Operations assignment

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Industrial Engineering

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Feb 20, 2024

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17.7 What is the overall reliability that bank loans will be processed accurately if each of the five clerks shown in the chart has the reliability shown? Reliability R s = First step: 1-(.95*.95) = 0.0975 ……….(a) Second step: 1-.95 = 0.05 ………..(b) Third step: 1-.95 =0.05 ………..(b) Total probability of failure: 1 – (a*b*c) = 0.99975 Total probability of the system: .95 * 0.99975 = 0.94976 17.13 Rick Wing, a salesperson for Wave Soldering Systems, Inc. (WSSI), has provided you with a proposal for improving the temperature control on your present machine. The machine uses a hot-air knife to cleanly remove excess solder from printed circuit boards; this is a great concept, but the hot-air temperature control lacks reliability. According to Wing, engineers at WSSI have improved the reliability of the critical temperature controls. The new system still has four sensitive integrated circuits controlling the temperature, but the new machine has a backup for each. The four integrated circuits have reliabilities of .90, .92, .94, and .96. The four backup circuits all have a reliability of .90. a) What is the reliability of the new temperature controller? b) If you pay a premium, Wing says he can improve all four of the backup units to .93. What is the reliability of this option? R s (total reliability of the system) = [0.90 + {(1-0.90)*0.90}] * [0.92 + {(1-0.92) *0.90}] * [0.94 + {(1-0.94)*0.9}] * [0.96 + {(1- 0.96)*0.90}] = 0.9723 .90 .90 .90 .90 .96 .94 .92 .90 .93 .93 .93 .93
R s (total reliability of the system) = [0.90 + {(1-0.90)*0.93}] * [0.92 + {(1-0.92) *0.93}] * [0.94 + {(1-0.94)*0.93}] * [0.96 {(1- 0.96)*0.93}] = 0.9805 17.14 As VP for operations at Méndez-Piñero Engineering, you must decide which product design, A or B, has the higher reliability. B is designed with backup units for components R3 and R4. What is the reliability of each design Reliability R s (Product design A) = 0.99*0.95*0.998*0.995 = 0.934 Reliability R s (Product design B) = 0.99 * 0.95 * [ 0.985 + {(1- 0.985) * 0.95] *[0.99 + {(1- 0.99) * 0.99}] = 0.94 17.21 The fire department has a number of failures with its oxygen masks and is evaluating the possibility of outsourcing preventive maintenance to the manufacturer. Because of the risk associated with a failure, the cost of each failure is estimated at $2,000. The current maintenance policy (with station employees performing maintenance) has yielded the following history: This manufacturer will guarantee repairs on all failures as part of a service contract. The cost of this service is $5,000 per year. a. What is the expected number of annual breakdowns with station employees performing maintenance? b. What is the cost of the current maintenance policy? c. What is the more economical policy? Answer: Number of Number of years in Frequency Expected breakdowns .96 .94 .92 .90
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