A myelearning.sta.uwi.edu C U Sovereignty in Intern. W Yang Zewei: The Leg. Sovereignty, Internati page 2 Question 1 (20 marks) A craft brewing company packages batches of its custom beer by using automatic fill machines fitted with sensors to dispense into foil-sealed single-serve beer mugs. The production operator is tasked with taking a sample each hour, where every sample must consist of 4 sealed mugs. The operator measures the volume of beer in each mug and records the 4 values in a spreadsheet. Then she calculates the average beer volume and the range of volumes for each sample. The table below shows the average volumes and range of volumes for samples she tested across her 10-hour shift. Sample Average beer volume in Range of volume in 4 sampled beer bottles 4 sampled beer bottles /ml /ml 265 2 277 274 275 282 274 273 10 8 270 276 14 10 264 a) Showing your calculations clearly, construct the appropriate control chart for determining if the process is in control for the data provided. (10 marks) b) What type of data does the control chart analyse? (1 mark) c) Determine whether the process is in control. (I mark) d) If there are any out of control points, outline 2 possible cause types that could have caused them. Giving a specific example of each type, outline how you could address your specific cause in order to be able to return the process to a state of control (4 marks) () Assume assignable causes and determine the revised control limits. (4 marks) Question 2 (20 marks) 2 MacBook Air 20 DD DII DD F3 F4 FS F6 F7 F8 FO % "> & A 5 6 E R T Ymyelearning.sta.uwi.edu U Sovereignty in Intern.. W Yang Zewei: The Leg. O Sovereignty, Internati page 4 TABLE OF CONSTANTS FOR CONTROL CHARTS Below is a table of control chart constants used to calculate Control Limits. The constants are used as follows: D3 and D4 are used in X-MR (1-MR) charts A2, D3, and D4 are used in x-bar and R charts A3, B3, and B4 are used in x-bar and s charts n A2 D3 D4 A3 B3 B4 N 1.88 0 3.27 2.66 0 3.27 1.02 0 2.57 1.95 0 2.57 0.73 2.28 1.63 0 2.27 0.58 0 2.11 1.43 0 2.09 0.48 0 2.00 1.29 0.03 1.97 0.42 0.08 1.92 1.18 0.12 1.88 8 0.37 0.14 1.86 1.10 0.19 9 1.81 0.34 0.18 1.82 1.03 0.24 1.76 10 0.31 0.22 1.78 0.98 0.28 11 1.72 0.29 0.26 N.74 0.93 0.32 1.68 12 0.27 0.28 1.72 0.89 0.35 13 0.25 1.65 0.31 1.69 0.85 14 0.38 1.62 0.24 0.33 1.67 0.82 0.41 15 0.22 1.59 0.35 1.65 16 0.79 0.43 0.21 1.57 0.36 1.64 0.76 17 0:45 0.20 1.55 0.38 1.62 0.74 0.47 18 0.19 1.53 0.39 1.61 0.72 19 0.19 0.48 1.52 0.40 1.60 0.70 20 0.50 0.18 1.50 0.41 1.59 0.68 0.51 1.49 END OF EXAMINATION IHAS