I hope you can help write down the calculation process and answers to these questions. Thank you very very very much.

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1. (20 points) Thirty samples each of size 7 have been collected to establish control over a process. The 30 30 following data were collected: 2700 and R, -120. i-l i and standard deviation. (a) (5 points) Estimate the process mean (b) (5 points) Establish an chart for this process. (c) (5 points) Establish an R chart for this process. (d) (5 points) Establish an S chart for this process. 8012. Assume that -86 and chart are calculated as UCL-92 and 2. (30 points) The Engineering specifications for a torque of a fastener are =4 of the process are known. The 3-sigma control limits for LCL-80. Assume that the torque values are normally distributed and the process is in control. (a) (5 points) What is the sample size for the (b) (5 points) Establish an R chart for this process. chart? (c) (5 points) Establish an S chart for this process. (d) (5 points) What are the PCR, PCR, and PCR for this process? (e) (5 points) If the process is in control, what is the current fraction of nonconforming? (f) (5 points) If we wish to use p chart to maintain the fraction of nonconforming in (e) with samples of size 36, establish the p chart for this process. 3. (10 points) A process is being in-control with a p-chart. The average fraction of nonconforming this process is 0.07. Suppose that 3-sigma control limits are used and sample size is 400. (a) (5 points) What are the UCL and LCL for the np-chart? (b) (5 points) What is the smallest sample size that would yield a positive LCL? 4. (15 points) A c chart with center line at 2.5 is used to monitor a manufacturing process. Two limits are used for the chart: an control limit at +3 and a warning limits at +20. If a point falls above the control limit or two consecutive points fall between the control limit and the warning limit, then the process is stopped until the problem is corrected. (a) (5 points) Find the values of the control limit and the warning limit. (b) (5 points) If the process suddenly shifts to a mean value of 6, what is the probability that a point falls between the control limit and the warning limit? (c) (5 points) If the process suddenly shifts to a mean value of 6, what is the probability that two out of three consecutive points fall between the control limit and the warning limit? 5. (10 points) A sample of size n is collected and the estimated process capability is computed as C. Find the two-sided confidence interval for C, with significant level (1-a) where a=a+a, a is upper- tail probability and a, is lower-tail probability. 6. (15 points) A rectangular piece of metal of width W and length L is cut from a plate of thickness T. If W, L, and I are independent random variables with -10cm, =0.2cm H =20cm. =0.3cm, and ,3cm, =0.1cm,. We know that the density of the metal is 0.08 g/cm. what would be the estimated mean and standard deviation of the weights of the pieces produced by this process? (a) (5 points) What would be the estimated mean the weights of the pieces produced by this process? (b) (10 points) What would be the estimated standard deviation of the weights of the pieces produced by this process? 1. (20 points) Thirty samples each of size 7 have been collected to establish control over a process. The 30 30 following data were collected: 2700 and R, -120. i-l i and standard deviation. (a) (5 points) Estimate the process mean (b) (5 points) Establish an chart for this process. (c) (5 points) Establish an R chart for this process. (d) (5 points) Establish an S chart for this process. 8012. Assume that -86 and chart are calculated as UCL-92 and 2. (30 points) The Engineering specifications for a torque of a fastener are =4 of the process are known. The 3-sigma control limits for LCL-80. Assume that the torque values are normally distributed and the process is in control. (a) (5 points) What is the sample size for the (b) (5 points) Establish an R chart for this process. chart? (c) (5 points) Establish an S chart for this process. (d) (5 points) What are the PCR, PCR, and PCR for this process? (e) (5 points) If the process is in control, what is the current fraction of nonconforming? (f) (5 points) If we wish to use p chart to maintain the fraction of nonconforming in (e) with samples of size 36, establish the p chart for this process. 3. (10 points) A process is being in-control with a p-chart. The average fraction of nonconforming this process is 0.07. Suppose that 3-sigma control limits are used and sample size is 400. (a) (5 points) What are the UCL and LCL for the np-chart? (b) (5 points) What is the smallest sample size that would yield a positive LCL? 4. (15 points) A c chart with center line at 2.5 is used to monitor a manufacturing process. Two limits are used for the chart: an control limit at +3 and a warning limits at +20. If a point falls above the control limit or two consecutive points fall between the control limit and the warning limit, then the process is stopped until the problem is corrected. (a) (5 points) Find the values of the control limit and the warning limit. (b) (5 points) If the process suddenly shifts to a mean value of 6, what is the probability that a point falls between the control limit and the warning limit? (c) (5 points) If the process suddenly shifts to a mean value of 6, what is the probability that two out of three consecutive points fall between the control limit and the warning limit? 5. (10 points) A sample of size n is collected and the estimated process capability is computed as C. Find the two-sided confidence interval for C, with significant level (1-a) where a=a+a, a is upper- tail probability and a, is lower-tail probability. 6. (15 points) A rectangular piece of metal of width W and length L is cut from a plate of thickness T. If W, L, and I are independent random variables with -10cm, =0.2cm H =20cm. =0.3cm, and ,3cm, =0.1cm,. We know that the density of the metal is 0.08 g/cm. what would be the estimated mean and standard deviation of the weights of the pieces produced by this process? (a) (5 points) What would be the estimated mean the weights of the pieces produced by this process? (b) (10 points) What would be the estimated standard deviation of the weights of the pieces produced by this process?