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QUALITY DATA ANALYSIS 18/06/2021 General recommendations: • write the solutions in CLEAR and READABLE way on paper and show (qualitatively) all the relevant plots; • avoid (if not required) theoretical introductions or explanations covered during the course; • always state the assumptions and report all relevant steps/discussion/formulas/expression to present and motivate your solution; • when using hypothesis tests provide the numerical value of the test statistic and the test conclusion in terms of p-value. • For exams in presence: to access the software on the provided laptops, go on b rowser → Favourites → Managed favourites → Virtual Desktop and enter your Polimi credentials. • Exam duration: 2h 10min Exercise 1 (15 points) A process for the production of piston rings is monitored by means of an 𝑋̅ control chart on the mean piston ring diameter. Samples are collected every 2 hours, and the control chart is designed with 𝐴𝑅𝐿0 = 300. 1) Estimate the curves of the average time to signal (ATS) as a function of the mean shift 𝛿 expressed in standard deviation units with a sample size 𝑛 = 4 and 𝑛 = 8, respectively (show the two curves for 𝛿 ∈ [0 4] and report the ATS values for 𝛿 = 1 and 𝛿 = 2). 2) Estimate the curves of the ATS as a function of the sample size n for two values of the shift, 𝛿 = 1 and 𝛿 = 2 (show the two curves for 𝑛 ∈ [2 20]). 3) The head of the quality assurance department is interested in optimizing the process monitoring solution for two mean shifts of major interest, i.e., 𝛿 = 1 and 𝛿 = 2. Assuming the cost of a process in its in-control state as reference baseline, when the proc ess mean shifts to an out -of-control state, an additional cost is due and equal to C1 = 2€ for each hour spent in the out -of-control state when 𝛿 = 1 or equal to C1 = 7€…