GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY.

Hi,kindly reply with whole answers correct,accurate answers and step by step working.Do not skip step.Be very clear and mention about the formula for each step.Make sure the answers are correct and accurate. Be very organised with the working and systematic.Please explain to support and make it clear.

STA September 2015

QUESTION 5 a) Suppose the process for manufacturing electrical shafts is in control. At the end of each hour, for a period of 10 hours, the manufacturer selected a random sample of five shafts and measured the diameter of each. The mean and range of measurements (in inches) for the 20 samples are recorded below. Sample Number Mean Range Sample Number Mean Range 3.55 0.15 11 3.49 0.16 3.55 0.16 12 3.48 0.17 3.54 0.09 13 3.45 0.18 3.49 0.08 14 3.42 0.11 3.49 0.10 15 3.49 0.09 3.50 0.12 16 3.50 0.12 3,53 0.11 17 3.53 0.15 3.47 0.09 18 3.47 0.16 3.52 0.12 19 3.53 0.11 10 3.51 0.15 20 3.54 0.09 i) What are the center line and 30 trial control limits for the mean and range control charts? (6 marks) ii) Establish the mean and range control charts using the above information obtained in (a). Comment on the process based on the two control charts. (7 marks) b) The following measurements were obtained from a standard process of spectacles manufacturing uses a thin layer of plastic material. Measurement X S Thickness 57 1.5 Assume that the thickness of spectacles manufacturing processes is normally distributed with specifications is at 54 + 6. i) Estimate the natural tolerance limit for the process and interpret the limit obtained. (3 marks) i) Find the Co and Cox for the process and make a conclusion based on the value obtained. (4 marks)