1. For the following processes, complete the given table:

Specification Process % above % below

Nominal Tol Mean StdD. %OK USL LSL Cp Cpk

10.00 + 0.04 10.00 0.02 95.45 = (100 2*2.275) 2.275% 2.275% 0.67 0.67

10.00 + 0.04 9.99 0.02

10.00 + 0.04 10.01 0.02

10.00 + 0.05 10.00 0.02

10.00 + 0.06 10.01 0.02

2. The Lowell MFG Co. has a policy of Cp = 1.2 for all new products. All sheet metal specifications are designed with a tolerance of + 4 mils. The control charts of the sheet metal process in manufacturing are maintained with a daily monitoring of 16 samples. The cost of each reject was calculated at $ 5.00. Assume a manufacturing process average or X double bar of 100 mils.

a. What should the X bar and R chart control limits be to meet the CP target?

X double bar ____ UCLx ______ LCLx _____ Rbar____ QLF ______

b. What is the reject rate for new parts ________, _______ppm

c. If the sheet metal punch press average was shifted by 1 mil, what will the new Reject Rate be:

PPM___, Cpk ______

d. If the Motorola definition of Cp was used (1.5 sigma shift), what is the reject rate?

________%, _______PPM, Cpk _______

3. The Lawrence MFG Co. has a policy of Cp = 1.2 for all new products. The sheet metal department has an X Bar control chart with X double bar at 100 mils, Upper Control Limit of 109 mils and Lower Control Limit of 91 mils, based on taking 9 daily samples. A new housing is being designed with a critical parameter of 100 mils. The cost of each reject was calculated at $1.00.

a. What should the product specifications be to meet the Cp target?

USL______ LSL_________

b. What do expect the reject rate ____%, ____PPM

c. If you were using the MOTOROLA definition of Cp= 1.2 (all processes have an average shift of 1.5 sigma). What is the reject rate in ppm? QLF using the actual process as indicated by the Xbar chart?

RR ______ppm, QLF _____