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Product S is designed with thickness specification of 12 +0.20 mm. Quality team has decided to take four samples randomly during the production process for quality monitoring. A total of 10 subgroups of samples were taken and the data is shown in Table 3 (Assume the number of subgroups is enough for the inspection process). Table 3: Thickness sampling data for product S Sample in mm) Subgroup X1 X2 X3 X4 12.00 11.97 12.10 12.08 11.91 11.94 12.10 11.96 11.89 11.97 11.99 12.02 12.10 12.05 11.95 12.09 11.82 12.08 12.05 12.32 11.99 11.97 12.02 11.89 12.00 12.00 12.03 12.09 12.04 12.01 11.99 11.95 11.90 12.06 12.12 12.05 12.09 11.94 12.00 11.92 a. Develop suitable control chart and establish the central line, upper and lower control limits. Assume the process includes 99.73% of the associated random variation. Appendix A provides additional information to assist you in the control limits calculations. Note: All answers are to be calculated to two (2) decimal points. (10 marks) b. Plot the graph. Analyse the current production performance and suggest appropriate actions to be taken. Based on the performance of the process, should Cpk be calculated? Justify your answer. (6 marks) c. The assignable causes have been found and actions have been taken. New data has been collected as shown below: x= 12.02mm, R=0.15mm and o=0.05 mm Calculate process capability (Cp and Cpk). Comment on the results in terms of capability to fulfill thickness specification of 12 +0.20 mm. Note: All answers are to be calculated to two (2) decimal points. (4 marks)