Question

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?

Answer 1

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%