Chapter 7 - Homework Problems 1. Management at Cirquelectra Corp is concerned about the amount of scrap being generated in making an integrated circuit board. The specification was 0.675 +0.09 volts A team was formed to find the root cause of scrap, and they succeeded in finding a way to reduce the scrap cost to $12.15 per part. a. What is the Taguchi loss function for this project? b. What is the Taguchi loss function if the process deviation from target can be reduced from its current level to 0.05 volts? 2. 3. SickeTest tested eight microcircuits used for heavy duty use in commercial two-way radio transceivers in a 15,000-hour test. Compute the failure rate if two failed after 2,000, one after 4,750, two after 12,500 hours and the other three ran for the full 15.000 hours. The life of a Lapstrake Battery Co. battery for laptop computers is normally distributed with a mean of 1,800 days and standard deviation of 50 days. Using the Excel functions (see Chapter 6), determine the following: a. What fraction of batteries is expected to survive beyond 1930 days? b. What fraction will survive fewer than 1725 days? c. Draw a chart of the reliability function using Excel. d. What length of warranty is needed so that no more than 5 percent of the batteries will be expected to fail during the warranty period? Flatplane. Inc, makes wide screen flat panel TV's which have a failure rate of 0.000072 units per hour. What is the reliability function? Assuming an exponential distribution, what is the probability of failure within 8,000 hours? Calculate your answer using the appropriate mathematical formula and verify your result using Excel 4 5. A smartphone component made by Sabiophono, Ltd. has a failure rate of x=00005. Find the mean time to failure (MITF). What is the probability (assuming an exponential probability distribution) that the component will not have failed after 7,500 hours of operation? Calculate your answer using the appropriate mathematical formula and verify your result using Excel 6. Recluad Co. manufacturer of satellite radios purchases electronic components as modules. The reliabilities of components differ by supplier (see diagram, below). Suppose that the configuration of the components is given by A Note that one very critical component has two modules as "backup" in parallel with the main unit. The components can be purchased from three different suppliers. The reliabilities of the components are as follows Component Supplier 1 0.95 0.97 Supplier 3 0.98 A Supplier 2 0.96 095 0.96 B 0.98 0.93 0.94 D 0.93 0.99 0.99 0.92 0.96 E 0.98 Transportation and purchasing considerations require that only one supplier be chosen Which one should be selected if the radio is to have the highest possible reliability? 7 Dupliflex, Inc. has a process with three operations that are performed in series. Because of the nature of the process, machines frequently fall out of adjustment and must be repaired. To keep the system poing two identical machines are used at each stage: thus, if one fails, the other can be used while the first is repaired (see accompanying figure) Production System The reliabilities of the machines are as follows: Machine Reliability A 0.91 B 0.87 0.94 a. Analyze the system reliability, assuming only one machine at each stage (all the backup machines are out of operation) b. How much is the reliability improved by having two machines at each stage