QUESTION #1: [10 marks] Sand is an important component in a process that produces molds for cylinder blocks Foundry workers have determined that the compactibility of the sand is of key importance in making good molds. Compactibility is measured as the percent reduction in volume in a fixed amount of sand after being compacted with a standard force. Because testing sand samples is time consuming, an individuals chart (I or X chart) and MR chart are used to monitor the compactibility. The following data represent compactibility measurements (in percent) from 30 successive samples taken from the molding process (read the data across and then down i.e. left to right, i.e. x1 = 44, x2 = 39, X3 = 49, etc.): = 44 33 44 39 31 41 49 30 49 41 46 38 38 45 41 44 48 40 40 45 48 43 42 42 40 40 36 41 45 39 1. For the individuals chart, based on the sample standard deviation, what is an estimate for the process standard deviation? (1 mark) 2. For the individuals chart, based on the moving-range method, what is an estimate for the process standard deviation? (1 mark) 3. Use the moving-range estimate (part 2) to construct (calculate) the appropriate control chart limits to check whether the compactibility data is in statistical control? (5 marks ) 4. Are the and MR charts indicating any problems with the sand compactibility? (Explain and revise the control limits if need be. Assume assignable causes can be found and explained.) (1 mark) (NOTE: You do not need to plot and submit the control charts, just indicate which points, if any, are falling outside the control limits.) 5. Now use the standard-deviation estimate (part 1) to calculate the appropriate control chart limits you would use to monitor the process average and the process variability. (2 marks) QUESTION #1: [10 marks] Sand is an important component in a process that produces molds for cylinder blocks Foundry workers have determined that the compactibility of the sand is of key importance in making good molds. Compactibility is measured as the percent reduction in volume in a fixed amount of sand after being compacted with a standard force. Because testing sand samples is time consuming, an individuals chart (I or X chart) and MR chart are used to monitor the compactibility. The following data represent compactibility measurements (in percent) from 30 successive samples taken from the molding process (read the data across and then down i.e. left to right, i.e. x1 = 44, x2 = 39, X3 = 49, etc.): = 44 33 44 39 31 41 49 30 49 41 46 38 38 45 41 44 48 40 40 45 48 43 42 42 40 40 36 41 45 39 1. For the individuals chart, based on the sample standard deviation, what is an estimate for the process standard deviation? (1 mark) 2. For the individuals chart, based on the moving-range method, what is an estimate for the process standard deviation? (1 mark) 3. Use the moving-range estimate (part 2) to construct (calculate) the appropriate control chart limits to check whether the compactibility data is in statistical control? (5 marks ) 4. Are the and MR charts indicating any problems with the sand compactibility? (Explain and revise the control limits if need be. Assume assignable causes can be found and explained.) (1 mark) (NOTE: You do not need to plot and submit the control charts, just indicate which points, if any, are falling outside the control limits.) 5. Now use the standard-deviation estimate (part 1) to calculate the appropriate control chart limits you would use to monitor the process average and the process variability. (2 marks)
