University of Alberta
Department of Mathematical and Statistical Sciences
Stat 335 Mid-term II (Closed Book Exam)
Nov 10 2010 2pm-2.50pm
Answer All Questions
1. A control chart for the number of nonconforming piston rings is maintained on a forging process with np=17.0. A sample of size 100 is taken each day and analyzed.
(a)What is the probability that a shift in the process average to np=21 will be detected on the first day following the shift? (Use normal approximation)
(b)What is the probability that the shift will be detected by at least the end of second day? (Use normal approximation)
(c) Find the smallest sample size that will give a positive lower control limit.
2. The number of nonconformities observed in the final inspection of assembled units has been tabulated as shown in the following table. Construct a suitable control chart . Does the process appear to be in control?
Day / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10No. Inspected / 2 / 4 / 3 / 2 / 3 / 3 / 2 / 3 / 3 / 1
Total No. defects / 10 / 25 / 15 / 10 / 18 / 22 / 15 / 24 / 20 / 6
3. Two different sizes of a certain type of fastener are being manufactured by a cold heading process. The nominal outside diameters of the fastener heads, with associated specifications , are
Fastener A: 0.600+/ 0.020 centimeters,
Fastener B: 0.800+/- 0.020 centimeters.
SPC studies show the process to be in good statistical control. The individual measurements follow the normal distribution. After collecting 50 samples of size n=4:
Fastener A: and
Fastener B: and
a). For each fastener dimension of interest, find the percent conforming.
b). If the process mean for fastener A could be brought to the nominal, what would be the percent conforming?
c). If the variation (standard deviation) in the process for fastener B could be reduced by a factor of one-half, what would be the percent conforming?