Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Is the process under control? Unit # Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 73.5 70.8 72.2 73.6 71.0 2 71.3 71.0 73.1 72.7 72.2 3 70.0 72.6 71.9 72.4 73.3 4 71.1 70.6 70.3 74.2 73.6 5 70.8 70.7 70.7 73.5 71.1
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- You work for Raider Data Systems where thousands of insurance records are entered by clerks each day for a variety of client firms. You are in charge of setting control limits to include 99.73% of the random variation in the data entry process when it is in control. Samples that you collected from 20 employees are shown below. You carefully examine 100 records entered by each employee and count the number of errors entered by each clerk. You also compute the proportion defective in each sample. Using a p-chart, what are the upper and lower control limits? Sample Errors Made Proportion Defective 1 4 0.04 2 5 0.05 3 6 0.06 4 3 0.03 5 8 0.08The 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 17.2At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, an average of four lumps per tube of caulk will remain. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained: Tube No. Lumps Tube No. Lumps Tube No. Lumps 1 6 5 6 9 5 2 5 6 4 10 0 3 0 7 1 11 9 4 4 8 6 12 2 Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control?
- Refer to the table Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. 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 mean weight 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: Sample 1 2 3 4 5 6 7 8 9 10 x 55 47 49 50 52 57 55 48 51 56 R 3 1 5 3 2 6 3 2 2 3 Part 2 Set the control limits for this process for the x-chart when the machine is working properly. a) What are the x overbar-chart control limits when the machine is working properly? Calculate the upper control limit of the x overbar-chart Calculate the…A shirt manufacturer buys clothes by the 100-yard roll from a supplier. For setting a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier. Sample 1 2 3 4 5 6 7 8 9 10 Irregularities 3 5 2 6 5 4 6 3 4 5 Which type of control chart should be used? Construct a control chart with two-sigma control limits. Suppose the next five rolls from the supplier had three, two, five, three, and seven irregularities. Is the supplier process under control? Explain and show workThe 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 1.50
- The following data represents the number of weld defects observed in 24 samples of five printed circuit boards: 7 6 8 10 24 6 5 4 8 11 15 8 4 16 11 12 8 6 5 9 7 14 8 21. a) Using all the data, calculate the control limits. b) Can it be concluded that the process is in control? If not, suppose they can find the assignable causes, and recalculates the control limits once out of control points eliminated.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.)Using samples of 200 credit card statements, an auditor found the following: Sample 1 2 3 4 Number with errors 4 2 5 9 a. Determine the fraction defective in each sample. b. If the true fraction defective for this process is unknown, what is your estimate of it? c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? d. What control limits would give an alpha risk of .03 for this process? Page 457 e. What alpha risk would control limits of .047 and .003 provide? f. Using control limits of .047 and .003, is the process in control? g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control? Can you show me the steps and formulas using excel
- Representatives of the Patriot Insurance Company take medical information over the telephone from prospective policy applicants prior to a visit to the applicant’s place of residence by a registered nurse who takes vital sign measurements. When the telephone interview has incorrect or incomplete information, the entire process of approving the application is unnecessarily delayed and has the potential of causing loss of business. The following data were collected to see how many applications contain errors. Each sample has 200 randomlyselected applications. Sample Defects Sample Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20 18 29 12 14 11 30 25 27 16 25 18 25 16 20 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 15 40 35 21 24 9 20 17 28 10 17 22 14 19 20 a. What are the upper and lower control limits of a p-chart for the number of defective applications? Use z = 3.b. Is the process in statistical control?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, eThe output of a certain integrated-circuit productionline is checked daily by inspecting a sample of 100 units.Over a long period of time, the process has maintaineda yield of 80 percent, that is, a proportion defective of 20 percent, and the variation of the proportion defec-tive from day to day is measured by a standard devi-ation of 0.04. If on a certain day the sample contains 38 defectives, find the mean of the posterior distribu-tion of as an estimate of that day’s proportion defec-tive. Assume that the prior distribution of Θ is a beta distribution.