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Engineering · Mechanical Engineering
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This question takes the form of analysing business processes in an organisation and using the appropriate quality tools to formulate improvement suggestions. This assesses the students' ability to apply the theory and concepts in a practical real-life situation. A production process produces primer paint. The viscosity of the paint is used as a measure of its quality and you have been employed to set up mean and range charts to monitor the process. In order to set up the charts, 40 samples, each of size five, have been taken when the process is thought to be in control. The viscosity data from these samples are shown in the Table 1.

Table 1. Viscosity of primer paint [Pa s 34.19 34.00 34.10 34.2234.19 34.20 34.44 34.20 34.1834.19 34.20 34.36 34.18 34.20 34.21 34.17 34.32 34.20 34.2834.19 34.20 34.72 34.14 34.20 34.17 34.22 34.28 34.8834.20 34.21 34.24 34.32 34.24 34.18 34.21 34.19 34.96 34.19 34.20 34.20 34.20 34.84 34.18 34.26 34.21 34.20 34.00 34.21 34.20 34.19 34.21 34.20 34.24 34.20 34.20 34.18 34.84 34.26 34.20 34.20 34.21 34.04 34.12 34.1034.18 34.21 34.24 34.18 34.14 34.21 34.19 34.72 34.26 34.26 34.20 34.1934.92 34.17 34.20 34.21 34.21 34.24 34.10 34.24 34.22 34.18 34.12 34.20 34.14 34.22 34.19 34.18 34.14 34.1034.18 34.20 34.60 34.20 34.20 34.20 34.17 34.48 34.18 34.20 34.18 34.20 34.60 34.2834.2834.20 34.17 34.32 34.18 34.12 34.21 34.18 34.16 34.24 34.2834.19 34.17 34.44 34.10 34.22 34.22 34.21 34.40 34.20 34.16 34.20 34.19 34.60 34.10 34.20 34.20 34.17 34.84 34.10 34.20 34.18 34.21 34.20 34.2834.16 34.20 34.20 34.00 34.26 34.16 34.19 34.19 34.48 34.20 34.20 34.20 34.21 34.32 34.2834.1034.20 34.20 34.64 34.10 34.16 34.19 34.22 34.00 34.26 34.20 34.20 34.24 34.80 34.20 34.26 34.21 34.20 34.40 34.10 34.20 34.23 2 3 4 6 7 8 20 23 24 25 26 27 28 29 30 32 34 35 36

34.22 34.20 34.24 34.20 34.23 34.25 34.60 34.22 34.20 34.24 37 38 39 40 34.22 34.08 34.26 34.2034.24 34.21 34.40 34.24 34.20 34.20 34.12 34.36 34.23 34.7134.25

(1a) For samples from 11 to 23, calculate the corresponding values of mean and range. Show your working. Provide relevant equations. (15 marks)

(1b) Using the data in the Table 1, set up the range chart with 3σ control limits. Does the process variability appear to be in control? (15 marks)

(1c) Construct the mean chart, again with 3σ control limits. Is there any indication that the process was out of control when the data was collected? (20 marks)

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