Posted: September 13th, 2017

Statistical Process Control

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The calculations were spot on…Very nice work so far…
With that said, I have a follow-up question:
•Cp = .21 and a Cpk of .10 leads to certain decisions, when the process limits are 42 to 46, and a grand average of 45.03..
•What if any process actions should be taken?
Feel free to research Cp and Cpk prior to answering.

Question 2 Already answered but the question above is follow up.
Question 2:
FOLLOW UP QUESTION BELOW.
The process engineers have designed our drink process with an upper tolerance of 46 ounces and a lower tolerance of 42 ounces. I wonder what our process capability really is? I’ve been reading about Six Sigma, it would be fantastic if we could add that to our already fantastic slogan regarding this new beverage!”
Calculate the process capability (Cp and Cpk)
________________________________________
Control Chart Formulas

Tabular values for X-bar and range charts
Subgroup Size A2 d2 D3 D4
2 1.880 1.128 —– 3.268
3 1.023 1.693 —– 2.574
4 0.729 2.059 —– 2.282
5 0.577 2.326 —– 2.114

Process Capability Formulas:

(Process sigma) = Rbar / d2
(where Rbar = Average Range and d2 = statistical constant)

Answer
Question 2:
Process capability:
Cp = (USL – LSL)/(6σ ̂ )
CpU = (USL-X ̅)/(3σ ̂ )
CpL = (X ̅- LSL)/(3σ ̂ )
Cpk = min (CpU, CpL)
̂ =s
USL = 46 and LSL = 42
d2 = 2.326
̂ = = 3.174s
Cp = (USL – LSL)/(6σ ̂ )= (46 – 42)/(6(3.174))= 4/19.044 = 0.21
CpU = (USL-X ̅)/(3σ ̂ )= (46 – 45.0298)/(3(3.174))=0.9702/9.522 = 0.102
CpL = (45.0298 – 42)/(3(3.174))=3.0298/9.522 = 0.318
Cpk = min (0.102, 0.318) = 0.102
Cp = 0.21 and Cpk = 0.102
The value of Cp is the measure that the distribution fits the specification and the value of Cpk measures whether the overall average is centrally located for the specification. The Cp value and Cpk value are not same and Cpk is less than Cp. So the distribution will fit into the specification limits, but the difference between Cp and Cpk shows that the process average is not located exactly in the center of the distribution.

Follow up Question:
The calculations were spot on…Very nice work so far…
With that said, I have a follow-up question:
Cp = .21 and a Cpk of .10 leads to certain decisions, when the process limits are 42 to 46, and a grand average of 45.03..
What if any process actions should be taken?
Feel free to research Cp and Cpk prior to answering.