b. Determine X and R. Note: Round your answers to 3 decimal places. X bar R bar c. Determine the UCL and LCL for a X chart. Note: Round your answers to 3 decimal places. UCL LCL d. Determine the UCL and LCL for R-chart. Note: Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 3 decimal p UCL LCL e. What comments can you make about the process? O Process is in statistical control
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- Factors for Computing Control Chart Limits (3 sigma) Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean x (mm) Range R (mm) 1 156.9 4.2 2 153.2 4.6 3 153.6 4.1 4 155.5 5.0 5 156.6 4.5 Part 4 c) What are the (UCLx) and (LCLx) using 3-sigma? (UCLx) = mm (round your response to two decimal places). (LCLx) = mm1. An ad agency tracks the complaints, by week received, about the billboards in its city: Week No. of Complaints 1 8 2 4 3 11 4 16 5 8 6 9 This exercise contains only parts a, b, and c. a) The type of control chart that is best to monitor this process is c minus chartc−chart . b) Using z = 3, the control chart limits for this process are (assume that the historical complaints rate is unknown): UCLc =?complaints per week (round your response to two decimal places). LCLc =?complaints per week (round your response to two decimal places).Refer to Table 56.1-Factors for Computing Control Chart Limits.(3.sigma) for this problem. Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? mm (round your response to two decimal places). b) What is the value of R? R=mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Day 1 2 3 4 5 Upper Control Limit (UCL;)mm (round your response to two decimal places) Lower Control Limit (LCL;)mm (round your response to two decimal places). d) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCLR)-mm (round your response to two decimal places). Lower Control Limit (LCL)-mm (round your response to two decimal places) Mean x (mm) 154.9 151.2 155.6 155.5 154.6 Range R (mm) 4.4 4.8 4.3 5.0 4.7 Next
- 63. X control charts are used to maintain control of the manufacture of the cases used to house a generic brand of personal computer. Separate charts are maintained for length, width, and height. The length chart has UCL = 20.5 inches, LCL = 19.5 inches, and a target value of 20 inches. This chart is based on using subgroups of size 4 and three- sigma limits. However, the customer's specifications require that the target length should be 19.75 inches with a tolerance of ±0.75 inch. What percentage of the cases shipped will fall outside the customer's specifications?An e-commerce website has received some complaints on Billing errors. Managers ask the accounting department to monitor the shipping process and make sure of the quality in their process. To monitor the process, for 10 consecutive weeks, they look into the first 100 shipments and count the number of Billing errors as shown in table below: 45 52 6 3 63 7 8 9 10 1 6 1 2 Construct a two-sigma limit control chart to show whether the shipping process in this e-commerce firm needs any improvement or performs at an acceptable level. (Round your answer to three decimal places.) Week 1 2 3 Number of Billing errors. 5 1 3 Upper Control Limit Lower Control LimitAn automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approximately normal with a mean of 1.0 liter and standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. Determine upper and lower control limits that will include roughly 97% of the sample means when the process is in control. Using Appendix B, Table A to find the value of Z corresponding to the mean control limits.
- 7. An ad agency tracks the complaints, by week received, about the billboards in its city: Week No. of Complaints 1 3 2 6 3 4 4 12 5 2 6 9 This exercise contains only parts a, b, and c. Part 2 a) The type of control chart that is best to monitor this process is c minus chart ______ . Part 3 b) Using z = 3, the control chart limits for this process are (assume that the historical complaints rate is unknown): UCLc = ________ complaints per week (round your response to two decimal places). The upper control limit is: ________ The lower control limit is: _________ The central limit is ___________Arana is a company that produces homemade Rotini pasta. They use statistical process control to monitor the manufacturing process. The company collects five samples, each containing six packs of pasta. Below is the sample data, but the standard deviation of the process output is unknown. If an R chart is created using three-sigma limits (i.e., z = 3) to monitor the variability of products, what would be the upper control limit for this R chart? Sample 1 Sample 2 Sample 3 Pack 1 452.3 451.6 448.6 Sample 4 454.7 Sample 5 448.9 7.614 9.328 11.653 13.427 Pack 2 452.8 451.2 455.6 451.7 453.4 Pack 3 456 454.6 456.5 451 456.7 Pack 4 457.2 455.3 451.9 452.6 456.3 Pack 5 457.8 452.2 455.6 454.7 452.4 Pack 6 451.8 451.9 448.3 458.4 456A machine at the Pacific Fruit Company fills boxes withraisins. The labeled weight of the boxes is 9 ounces. The company wants to construct an R-chart to monitor the fill-ing process and make sure the box weights are in control. The quality-control department for the company sampledfive boxes every two hours for three consecutive workingdays. The sample observations are as follows: Construct an R-chart from these data with 3 control lim-its, plot the sample range values, and comment on process control. Samples Box Weights (oz)1 9.06 9.13 8.97 8.85 8.462 8.52 8.61 9.09 9.21 8.953 9.35 8.95 9.20 9.03 8.424 9.17 9.21 9.05 9.01 9.535 9.21 8.87 8.71 9.05 9.356 8.74 8.35 8.50 9.06 8.897 9.00 9.21 9.05 9.23 8.788 9.15 9.20 9.23 9.15 9.069 9.98 8.90 8.81 9.05 9.1310 9.03 9.10 9.26 9.46 8.4711 9.53 9.02 9.11 8.88 8.9212 8.95 9.10 9.00 9.06 8.95
- Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? = x= 156.76 mm (round your response to two decimal places). b) What is the value of R? R= mm (round your response to two decimal places). Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 Range R (mm) 4.2 4.4 4.3 4.8 4.3Boxes of Honey-Nut Oatmeal are produced to contain 15.0 ounces, with a standard deviation of 0.10 ounce. For a sample size of 49, the 3-sigma x chart control limits are: Upper Control Limit (UCL) = | ounces (round your response to two decimal places). Lower Control Limit (LCL;) = ounces (round your response to two decimal places).Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Twelve samples, each containing five parts, were taken from a process that produces steel rods at Emmanual Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: Sample Mean (in.) Range (in.) Sample Sample Sample Mean (in.) Range (in.) 1 9.404 0.044 7 9.403 0.021 2 9.402 0.051 8 9.405 0.058 3 9.393 0.042 9.395 0.039 4 9.404 0.037 10 9.401 0.038 9.399 0.048 11 9.401 0.054 9.397 0.053 12 9.404 0.061 For the given data, the x = inches (round your response to four decimal places). Based on the sampling done, the control limits for 3-sigma x chart are: Upper Control Limit (UCL;) = inches (round your response to four decimal places). Lower Control Limit (LCL;) = inches (round your response to four decimal places).