Using an Xbar Chart, what are the upper and lower control limits?
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The weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means, and given is the population (process) standard deviation, which is 1.13.
You are in charge of randomly selecting four boxes each hour, for three hours.
The data you collected is located in the table below:
Using an Xbar Chart, what are the upper and lower control limits?
Sample | Avg. of 4 boxes |
1 | 16.8 |
2 | 17.1 |
3 | 17.2 |
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- The weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means and given is the population (process) standard deviation, which is 1.13. You are in charge of randomly selecting four boxes each hour, for three hours. The data you collected is in the table below: Using an R Chart, what are the upper and lower control limits? Sample Lightest Obs. (n=4) Heaviest Obs. (n=4) Range (Ri) in difference 1 15.00 17.00 2.00 2 15.30 16.90 1.60 3 15.20 16.70 1.50Specifications for a part for a 3-D printer state that the part should weigh between 24 and25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample means of this process fall if samples of n = 16 are taken and the process is in control (random)? Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approxi- mately normal with a mean of 1.0 liter and a 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 percent of the sample means when the process is in control. Given the following sample means—1.005,…Answer the given question with a proper explanation and step-by-step solution. Johnson & Johnson manufactures needles that are subjected to a bend test. They use statistical process control (SPC) and the results (measured in grams) are plotted on a chart. If the process average is 26,1 and the average range is 5; what will the control limits be if the sample size n=8? The factor for calculation of control limits is 0,373 for sample size n=8. Which statement(s) is/are true? a The process is "out of control". b The process is "in control". c The upper control limit equals 27,965. d The upper control limit equals 24,235. e The lower control limit equals 27,965. 1. a 2. b, c 3. a, c 4. b, c, d 5. a, d, e
- A distributor buys Tires from manufacturers. In his store, Phillip Johnson, the supplier quality manager for the distribution company, selects a tire at random which was received in the warehouse the prior day. Small imperfections (minor wears in trade, uneven surfaces, etc) are counted. Recent data show an average of six imperfections (nonconformities) in each sample. Using the formulas for a c chart, calculate the control limits and centerline for this situation. If management wants a process capability of five nonconformities per sample, will this supplier be able to meet that requirement?Your supervisor, Lisa Lehmann, has asked that you report on the output of a machine on the factory floor. This machine is supposed to be producing optical lenses with a meanweight of 50 grams and a range of 3.5 grams. The following table contains the data for a sample size of n = 6 taken during the past 3 hours: a) What are the :X-chart control limits when the machine is working properly?b) What are the R-charL control limits when the machine is working properly?c) What seems to be happening? (Hint: Graph the data points. Run charts may be helpful.)A large national producer of cookies and baked goods uses a c chart to monitor the number of chocolate chips in its chocolate chip cookies. The company would like to have an average of six chips per cookie. One cookie is sampled each hour. The results of the last 12 hours were (given) a. Assuming a target value of c = 6, what are the upper and the lower control limits for a c chart?b. Are the 12 observations consistent with a target value of c = 6? If those 12 observations constitute a baseline, what upper and lower control limits result? (Use the normal approximation for your calculations.)
- The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box-filling line to be set so that the process average weight per packet is 49 grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of 7 packets and weighs each packet. When the process is in control, the range in the weight of each sample has averaged 7 grams. The UCLR equals .--------- grams and the LCLR equals --------- grams. (Enter your response rounded to two decimal places.) More Information Factors for calculating three-sigma limits for the x-chart and R-chart Size of Sample (n) Factor for UCL and LCL for x-chart (A2) Factor for LCL for R-Chart (D3) Factor for UCL for R-Chart (D4) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924…Rosters Chicken advertises " lite" chicken with 30% fewer calories than standard chicken. When the process for "lite" chicken breast production is in control, the average chicken breast contains 420 calories, and the standard deviation in caloric content of the chicken breast population is 25 calories. Rosters wants to design an x-chart to monitor the caloric content of chicken breasts, where 25 chicken breasts would be chosen at random to form each sample.a) What are the lower and upper control limits for th.is chart if these limits are chosen to be four standard deviations from the target?b) What a re the limits with three standard deviations from the target?At Quick Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 9 cars is 8 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. LOADING... Click the icon to view the table of factors for calculating three-sigma limits for the x overbarx-chart and R-chart. Factors for calculating three-sigma limits for the x overbarx-chart and R-chart Size of Sample (n) Factor for UCL and LCL for x overbarx-chart (Upper A 2A2) Factor for LCL for R-Chart (Upper D 3D3) Factor for UCL for R-Chart (Upper D 4D4) 2 1.8801.880 00 3.2673.267 3 1.0231.023 00 2.5752.575 4 0.7290.729 00 2.2822.282 5 0.5770.577 00 2.1152.115 6 0.4830.483 00 2.0042.004 7 0.4190.419 0.0760.076 1.9241.924 8 0.3730.373…
- At Quick Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 9 cars is 8 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. LOADING... Click the icon to view the table of factors for calculating three-sigma limits for the x overbarx-chart and R-chart. Factors for calculating three-sigma limits for the x overbarx-chart and R-chart Size of Sample (n) Factor for UCL and LCL for x overbarx-chart (Upper A 2A2) Factor for LCL for R-Chart (Upper D 3D3) Factor for UCL for R-Chart (Upper D 4D4) 2 1.8801.880 00 3.2673.267 3 1.0231.023 00 2.5752.575 4 0.7290.729 00 2.2822.282 5 0.5770.577 00 2.1152.115 6 0.4830.483 00 2.0042.004 7 0.4190.419 0.0760.076 1.9241.924 8 0.3730.373…A quality inspector took five samples in five hours, each with four observations, of the length time for glue to dry. The analyst compute the mean of each sample and the computed the grand mean. All values are in minutes. Use this information to obtain three-sigma control limits for means. It is known from previous experience that the standard deviation of the process is 0.02 minutes. Draw a control chart Please provide a step-by-step solutionAuto 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= 155.56 mm (round your response to two decimal places). b) What is the value of R? R 4.48 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) = 156.94 mm (round your response to two decimal places). Lower Control Limit (LCL-) = 154.18 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCL) = 7.96 mm (round your response to two decimal places). Mean x (mm) 154.9 153.2 155.6 155.5 158.6 Range R (mm) 4.0 4.8 3.9 5.0 4.7 Lower Control Limit (LCL) = 1.00 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want…