TO 313 - Winter 2013 Practice Problems on Quality and Capability Chapter 5 (Six Sigma Quality): Review and Discussion Questions: 1, 2, 3, 4, 7 (Textbook p. 145) Problem 2 (Textbook p. 145) Additional Problems is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 1. A company currently using an inspection process in its material receiving department is trying to install an overall cost reduction program. One possible reduction is the elimination of one inspection position. This position tests material that has a defective content on the average of 0.04. By inspecting all items, the inspector is able to remove all defects. The inspector can inspect 50 units per hour. The hourly rate for this position is $9. If the inspection position is eliminated, defects will go into product assembly and will have to be replaced later at a cost of $10 each when they are detected in final product testing. a. Should this inspection position be eliminated? b. What is the cost to inspect each unit? c. What is the benefit (or loss) from the current inspection process? 2. C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 0.003 inches. After trial runs on this machine, CSpec has determined that the machine has a sample mean of 4.001 inches with a standard devition of 0.002 inch. Calcuate the Cpk for this machine. Should C-Spec use this machine to produce this part? 3. Design specifictions require that a key dimension on a product measure 100 10 units. A process being considered for producing this product has a mean of 100 units and a standard deviation of 2 units. a. Calcuate the Cpk for this process. What percentage of the items produced will be defective? b. Suppose the process average shifts to 93, calculate the new Cpk. What percentage of the items produced will be defective? sh Th 4. A quality assurance manager is assessing the capability of a process that puts pressurized grease in an aerosol can. The design specifications call for an average of 60 pounds per square inch (psi) of pressure in each can with an upper tolerance limit of 65 psi and a lower tolerance limit of 55 psi. It is known that cans have an average of 60 psi. If the quality assurance manager wants to ensure that the fraction of cans that do not meet the specifications is as low as 2x10-9, what should be the standard deviation of the process? 5. At a manufacturing plant, materials go through three major work stations to be transformed into finished goods. The plant emphasizes quality and has maintained a good quality rate: the fraction of finished goods that are defective is 2%. Assume that the process at each station is centered and all the three work stations have the same capability index (Cpk) values. What is the probability that a station produces defective items? https://www.coursehero.com/file/11664721/TO-313-Quality-Control-Practice-Problems/ 6. At a steel processing plant, each sheet of steel goes through two steps to have its size trimmed. The first step trims its length, while the second its width. It is desired that the processed steel sheet has a length in the range of (2.97m, 3.03m) and a width in the range of (0.99m, 1.01m). Both processing steps are centered, which means the average length and width of a steel sheet coming off processing are 3m and 1m respectively, but there are variabilities in the process. It is estimated that the first step has a standard deviation of 0.01m and the second step has a standard deviation of 0.0025m. What is the probability that a processed steel sheet meets the specifications on both length and width? sh Th is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 7. There is 5 percent error rate at a specific point in a production process. If an inspector is placed at this point, the error rate can be reduced to 1 percent. The inspector is paid $8 per hour and the processes' rate is 30 per hour. There is a cost of $10 per unit to correct the defect coming off the end of the entire process. Should an inspector be hired? https://www.coursehero.com/file/11664721/TO-313-Quality-Control-Practice-Problems/ Powered by TCPDF (www.tcpdf.org)