Cpk=distance/3s between the mean and the value closest to the specified limit
Where s=standard deviation of the sample.
Definitions:
Process Range = Standard Deviation of the array = SD
Process Mean = Mean of the array = Avg
Process Target = Target
Prescribed Upper Limit = USL
Prescribed Lower Limit = LSL
If the target of the center process = 0, then USL = LSL
Definition of prescribed limit for center process = SL = USL = -1 x LSL
Definition of prescribed width is SW = USL - LSL, then for center process:
SW = SL - (-1 x SL) = 2 x SL
Generic indices of process capability, Cp and Cpk, are:
Cp=SW/( 6×SD)
Cpk=Cp×(1-K)
Where K=(Target-Avg)/(SW/2)
For the center's process
Cp=2×SL/(6×SD)=SL/3×SD
Cpk=((SL/3SD)×(1-K)
where K=(0-Avg)/(2×SL/2)=-Avg/SL
Replacing Cp and K in the Cpk expression yields:
Cpk=(SL/(3×SD))×(1-Avg/SL)=SL/(3×SD)+SL*Avg/(3×SD×SL)=SL/(3×SD)+Avg/(3 × SD)
The cp value of water is: 4.187 kJ/kgK