MIE1727 Assignment 2

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University of Toronto *

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1727

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Mechanical Engineering

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Apr 3, 2024

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University of Toronto Department of Mechanical and Industrial Engineering MIE1727: Quality Assurance I (Winter 2023) Assignment 2 Due: Monday, March 20, 2023, at 5pm. Submit to Crowdmark. Please post questions to Piazza Question 1 (12 points) Provide answers to the follow questions. a) In some cases, the quality characteristic that you are measuring may be eligible for variables control chart or an attributes control chart. Discuss the pros and cons of choosing one or the other. (3 points) b) Explain the difference between control charts for nonconformity (c-chart) number of nonconforming (np-chart) and fraction of nonconforming (p-chart). (3 points) c) What is the difference between actual process capability and process potential capability? Why should we calculate the actual process capability ratio for some cases? Explain. (3 points) d) Estimating the process capability can be done using a histogram and probability plotting. Clearly state the advantages and disadvantages of both methods. (3 points) Question 2 (8 points) A process has an in control fraction nonconforming of p = 0.01. The sample size is n = 300. What is the probability of detecting a shift to an out of control fraction nonconforming of p = 0.05 on the first sample following the shift? Question 3 (10 points) A production line runs in batches of size 1000 where 64 units from each batch is sampled for quality assurance. The nominal fraction nonconforming is known to be ? = 0.1. a) Set up the control chart. You do not have to provide a graphical representation. (3 points) b) Suppose the customer risk is set to 0.5. What is the maximum fraction nonconforming that produces this risk level? You may estimate this answer using numerical tools. (3 points) c) Determine the sample size required to force a positive lower control limit for this chart. (2 points) d) Discuss why a positive LCL is preferable to LCL= 0. (2 points)
University of Toronto Department of Mechanical and Industrial Engineering MIE1727: Quality Assurance I (Winter 2023) Question 4 (10 points) A new scientific journal from Elsevier publisher has a new specification with managing the first decision of the new research paper submissions within 24 hours. Table 1 shows the number of decisions made each day for the last 20 days and the number of submissions that required more than 24 hours to be issued. Table 1: research papers’ submissions data . Day #Submissions Late decisions Day #Submissions Late decisions 1 200 3 11 219 0 2 250 4 12 238 10 3 240 2 13 250 4 4 300 5 14 302 6 5 200 2 15 219 20 6 250 4 16 246 3 7 246 3 17 251 6 8 258 5 18 273 7 9 275 2 19 245 3 10 274 1 20 260 1 a) Set up the fraction nonconforming control chart for this process, using the variable width control limit approach. Plot the preliminary data in Table 1 on the chart. Is the process in statistical control? (3 points) b) Assume that assignable causes can be found for any out of control points on this chart. What center line should be used for process monitoring in the next period, and how should the control limits be calculated? (3 points) c) Set up the fraction nonconforming control chart for this process, using the average sample size control limit approach. Plot the preliminary data in Table 1 on the chart. Is the process in statistical control? Compare this control chart to the one based on variable width control limits. (4 points)
University of Toronto Department of Mechanical and Industrial Engineering MIE1727: Quality Assurance I (Winter 2023) Question 5 (10 points) The IT department at the University of Toronto measures their efficacy by how many service tickets are completed within 48 hours of creation. Twenty months of data are shown in Table 2 . Table 2: Number of service tickets resolve outside of 48 hours. Month Total tickets >48 hours Month Total tickets >48 hours 1 150 2 11 100 1 2 150 1 12 100 0 3 250 9 13 100 1 4 250 7 14 200 4 5 200 5 15 200 3 6 200 3 16 200 4 7 200 6 17 200 10 8 250 8 18 200 4 9 250 7 19 150 0 10 250 6 20 150 2 a) Construct the trial control chart for this process. You are invited (but not required) to use Minitab, but still required to show the computations for your limits. (2 points) b) Discuss how you may use the results from part (a) to phase II control. (1 points) c) Repeat this exercise for an average sample size. Include necessary cautions. (3 points) d) Repeat this exercise using standard deviation units. (2 points) e) Since there are only a few sample sizes construct a special control chart that has four different sets of control limits all on one set of axes, one for each sample size. Discuss how it would be used, and how it compares to the chart from part (a). (2 points) Question 6 (15 points) The following fraction nonconforming control chart with ? = 400 is used to control a process: UCL = 0.0962 Center line = 0.0500 LCL = 0.0038 a) Find the width of the control limits in standard deviation units. (2 points)
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