Twenty samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 20 samples, a total of 140 items were found to bedefective.(a) What is an estimate of the proportion defective when the process is in control?(b) What is the standard error of the proportion if samples of size 100 will be used for statistical process control? (Round your answer to four decimal places.)(c) Compute the upper and lower control limits for the control chart. (Round your answers to four decimal places.)UCL =LCL =

Control charts are also known as process-behavior charts. It is a statistical process that helps in…

Answered: (a) What is an estimate of the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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
1. The data shown in Table 1 are x and R values for 20 samples of size n= 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 31.6 should be 0.50316). Please show all your work for full credit. (a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) Assume that diameter is normally distributed. Estimate the process standard deviation. Sample R Sample R 1 31.6 4 11 29.8 4 33.0 3 12 34.0 4 35.0 4 13 33.0 10 4 32.2 4 14 34.8 4 5 33.8 38.4 31.6 15 35.6 7 3 16 30.8 7 4 17 33.0 5 8 36.8 10 18 31.6 3 9. 35.0 15 19 28.2 9 10 34.0 6 20 33.8 Table 1: Bearing Diameter Data
Suppose that a quality characteristic is normally distributed with specifications at 100 ± 20. The process standard deviation is 6.(a) Suppose that the process mean is 100. What are the natural tolerance limits? Calculate Cp and Cpk and interpret these ratios. What fraction of parts do you expect to be defective?(b) Suppose that the process mean is 106. What are the natural tolerance limits? What is thefraction defective? Calculate Cp and Cpk and interpret these ratios.
Management at Webster Chemical Company is concerned as to whether caulking tubes are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packaged in large boxes of 135. Several boxes are inspected, and the following numbers of leaking tubes are found: View an example Sample 1 2 3 Get more help. 4 Tubes 7 7 8 5 1 5 6 7 Calculate p-chart three-sigma control limits to assess whether the capping process is in statistical control. The UCL, equals 1 Sample 8 8 9 10 11 12 13 14 Tubes 7 2 4 8 6 9 MacBook Pro 3 Sample 15 16 17 18 19 20 Total Tubes 8 3 3 5 and the LCL equals (Enter your responses rounded to three decimal places. If your answer for LCL, is negative, enter this value as 0.) 3 6 104 Clear all Check answer O
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? Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 R = 4.40 mm (round your response to two decimal places). c) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCL) = mm (round your response to two decimal places). Range R (mm) 4.2 4.4 4.3 4.8 4.3 Ç
6. The defect rate for your product has historically been about 4.50%. For a sample size of 500, the upper and lower 3-sigma control chart limits are: Part 2 UCLp = _______ (enter your response as a number between 0 and 1, rounded to four decimal places). The Standard deviation of defect rate of product is given __________. The Upper and Lower 3-sigma control charts limits are: UCLp ________ LCLp ________
Using samples of 197 credit card statements, an auditor found the following: Sample 1 3 errors Sample 2 3 errors Sample 3 5 errors Sample 4 9 errors 1. what alpha risk would control limits of .0470 and .0038 provide? 2. Using control limits of .0470 and .0038, is the process in control? 3. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control?
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 work
Describe a situation where a control chart is the right tool for quality conformance. If you were a Quality Manager, would you be an advocate for the use of control charts? Why or why not?
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= 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 4.3
Five data entry operators work at the data process-ing department of the Birmingham Bank. Each day for 30 days, the number of defective records in a sample of 250 records typedby these operators has been noted, as follows: a) Establish 3s upper and lower control limits.b) Why can the lower control limit not be a negative number? c) The industry standards for the upper and lower control lim-its are 0.10 and 0.01, respectively. What does this imply about Birmingham Bank’s own standards?
Over a period of 12 consecutive production hours, samples of size 50 resulted in the following proportions of defective items: (given) a. What are the three-sigma control limits for this process?b. Do any of the sample points fall outside of the control limits?c. The company claims a defect rate of 3 percent for these items. Are the observed proportions consistent with a target value of 3 percent defectives? What difficulty would arise if the control limits were based on a target value of 0.03? In view of the company’s claims, what difficulty would arise if the control limits computed in part (a) were used?

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