Concept explainers
a
Interpretation:
Cumulative distribution function of the time until failure.
Concept Introduction:
Probability Distribution Function is a likelihood of an event to occur for discrete random variables. Graphically, it shows how likely variables will fall under the probability area.
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
b
Interpretation:
The probability that a transducer can be chosen at random function for 8 years
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
c
Interpretation:
The probability that a transducer that has completed 8 years continues to function another eight years
Concept Introduction:
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
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EBK PRODUCTION AND OPERATIONS ANALYSIS
- Six thousand light bulbs light a large hotel and casino marquee. Each bulb fails completely at random, and each has an average lifetime of 3,280 hours. Assuming that the marquee stays lit continuously and bulbs that burn out are replaced immediately, how many replacements must be made each year on the average?arrow_forwardA subassembly in an industrial robot consists of 12 components in series, each of which fails completely at random at a rate of once every 50 years.a. What is the mean time between failures for this part of the robot?b. What is the probability that this subassembly does not fail within eight years of operation?arrow_forwardUnited Electric (UE) sells refrigerators for $400 with a one-year warranty. The warranty works as follows. If any part of the refrigerator fails during the first year after purchase, UE replaces the refrigerator foran average cost of $100. As soon as a replacement is made, another one-year warranty period begins for the customer. If a refrigerator fails outside the warranty period, we assume that the customer immediatelypurchases another UE refrigerator. Suppose that the amount of time a refrigerator lasts follows a normal distribution with a mean of 1.8 years and a standard deviation of 0.3 year.a. Estimate the average profit per year UE earns from a customer.b. How could the approach of this problem be used to determine the optimal warranty period?arrow_forward
- A subassembly in an industrial robot consists of 12 components in series, each ofwhich fails completely at random at a rate of once every 50 years.b. What is the probability that this subassembly does not fail within eight years ofoperation?arrow_forwardA collection of 30 Christmas tree lights are arranged in a pure series circuit; that is, ifone of the lights burns out, then the entire string goes out. Suppose that each light failscompletely at random at a rate of one failure every year. What is the probability that thelights will burn from the beginning of Christmas Eve (December 24) to the end of NewYear’s Day (January 1) without failure?arrow_forwardA local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it isrepaired the same day. Assume that breakdowns of individual cabs occur completely atrandom at a rate of two per year.d. What is the probability that there are more than five breakdowns between Thanksgiving Day (November 28) and New Year’s Day (January 1)?arrow_forward
- The length of time between breakdowns of an essential piece of equipment is important in the decision of the use of auxiliary equipment. An engineer thinks that the best “model” for time between breakdowns of a generator is the exponential distribution with a mean of 15 days. If the generator has just broken down, what is the probability that it will break down in the next 12 to 24 days?arrow_forwardA Florida lottery machine and printer at Store #8302 operates 360 days a year. If the machine does not work and breaks down, it costs the Florida Lottery Commission $2,160 per day. If store employees are trained to perform local tests on the machine each day plus the costs of machine repairpersons, these preventive maintenance costs average $850 per day. If preventive maintenance is performed daily, the probability the equipment fails is zero. The probability of store lottery machine breakdown is as follows. Number of Lottery Machine Breakdowns per Day 0 1 1/3 Probability of a breakdown What are the economics of the situation? Do not round intermediate calculations. Round your answers to the nearest dollar. The expected cost of a breakdown per day is $ The Florida Lottery Commission saves $ by performing preventive maintenance daily. 2 1/3 1/3 per yeararrow_forwardAn electronic chess game has a useful life that is exponential with a mean of 30 months. Determine each of the following:a. The probability that any given unit will operate for at least (1) 39 months, (2) 48 months,(3) 60 months.arrow_forward
- The warehouse management system (WMS) of RoyaTech's Delaware Valley warehouse tracks service level at the warehouse. A service level failure at the warehouse is an event where a customer's order could not be shipped out in full by the promised shipping time. RoyalTech's ordering system prevents customers from placing orders on products that are not in-stock at the warehouse. Therefore, we can make the statement that "the WMS is guaranteed to show 100% service level at the warehouse." Choose the most appropriate statement in response: O True, because orders will be placed only for products that are available. O False, because service level can never be 100%. O False, because resource constraint or human error may delay the shipping even though inventory is available in the system. O False, because WMS calculations are faulty.arrow_forwardA design engineer is considering the number of levels of redundancy to buildinto a particular circuit. The circuit will be part of a sensitive piece of equipmentwith cost estimated at $500 per failure. Each additional level of redundancy costs$100. If each component fails at random at a rate of one failure every five years,what level of redundancy most closely equates the cost of the design with the expected failure cost of the equipment over its 10-year life cycle?arrow_forwardJankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 20 percent are returned. If nine rings are sold today, what is the probability that fewer than four will be returned? A- 0.914 B- 0.962 C- 0.923 D- 0.935arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,