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Unformatted text preview: MIE364H1S Methods of Quality Control and Improvement Course Instructor: Prof. V. Makis Tutorial #5 1. Samples of size n = 5 are taken from a manufacturing process every hour. A quality characteristic is measured and X and R are computed for each sample. After 30 samples have been analyzed, we have: 30 1 705.3, i i X = = ∑ 30 1 128. i i R = = ∑ a. Find the control limits for the X and R charts. b. Assume that both charts exhibit control and that the quality characteristic is normally distributed. Estimate the process parameters and find the natural tolerance limits of the process. c. Assume that the specification limits are: LSL = 18, USL = 30. Perform capability analysis. Estimate the fraction nonconforming below the LSL and above the USL. d. Under the assumptions in part b, find a 95% confidence interval for For the construction of the confidence interval, assume that the sample standard deviation for the whole sample consisting of 150 observations is S = 1.8. To obtain the critical value . p C 2 , α υ χ for the Chi-squared distribution with υ degrees of freedom, one can use the approximate formula: 2 3 , 2 2 (1 ) 40 9 9 z for α υ α χ υ υ υ υ ≅ − + > . where z α is the critical value of the standard normal distribution, Ф (z α ) = 1 – α . e. The supplier claims that the process capability exceeds = 1.2. Under the assumptions in part b, c, and d, what conclusions can be drawn from the data? Use α = 0.05. p C 2. A supplier claims that his process capability exceeds = 1.35. He also wants that if the process capability exceeds 1.89 the probability of judging the process capable will be 0.95. The producer, on the other hand, wants to be sure that if the process capability is below 1.35 the probability of detecting this will be 0.95. Establish a procedure to test the hypothesis using the table in the textbook. p C 3. The time needed to overhaul a large diesel engine used in mining bauxite ore is an important quality characteristic. Assume that the shop manual specifies 85 to 115 hours for the job. 20 samples of size n = 5 are collected and the data are shown below. a. Construct control charts....
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This note was uploaded on 07/24/2010 for the course MIE MIE364 taught by Professor Makis during the Spring '10 term at University of Toronto.
- Spring '10