MIE364S_T_3_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 #3 1. A quality characteristic is monitored by a control chart designed so that the probability that a certain out-of-control condition will be detected on the first sample following the shift to that state is 1- β . Find the following: a. The probability that the out-of-control condition will be detected on the second sample following the shift. b. The probability that the out-of-control condition will be detected on the k th sample following the shift. c. The expected number of subgroups analyzed before the shift is detected. d. The probability that the first sample following the shift produces a statistic that plots inside the control limits. e. The probability that the shift is not detected on a sample. f. The probability that two consecutive samples produce statistics that plot outside of the control limits. g. The probability that at least one of the next k samples yields values of the test statistic that plot outside the control limits. 2. An X chart with 3-sigma control limits has parameters as follows: UCL = 20.5 LCL = 19.5 Construct an OC curve for the chart. 3. An X chart with 3-sigma control limits is used to monitor a manufacturing process. The process mean ( µ ) and standard deviation ( σ ) are given as 23.51 and 1.8344, respectively. Samples of size n = 5 are taken from the process every hour. a. Suppose the process mean shifts to 22 while the standard deviation remains constant. Find the average run length for the chart.
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MIE364S_T_3_09-1 - MIE364H1S Methods of Quality Control and...

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