Question 1: [35 Marks) The quality inspector at a company needs to make sure that the machine used for making a component is working properly. Each hour the inspector takes a sample of 10 components from the outputs and measures the width (in millimetre) of each components. The following table shows the statistics of 25 samples Sample Sample Mean Sample Range 1 40.2 2.9 2 40.1 3.2 3 39.7 3.7 4 40.6 3.1 5 40.9 2.5 6 40.2 2.8 7 40.5 3.2 8 41.2 2.3 9 40.1 2.9 10 41.0 3.4 11 41.2 2.3 12 40.6 2.2 13 41.0 1.5 Sample 14 15 16 17 18 19 20 21 22 23 24 25 Sample Mean 40.2 40.1 40.5 41.2 40.1 41.0 41.2 40.6 39.7 40.6 40.9 40.2 Sample Range 2.5 3.1 3.2 2.3 2.9 3.4 2.3 2.2 3.7 3.1 2.5 2.8 a. Given the above information, should we construct Phase 1 or Phase 2 SPC control charts? Why should the mean and range charts be used for this quality control problem? Provide your justifications. [4 marks) b. Construct both the mean and range charts using 3-sigma control limits. Based on the control charts, what conclusions can you draw about the above process and the control limits? You should clearly label your charts, otherwise marks will be deducted. [20 marks] C. If the specification range for the width of the component is 40+2 mm, is the process capable of meeting the width specification? Provide your justification. [6 marks) d. How large should the process standard deviation be if the process can be concluded as capable of meeting the width specification? [5 marks]