3-2. The Road King Tire Company in Birmingham wants to monitor the quality of the tires it manufactures. Each day the company quality-control manager takes a sample of 100 tires, tests them, and determines the number of defective tires. The results of 20 samples have been recorded as follows:
Construct a p-chart for this process using 2s limits and describe the variation in the process.
3-6. One of the stages in the process of making denim cloth at the Southern Mills Company is to spin cotton yarn onto spindles for subsequent use in the weaving process. Occasionally the yarn breaks during the spinning process, and an operator ties it back together. Some number of breaks is considered normal; however, too many breaks may mean that the yarn is of poor quality. In order to monitor this process, the quality-control manager randomly selects a spinning machine each hour and checks the number of breaks during a 15-minute period. Following is a summary of the observations for the past 20 hours:
Construct a c-chart using 3s limits for this process and indicate if the process was out of control at any time.
3-12. The Stryker Baseball Bat Company manufactures wooden and aluminum baseball bats at its plant in New England. Wooden bats produced for the mass market are turned on a lathe, where a piece of wood is shaped into a bat with a handle and barrel. The bat is cut to its specified length and then finished in subsequent processes. Once bats are cut to length, it is difficult to rework them into a different style, so it is important to catch defects before this step. As such, bats are inspected at this stage of the process. A specific style of wooden bat has a mean barrel circumference of 9 inches at its thickest point with a standard deviation of 0.6 inch. (The process variability is assumed to be normally distributed.)
• a. Construct a mean control chart for this process for 3s limits and a sample size of 10 bats.
• b. Three samples are taken, and they have average bat diameters of 9.05 inches, 9.10 inches, and 9.08 inches. Is the process in control?
• c. What effect will increasing the sample size to 20 bats have on the control charts? Will the conclusions reached in part (b) change for this sample size?
3-20. Use pattern tests to determine if the sample observations in Problem 3-5 reflect any nonrandom patterns.
• (3-5 problem: 3-5. The Great North Woods Clothing Company is a mail-order company that processes thousands of mail and telephone orders each week. They have a customer service number to handle customer order problems, inquiries, and complaints. The company wants to monitor the number of customer calls that can be classified as complaints. The total number of complaint calls the customer service department has received for each of the last 30 weekdays are shown as follows. a. Construct a c-chart for this process with 3s control limits and indicate if the process was out of control at any time. b. What nonrandom (i.e., assignable) causes might result in the process being out of control?)
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3-36. Elon Corporation manufactures parts for an aircraft company. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has a design (nominal) target of 1.275 inches with tolerances of . The CNC process that manufactures these parts has a mean of 1.281 inches and a standard deviation of 0.008 inch. Compute the process capability ratio and process capability index, and comment on the overall capability of the process to meet the design specifications.