MIE364S_T_4_11 - MIE364H1S Methods of Quality Control and...

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MIE364H1S Methods of Quality Control and Improvement Course Instructor: Prof. V. Makis Tutorial #4 1. Fifteen successive heats of a steel alloy are tested for hardness. The resulting data are shown below. Set up a control chart for the moving range and a control chart for individual hardness measurements. Heat Hardness (coded) Heat Hardness (coded) 1 52 9 58 2 51 10 51 3 54 11 54 4 55 12 59 5 50 13 53 6 52 14 54 7 50 15 55 8 51 2. The following X and S charts based on n = 4 have shown statistical control: X chart UCL = 710 Centre line = 700 LCL = 690 S chart UCL = 18.08 Centre line = 7.979 LCL = 0 a. Estimate the process parameters µ and σ . b. If the specifications are at 705 ± 15, and the process output is normally distributed, estimate the fraction of nonconforming. c. For the X chart, find the probability of a type I error, assuming σ is constant. d. Suppose the process mean shifts to 693 and the standard deviation simultaneously shifts to 12. Find the probability of detecting this shift on the X chart on the first subsequent sample. e. For the shift of part (d), find the average run length.
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MIE364S_T_4_11 - MIE364H1S Methods of Quality Control and...

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