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MIE364S_T_6_09-1

# MIE364S_T_6_09-1 - MIE364H1S Methods of Quality Control and...

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MIE364H1S Methods of Quality Control and Improvement Course Instructor: Prof. V. Makis Tutorial #6 1. A process that produces titanium forgings for automobile turbocharger wheels is to be controlled through use of a fraction nonconforming chart. Initially, one sample of size 150 is taken each day for 18 days and the process average has been shown to be 0.0185. a. Construct the p chart with probability limits, α = 0.002. b. Find the β -risk when the true value of p is 0.04. c. What sample size is required if we wish to detect a shift in the process fraction non- conforming to 0.03 with probability 0.5? 2. A control chart for the number nonconforming is to be established, based on samples of size 400. To start the control chart, 30 samples were selected and the number nonconforming in each sample determined, yielding . 1200 30 1 = = i i D a. What are the parameters of the np chart? b. Suppose the process average fraction nonconforming shifted to 0.15. What is the probability that the shift would be detected on the first subsequent sample? c. Find the average run length to detect a shift to a fraction nonconforming of 0.15. 3. The data below represents the number of nonconformities observed in an inspection unit of printed circuit boards. Twenty-six samples, each consisting of one inspection unit, are used to obtain the data. Set up a control chart for nonconformities using these data. Does the process appear to be in statistical control? Sample Number Number of Nonconformities Sample Number Number of Nonconformities 1 21 14 19 2 24 15 10 3 16 16 17 4 12 17 13 5 15 18 22 6 5 19 18 7 28 20 39 8 20 21 30 9 31 22 24 10 25 23 16 11 20 24 19 12 24 25 17 13 16 26 15

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