Before we dwelve upon explaining the inferences of these Cp, Cpk values, let us quickly revisit Cp, Cpk definition.
Cp, Cpk are Process Capability Indices. Process Capability is an inherent variability of a given characteristic in a stable process. It represents process performance
over a period of stable operations . A capable process is one in which the output always adheres to the customer specifications.
Let us see the definition of Cp. Cp is the ratio of the specification limits (of a characteristic) to the natural process variation of a process (under a state of
statistical control). In other words, Cp = Voice of the Customer/Voice of the Process = (USL-LSL)/(6*SD) where SD= Standard Deviation and denoted by 'Sigma' symbol. A Cp value of >= 1, indicates that process is technically capable. A Cp value of 2 represents that process performs at 6 sigma level. A Cp value of < 1 indicates that the process is poor.
If Cp portrays the capability to meet the customer specification limits, then why do we need Cpk. The answer is that Cp does not consider how well the output is centred on the target value. Cpk addresses the proximity of the centring of a process related to the spec. limits. Cpk splits the Cp into 2 parts, Cpkl and Cpku.
Cpk takes the lesser of the two values. The formulas related to this are
Cpku=(USL-XBAR)/(3*SD); Cpkl=(XBAR-LSL)/(3*SD) where SD is Standard Deviation and is actually denoted by 'Sigma' symbol. Taking the lesser of the two values,
the Cpk value would be Min(Cpku,Cpkl).
To explain the concept of Cp, Cpk more - let us take a couple of imaginary examples mimicking real time sports.
Example 1: Imagine a football team practising penalty kicks. Assuming the goal posts on both the ends to be the specification(spec) limits. The players think that putting the ball in between the posts is a goal (which it is). But the coach would like his/her wards to be highly consistent. He/she would expect his/her wards to
consistently hit a target within the goal post. Imagine the coach wants the football to be hit on topmost of the centre of the goal posts (or any other part)? Why ? Because goalkeepers normally try to distract the kickers(football players) and makes a pre-meditated move. Therefore , it is imperative that players hit their
practice-penalty goals consistently at the same target position as much as possible. While Cp talks about slotting of goals , Cpk talks about how much variation or drift is there in hitting the goals at topmost of the centre of the posts.
When Cp/Cpk would be high :
Example 2: Imagine a practice session going for a shooting competition which is bound to happen in a week. A team of 5 is trying its luck , keeping in mind the competition would be stiffer in the actual competition. The team is aiming a point of 9.8 (out of 10), which could a potential medal winning score ,as per the team.
The Qualifying range for the competition is 9.3 and above. If the team is consistently shooting 9.3 and beyond 9.3 say upto 9.5 , then the Cp value is good(high). But if the team is consistently shooting near say 9.7 or even 9.8, then the Cpk is good or high.
Now , let us go to the given statistics for this question:
USL=24; LSL=18;Ave=21.5;Standard Deviation = 0.75. As per the given calculator, we get the values of Cp as 1.33 and Cpk as 1.11.
What do we infer from this ?
1.Cp value of 1.33 indicates that the process is quite capable.
2.However, Cpk value of 1.11 conveys that the process sigma is 3.33 . Formula for calculating Sigma Level = 3 *Cpk = 3 * 1.11 =3.33 .
So if the sigma level is 3.33, then it shows that there is plenty of variation and there are so much defects for a process operating just over 3 sigma.Therefore, the variation needs to be reduced. Thats the reason why we look for Cpk . Remember from CP perspective it looked like good until we found this now !!
3.Ideal value for a Cpk should be either at 1.33 or 1.66(close to 4 or 5 sigma) since there can be space for a process drift either to the left or right of the nominal value (target value).
4. Applying the formulas which we discussed above, for Cpku and Cpkl , we find the values for them as
Cpku=(24-21.5)/(3*0.75)= 2.5/2.25=1.1111; Cpkl=(21.5-18)/(3*.75)=1.5555; Cpk=Min(Cpku,Cpkl)=Min(1.11,1.55) = 1.11
Conclusion:
From this, we can infer that the process is less capable relative to the upper specification limit. Though the variation in the process is acceptable, in order to improve the process performance, the mean needs to be moved away from the USL or back to the middle of the specification limits.