chapter 10 short answers - Lesson 14 Statistical Process...

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1 Lesson 14 Statistical Process Control Solutions Solved Problem #2: see textbook Solved Problem #4: see textbook Solved Problem #5: see textbook Solved Problem #6: see textbook (manual problem) #1: Checkout time at a supermarket is monitored using a range and mean chart. Six samples which contain 20 observations per sample have been collected and the sample means and sample ranges have been computed as shown below. Sample Mean Range 1 3.06 0.42 2 3.15 0.50 3 3.11 0.41 4 3.13 0.46 5 3.06 0.46 6 3.09 0.45 Perform the manual calculations necessary to answer the following questions. a. What is the sample size? 20 b. Is the variability of the checkout time known or unknown? Unknown c. Which chart is used to analyze the checkout time variability? Range chart d. Which chart is used to analyze the checkout time? Mean chart e. Should the range or mean chart be analyzed first? Explain your answer. Range chart should be analyzed before the mean chart because the variability of the process must be in control before the mean chart can be analyzed. Analyze the range chart by answering the following questions. f. What is the grand range? .45 g. Calculate the centerline, upper and lower control limits for the range chart?
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2 71325 . 585 . 1 * 45 . * 18675 . 415 . * 45 . * 45 . 4 3 = = = = = = = = = D R UCL D R LCL R range grand Centerline h. Plot the range chart showing the centerline, upper and lower control limits. Centerline LCL UCL Sample Range 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 01234567 i. Are the sample ranges within the control limits? Yes j. Count the number of A/B and U/D runs for the range chart. A/B B A B A A B 5 runs U/D U D U D D 4 runs k. What is the expected number of A/B runs? 4 1 2 6 1 2 # ) ( / = + = + = ns Observatio r E B A l. What is the variability of the expected number of A/B runs? 118 . 1 4 1 6 4 1 # ) ( / = = = ns Observatio r B A σ m. What is the test statistic for the expected number of runs? 89 . 118 . 1 4 5 ) ( ) ( # ) ( / / / = = = B A B A B A r r E runs r Z n. Based on 3-sigma control limits for the runs test, does the pattern analysis indicate the A/B runs are random? Why?
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3 Yes, because it is between -3 and 3. o. What is the expected number of U/D runs? 67 . 3 3 1 6 * 2 3 1 ) (# 2 ) ( / = = = ns Observatio r E D U p. What is the variability of the expected number of A/B runs? 86 . 90 29 6 * 16 90 29 ) (# 16 ) ( / = = = ns Observatio r D U σ q. What is the test statistic for the expected number of runs? 38 . 86 . 67 . 3 4 ) ( ) ( # ) ( / / / = = = D U D U D U r r E runs r Z r. Based on 3-sigma control limits for the runs test, does the pattern analysis indicate the U/D runs are random? Why? Yes, because it is between -3 and 3 s. Is the variability of the checkout times in control (i.e is the range chart in control)? Why? Yes. The sample ranges are within the limits, the A/B runs are random, and the U/D runs are random. Analyze the mean chart by answering the following questions. t. What is the grand mean? 3.10 u. Calculate the centerline, upper and lower control limits for the mean chart?
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This note was uploaded on 12/13/2011 for the course MANAGEMENT 103 taught by Professor Mr.singh during the Spring '11 term at Aristotle University of Thessaloniki.

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chapter 10 short answers - Lesson 14 Statistical Process...

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