Introduction to Operations Management Answer Key Part 4

True / False Questions 1. An important dimension of reliability relates to "prescribed set of conditions". TRUE 2. One operational definition of reliability is the probability that a product or system will function when activated. TRUE 3. If a system is composed of two parts which must both operate, and each has a probability of .7 of operating, it is more likely than not that the system will fail. TRUE 4. "Independent components" cannot exist in the same product. FALSE 5. A component in a product can be considered an "independent" component if it has no relation to whether any other component in the product functions or not. TRUE 6. Events can be considered "independent events" if they have no relation to the occurrence or non-occurrence of each other. TRUE 7. Redundancy in product design refers to backup parts or systems. TRUE 8. Availability measures the fraction of time a piece of equipment or a repairable product is expected to be available for operation. TRUE 9. Mean time between failure is the average length of time to repair a failed item. FALSE Multiple Choice Questions 10. The probability that a product will perform its intended function under prescribed conditions is: A. reliability. B. failure. C. functionality. D. redundancy. E. manufacturability. 11. A system is comprised of two separate units which must both function in order for the system to perform as intended. The reliability of one is .4, and the reliability of the other is .5. The overall system reliability is: A. .90 B. .30 C. .20 D. .10 E. .02 12. A product comprised of two components whose failure probabilities are .9 each, has a reliability of: A. 1.80 B. 90 C. 81 D. 80 E. 20 13. An early warning security fence has three major components which must each perform in order for the system to perform. Their reliabilities are .4, .3, and .2. The system reliability is equal to: A. .024 B. .076 C. .100 D. .336 E. .900 14. One of the solar instruments on a satellite has three major parts which must all operate. Two have reliabilities of .7, and the other has a reliability of .9. In case the system fails, there is an identical backup system for each component which kicks on automatically. The overall reliability of the system, including the backups, is closest to: A. .40 B. .50 C. .60 D. .70 E. .80 15. A garage door opener has three sections, which have reliabilities of .9, .8, and .9. The lowest of these has an identical backup which automatically goes on if the original fails. All three parts must operate to perform its intended function. The system reliability is closest to: A. .40 B. .50 C. .60 D. .70 E. .80 16. A system is composed of two parts which must both operate in order for the system to perform as intended. The parts have reliabilities of .6 and .5. There is an identical backup for each part. The backup system is connected to the main system by a switch which has a reliability of .9. The probability that the overall system will operate is closest to: A. .30 B. .40 C. .50 D. .60 E. .70 17. The probability that a product will fail within a given amount of time is often described by the: A. beta distribution. B. binomial distribution. C. negative Gaussian distribution. D. normal distribution. E. uniform distribution. 18. A P/OM student has purchased a four-function calculator for use during exams. This calculator is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will fail in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed, what is the probability that the battery will perform reliably during a one-hour exam? A. 0.05 B. 0.10 C. 0.20 D. 0.90 E. 0.95 19. A P/OM student has purchased a four-function calculator for use during exams. This calculator is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will fail in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed, what is the probability that the calculator will perform reliably during a one-hour exam? A. 0.800 B. 0.855 C. 0.900 D. 0.950 E. 1.850 20. A P/OM student has purchased a four-function calculator for use during exams. This calculator is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will fail in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed and the student brings one spare battery with him, what is the probability that the calculator will perform reliably during a one-hour exam? A. 0.89775 B. 0.9405 C. 0.987525 D. 0.99 E. 0.9975 21. A P/OM student has purchased a four-function calculator for use during exams. This calculator is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will fail in five hours, with a standard deviation of 30 minutes. What is the probability that a new battery will fail within six hours? A. 0.0228 B. 0.4772 C. 0.5 D. 0.9544 E. 0.9772 22. A P/OM student has purchased a four-function calculator for use during exams. This calculator is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will fail in five hours, with a standard deviation of 30 minutes. What service life should the manufacturer specify in order to have a . 8413 probability that a battery will not fail within that amount of time? A. 3.5 hours B. 4 hours C. 4.5 hours D. 5 hours E. 5.5 hours 23. The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems. This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation. What is the probability that this system will perform reliably for a period of one year? A. 0.4 B. 0.5 C. 0.8 D. 0.9 E. 1.3 24. The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems. This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation. If he were to add just a backup generator, with the same failure rate, what would be the probability that this system would perform reliably for a period of one year? A. 0.48 B. 0.60 C. 0.72 D. 0.75 E. 0.96 25. The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems. This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation. If he were to add both a backup generator and a backup transformer, with the same failure rates, what would be the probability that this system would perform reliably for a period of one year? A. 0.48 B. 0.60 C. 0.72 D. 0.75 E. 0.96 26. The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems. This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation. If the transformer has a mean time to wear-out of 20 years with a standard deviation of 2 years, what is the probability that it will fail within 19 years? A. 0.1915 B. 0.3085 C. 0.383 D. 0.5 E. 0.6915 27. The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems. This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation. If the transformer has a mean time to wear-out of 20 years with a standard deviation of 2 years, what service life should the manufacturer specify in order to have a . 9332 probability that it will last at least that long before failing? A. 17 years B. 18 years C. 19 years D. 20 years E. 21 years 28. The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery, which has a random failure rate of one in every five hours of operation; and the light bulb, which has a random failure rate of three in every ten hours. What is the probability that the battery will perform reliably for one hour? A. 0.2 B. 0.3 C. 0.5 D. 0.7 E. 0.8 29. The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery, which has a random failure rate of one in every five hours of operation; and the light bulb, which has a random failure rate of three in every ten hours. What is the probability that the flashlight will perform reliably for one hour? A. 0.50 B. 0.56 C. 0.70 D. 0.80 30. The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery, which has a random failure rate of one in every five hours of operation; and the light bulb, which has a random failure rate of three in every ten hours. If the company includes a backup light bulb with each flashlight, what is the probability that the flashlight will perform reliably for one hour (excluding light bulb replacement time, if any)? A. 0.6720 B. 0.7280 C. 0.8736 D. 0.9100 E. 0.9600 31. The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery, which has a random failure rate of one in every five hours of operation; and the light bulb, which has a random failure rate of three in every ten hours. If the company includes both a backup light bulb and a backup battery with each flashlight, what is the probability that the flashlight will perform reliably for one hour (excluding replacement time)? A. 0.6720 B. 0.7280 C. 0.8736 D. 0.9100 E. 0.9600 32. The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery, which has a random failure rate of one in every five hours of operation; and the light bulb, which has a random failure rate of three in every ten hours. Devices, Inc. supplies Readylite with the on-off switch for this flashlight. These switches, on average, fail in fifty hours with a standard deviation of four hours. What service life should Devices specify to have a .8944 probability that a switch will last at least that long before failing? A. 43 hours B. 45 hours C. 46 hours D. 50 hours E. 54 hours 33. The chief of the design team for a new missile wants to know the reliability of its guidance system. This system is comprised of three components: a gyroscope, which has a random failure rate of 3 in every 10 launches; a computer, which has a random failure rate of 2 in every 10 launches; and a rocket motor, which has a random failure of 1 in every 10 launches. What is the probability that the gyroscope will perform reliably during a launch? A. 0.300 B. 0.504 C. 0.700 D. 0.889 E. 0.910 34. The chief of the design team for a new missile wants to know the reliability of its guidance system. This system is comprised of three components: a gyroscope, which has a random failure rate of 3 in every 10 launches; a computer, which has a random failure rate of 2 in every 10 launches; and a rocket motor, which has a random failure of 1 in every 10 launches. What is the probability that the guidance system will perform reliably during a launch? A. 0.300 B. 0.504 C. 0.700 D. 0.889 E. 0.910 35. The chief of the design team for a new missile wants to know the reliability of its guidance system. This system is comprised of three components: a gyroscope, which has a random failure rate of 3 in every 10 launches; a computer, which has a random failure rate of 2 in every 10 launches; and a rocket motor, which has a random failure of 1 in every 10 launches. If they were to connect an identical, backup gyroscope with a perfectly reliable switch to the primary gyroscope, what would be the reliability of the gyroscope function during a launch? A. 0.3 B. 0.504 C. 0.7 D. 0.889 E. 0.91 36. The chief of the design team for a new missile wants to know the reliability of its guidance system. This system is comprised of three components: a gyroscope, which has a random failure rate of 3 in every 10 launches; a computer, which has a random failure rate of 2 in every 10 launches; and a rocket motor, which has a random failure of 1 in every 10 launches. If they were to connect a backup gyroscope with a.90 reliability to the primary gyroscope, what would be the reliability of the gyroscope function during a launch? A. 0.3 B. 0.504 C. 0.7 D. 0.889 E. 0.97 37. The chief of the design team for a new missile wants to know the reliability of its guidance system. This system is comprised of three components: a gyroscope, which has a random failure rate of 3 in every 10 launches; a computer, which has a random failure rate of 2 in every 10 launches; and a rocket motor, which has a random failure of 1 in every 10 launches. If the battery used to power the computer has a mean time to fail of 60 minutes with a standard deviation of 20 minutes, what is the probability that it will last for a launch of 30 minutes duration without failing? A. 0.9332 B. 0.8664 C. 0.5668 D. 0.4332 E. 0.0668 38. The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle. One (either) lamp is to be lit if steam pressure drops below the desired level, and two (both) are to be lit if temperature drops below a desired level. His supplier estimates that a lamp has a failure rate of .2 per hour of operation, and a mean wear-out time of seven years with a standard deviation of eight months. What is the probability that a lamp will perform reliably for one hour? A. 0 B. .2 C. .8 D. .9 E. 1 39. The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle. One (either) lamp is to be lit if steam pressure drops below the desired level, and two (both) are to be lit if temperature drops below a desired level. His supplier estimates that a lamp has a failure rate of .2 per hour of operation, and a mean wear-out time of seven years with a standard deviation of eight months. If the temperature drops below the desired level, what is the probability the system will perform reliably for one hour? A. .04 B. .40 C. .60 D. .64 E. .96 40. The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle. One (either) lamp is to be lit if steam pressure drops below the desired level, and two (both) are to be lit if temperature drops below a desired level. His supplier estimates that a lamp has a failure rate of .2 per hour of operation, and a mean wear-out time of seven years with a standard deviation of eight months. If the pressure drops below the desired level, what is the probability the system will perform reliably for one hour? A. .04 B. .4 C. .6 D. .64 E. .96 41. The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle. One (either) lamp is to be lit if steam pressure drops below the desired level, and two (both) are to be lit if temperature drops below a desired level. His supplier estimates that a lamp has a failure rate of .2 per hour of operation, and a mean wear-out time of seven years with a standard deviation of eight months. What is the probability that a lamp will last at least until the expiration of the warranty, which is six years? A. .9772 B. .9332 C. .8664 D. .8413 E. .4332 42. The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle. One (either) lamp is to be lit if steam pressure drops below the desired level, and two (both) are to be lit if temperature drops below a desired level. His supplier estimates that a lamp has a failure rate of .2 per hour of operation, and a mean wear-out time of seven years with a standard deviation of eight months. What warranty period for a lamp would give a probability of .9987 that it would not require warranty service? A. 5 years B. 5.67 years C. 6.33 years D. 7 years E. 9 years 43. Usually, a number of products or parts fail shortly after they are put into service, because they are defective to begin with. This relationship is depicted in which of the following? A. Reliability curve B. Bathtub curve C. MTBF chart D. Exponential distribution E. Normal curve 44. The average length of time before failure of a product or component is called: A. Mean time between failures B. Mean time to failure C. Failure rate D. Reliability E. Average time to failure 45. Overall reliability can be increased through which of the following three approaches? A. Failure rate, MTBF, MTTF B. Simplify, failure rate, reliability C. Reliability, redundancy, availability D. Overdesign, simplify, redundancy E. Availability, overdesign, failure rate 46. The failure rate for a component is 2 failures for every 75 hours of operating time. How many hours can the component operate before a failure can be expected? A. 0.027 B. 4.0 C. 75 D. 37.5 E. 150 47. The failure rate for a component is 3 failures for every 175 hours of operating time. How many hours can the component operate before a failure can be expected? A. 0.017 B. 58.33 C. 0514 D. 175 E. 525 48. An air purification system is expected to operate for 510 hours after changing the filters, general cleaning and maintenance. If it takes 3 hours to perform the maintenance what is the availability of the system? A. .875 B. .922 C. .994 D. .956 E. 960 49. An automatic beverage dispensing machine is expected to operate for 40 hours after changing the filters and replenishing the drink mixes. If it takes 1.5 hours to perform the maintenance what is the availability of the system? A. .875 B. .925 C. .940 D. .953 E. .964