Two machined parts must be assembled as shown in the diagram below. To function properly a clearance must be maintained between the two parts. The critical dimension on Part A has specifications of 1.8 + 0.05 and the critical dimension on Part B has specifications of 1.4 + 0.05 as indicated. The design engineers have specified that the clearance on each side be 0.2 + 0.05. Production data indicates that for Part A the average dimension is 1.790 with a standard deviation of 0.0189; for Part B the average dimension is 1.406 and a standard deviation of 0.0220.
a. Assuming a normal distribution, what proportion of the production of Part A is outside the specification limits? Above the upper specification limit? Below the lower specification limit?
b. Assuming a normal distribution, what proportion of the production of Part B is outside the specification limits? Above the upper specification limit? Below the lower specification limit?
c. Approximately what proportion of the distribution of clearances will lie outside specification limits? Above the upper specification limit? Below the lower specification limit?
d. What assumptions did you make in answering part c?
e. Assuming the process for machining Part A can be re-centered to the target dimension of 1.8, estimate the proportion of the Part A distribution that would be out of specification on the upper and lower sides respectively.
f. If the process for Part A machining can be re-centered to the target dimension of 1.8, what proportion of the clearance distribution will lie outside the specification limits on the high and low sides respectively?
g. If you assume that six standard deviations covers most of the distribution, can you suggest a tighter specification range for the clearance specifications?