a. Construct the ... control chart for this process if samples of size 4 are to be used.
b. Repeat part (a) for samples of size 8 and 16.
c. What happens to the limits of the control chart as the sample size is increased? Discuss why this is reasonable.
Get solution
20.2 Twenty-five samples, each of size 5, were selected from a process that was in control. The sum of all the data collected was 677.5 pounds.
a. What is an estimate of the process mean (in terms of pounds per unit) when the process is in control?
b. Develop the ... control chart for this process if samples of size 5 will be used. Assume that the process standard deviation is .5 when the process is in control, and that the mean of the process is the estimate developed in part (a).
Get solution
20.3 Twenty-five samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 25 samples, a total of 135 items were found to be defective.
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?
c. Compute the upper and lower control limits for the control chart.
Get solution
20.4 A process sampled 20 times with a sample of size 8 resulted in ... and .... Compute the upper and lower control limits for the and R charts for this process.
Get solution
20.5 Temperature is used to measure the output of a production process. When the process is in control, the mean of the process is μ = 128.5 and the standard deviation is σ = .4.
a. Construct the chart for this process if samples of size 6 are to be used.
b. Is the process in control for a sample providing the following data?...
c. Is the process in control for a sample providing the following data?...
Get solution
20.6 A quality control process monitors the weight per carton of laundry detergent. Control limits are set at UCL = 20.12 ounces and LCL = 19.90 ounces. Samples of size 5 are used for the sampling and inspection process. What are the process mean and process standard deviation for the manufacturing operation?
Get solution
20.7 The Goodman Tire and Rubber Company periodically tests its tires for tread wear under simulated road conditions. To study and control the manufacturing process, 20 samples, each containing three radial tires, were chosen from different shifts over several days of operation, with the following results. Assuming that these data were collected when the manufacturing process was believed to be operating in control, develop the R and ... charts....
Get solution
20.8 Over several weeks of normal, or in-control, operation, 20 samples of 150 packages each of synthetic-gut tennis strings were tested for breaking strength. A total of 141 packages of the 3000 tested failed to conform to the manufacturer’s specifications.
a. What is an estimate of the process proportion defective when the system is in control?
b. Compute the upper and lower control limits for a p chart.
c. With the results of part (b), what conclusion should be made about the process if tests on a new sample of 150 packages find 12 defective? Do there appear to be assignable causes in this situation?
d. Compute the upper and lower control limits for an np chart.
e. Answer part (c) using the results of part (d).
f. Which control chart would be preferred in this situation? Explain.
Get solution
20.9 An automotive industry supplier produces pistons for several models of automobiles. Twenty samples, each consisting of 200 pistons, were selected when the process was known to be operating correctly. The numbers of defective pistons found in the samples follow....
a. What is an estimate of the proportion defective for the piston manufacturing process when it is in control?
b. Construct the p chart for the manufacturing process, assuming each sample has 200 pistons.
c. With the results of part (b), what conclusion should be made if a sample of 200 has 20 defective pistons?
d. Compute the upper and lower control limits for an np chart.
e. Answer part (c) using the results of part (d).
Get solution
20.10 For an acceptance sampling plan with n = 25 and c = 0, find the probability of accepting a lot that has a defect rate of 2%. What is the probability of accepting the lot if the defect rate is 6%?
Get solution
20.11 Consider an acceptance sampling plan with n = 20 and c = 0. Compute the producer’s risk for each of the following cases.
a. The lot has a defect rate of 2%.
b. The lot has a defect rate of 6%.
Get solution
20.12 Repeat exercise 11 for the acceptance sampling plan with n = 20 and c = 1. What happens to the producer’s risk as the acceptance number c is increased? Explain.
Get solution
20.13 Refer to the KALI problem presented in this section. The quality control manager requested a producer’s risk of .10 when p0 was .03 and a consumer’s risk of .20 when p1 was .15. Consider the acceptance sampling plan based on a sample size of 20 and an acceptance number of 1. Answer the following questions.
a. What is the producer’s risk for the n = 20, c = 1 sampling plan?
b. What is the consumer’s risk for the n = 20, c = 1 sampling plan?
c. Does the n = 20, c = 1 sampling plan satisfy the risks requested by the quality control manager? Discuss.
Get solution
20.14 To inspect incoming shipments of raw materials, a manufacturer is considering samples of sizes 10, 15, and 20. Use binomial probabilities to select a sampling plan that provides a producer’s risk of α = .03 when p0 is .05 and a consumer’s risk of β = .12 when p1 is .30.
Get solution
20.15 A domestic manufacturer of watches purchases quartz crystals from a Swiss firm. The crystals are shipped in lots of 1000. The acceptance sampling procedure uses 20 randomly selected crystals.
a. Construct operating characteristic curves for acceptance numbers of 0, 1, and 2.
b. If p0 is .01 and p1 = .08, what are the producer’s and consumer’s risks for each sampling plan in part (a)?
Get solution
20.16 Samples of size 5 provided the following 20 sample means for a production process that is believed to be in control....
a. Based on these data, what is an estimate of the mean when the process is in control?
b. Assume that the process standard deviation is σ = .50. Develop the ... control chart for this production process. Assume that the mean of the process is the estimate developed in part (a).
c. Do any of the 20 sample means indicate that the process was out of control?
Get solution
20.17 Product filling weights are normally distributed with a mean of 350 grams and a standard deviation of 15 grams.
a. Develop the control limits for the ...chart for samples of size 10, 20, and 30.
b. What happens to the control limits as the sample size is increased?
c. What happens when a Type I error is made?
d. What happens when a Type II error is made?
e. What is the probability of a Type I error for samples of size 10, 20, and 30?
f. What is the advantage of increasing the sample size for control chart purposes? What error probability is reduced as the sample size is increased?
Get solution
20.18 Twenty-five samples of size 5 resulted in ... and .... Compute control limits for the ... and R charts, and estimate the standard deviation of the process.
Get solution
20.19 The following are quality control data for a manufacturing process at Kensport Chemical Company. The data show the temperature in degrees centigrade at five points in time during a manufacturing cycle. The company is interested in using control charts to monitor the temperature of its manufacturing process. Construct the chart and R chart. What conclusions can be made about the quality of the process?...
Get solution
20.20 The following were collected for the Master Blend Coffee production process. The data show the filling weights based on samples of 3-pound cans of coffee. Use these data to construct the ... and R charts. What conclusions can be made about the quality of the production process?...
Get solution
20.21 Consider the following situations. Comment on whether the situation might cause concern about the quality of the process.
a. A p chart has LCL = 0 and UCL = .068. When the process is in control, the proportion defective is .033. Plot the following seven sample results: .035, .062, .055, .049, .058, .066, and .055. Discuss.
b. An chart has LCL = 22.2 and UCL = 24.5. The mean is μ = 23.35 when the process is in control. Plot the following seven sample results: 22.4, 22.6, 22.65, 23.2, 23.4, 23.85, and 24.1. Discuss.
Get solution
20.22 Managers of 1200 different retail outlets make twice-a-month restocking orders from a central warehouse. Past experience shows that 4% of the orders result in one or more errors such as wrong item shipped, wrong quantity shipped, and item requested but not shipped. Random samples of 200 orders are selected monthly and checked for accuracy.
a. Construct a control chart for this situation.
b. Six months of data show the following numbers of orders with one or more errors: 10, 15, 6, 13, 8, and 17. Plot the data on the control chart. What does your plot indicate about the order process?
Get solution
20.23 An n = 10, c = 2 acceptance sampling plan is being considered; assume that p0 = .05 and p1 = .20.
a. Compute both producer’s and consumer’s risk for this acceptance sampling plan.
b. Would the producer, the consumer, or both be unhappy with the proposed sampling plan?
c. What change in the sampling plan, if any, would you recommend?
Get solution
20.24 An acceptance sampling plan with n = 15 and c = 1 has been designed with a producer’s risk of .075.
a. Was the value of p0 .01, .02, .03, .04, or .05? What does this value mean?
b. What is the consumer’s risk associated with this plan if p1 is .25?
Get solution
20.25 Amanufacturer produces lots of a canned food product. Let p denote the proportion of the lots that do not meet the product quality specifications. An n = 25, c = 0 acceptance sampling plan will be used.
a. Compute points on the operating characteristic curve when p = .01, .03, .10, and .20.
b. Plot the operating characteristic curve.
c. What is the probability that the acceptance sampling plan will reject a lot containing .01 defective?
Get solution
