A company has a policy of Cp = 1.2 for all new products. All sheet metal specifications are designed with a tolerance of + 5 mils. Assume a manufacturing process average of 100 mils.
a. What is the reject rate for new parts?
b. If the sheet metal punch press average was shifted by 1 mil, what will the new Reject Rate be in PPM? What will the new Cpk be?
c. If the Cp was changed to 1.0, what will the new reject rate in %?
A company has a policy of Cp = 1.2 for all new products. A new housing is being designed with a critical parameter of 100 mils. The company’s manufacturing process has σ = 6.
d. What should the product specifications be to meet the Cp target? USL _?_ / LSL _?_
e. What do expect for a reject rate in %? In PPM?
1.
(a)
USL = 105 mils
LSL = 95 mils
Cp = (USL - LSL)/6σ = 10/6σ
or, 1.2 = 10 / 6σ
or, σ = 1.389 mils
Prob(Dimension within spec) = normdist(105,100,1.389,1) - normdist(95,100,1.389,1) = 0.9996814
So, rejection rate = 1 - 0.9996814 = 0.000318 or 318 ppm approx.
(b)
Say, the process shifts towards right i.e. the mean is now 101 mil
Cpu = (USL - process mean) / 3σ = (105 - 101)/(3*1.389) =
0.9599
Cpl = (process mean - LSL) / 3σ = (101 - 95)/(3*1.389) = 1.44
Cpk = Min(Cpu, Cpl) = 0.9599
Reject rate = 1 - normdist(105,101,1.389,1) + normdist(95,101,1.389,1) = 0.001998 or 1998 ppm approx.
(c)
Cp = (USL - LSL)/6σ = 10/6σ
or, 1.0 = 10 / 6σ
or, σ = 1.667 mils
Reject rate = 1 - normdist(105,100,1.667,1) + normdist(95,100,1.667,1) = 0.002705 or 2705 ppm
2.
(a)
Cp = (USL - LSL)/6σ
or, 1.2 = (USL - LSL)/(6*6)
or, USL - LSL = 43.2
So, (USL - LSL)/2 = 21.6
So, USL = 100 + 21.6 = 121.6 mils and LSL = 100 - 21.6 = 78.4 mils
(b)
Reject rate = 1 - normdist(121.6,100,6,1) + normdist(78.4,100,6,1) = 0.000318 or 0.0318%
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