Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Question
Chapter 13.2, Problem 9P
a
Summary Introduction
Interpretation:
Reliability and CDF of the time until failure.
Concept Introduction:
Cumulative distribution function is a probability function in which probability is calculated that the variable takes less than or equal to x.
b
Summary Introduction
Interpretation:
Value of t
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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a factory that produces a small number of items per day. In about 30% of working days the factory produces 7 units of the product, in 45% of working days it produces 8 units, and the rest of working days it produces 9 units. After production is completed, each unit is thoroughly inspected. Each unit fails inspection with probability ??. If two or more units fail inspection on the same day, the factory closes for a week to re-calibrate equipment. Say the factory opens today after being closed for a week, write a mathematical expression to calculate the probability that the factory will remain open at least 30 days before closing again.
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Chapter 13 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 13.1 - Prob. 3PCh. 13.1 - Prob. 4PCh. 13.1 - Prob. 5PCh. 13.1 - Prob. 6PCh. 13.2 - Prob. 7PCh. 13.2 - Prob. 9PCh. 13.3 - Prob. 13PCh. 13.3 - Prob. 14PCh. 13.4 - Prob. 15PCh. 13.4 - Prob. 16P
Ch. 13.4 - Prob. 17PCh. 13.4 - Prob. 18PCh. 13.4 - Prob. 19PCh. 13.4 - Prob. 20PCh. 13.6 - Prob. 21PCh. 13.6 - Prob. 22PCh. 13.6 - Prob. 23PCh. 13.6 - Prob. 24PCh. 13.6 - Prob. 25PCh. 13.7 - Prob. 26PCh. 13.7 - Prob. 27PCh. 13.7 - Prob. 28PCh. 13.7 - Prob. 30PCh. 13.7 - Prob. 31PCh. 13.7 - Prob. 32PCh. 13.7 - Prob. 33PCh. 13.7 - Prob. 34PCh. 13.8 - Prob. 35PCh. 13.8 - Prob. 36PCh. 13.8 - Prob. 37PCh. 13.8 - Prob. 38PCh. 13.8 - Prob. 39PCh. 13.8 - Prob. 40PCh. 13.8 - Prob. 41PCh. 13 - Prob. 42APCh. 13 - Prob. 43APCh. 13 - Prob. 44APCh. 13 - Prob. 45APCh. 13 - Prob. 46APCh. 13 - Prob. 48APCh. 13 - Prob. 49APCh. 13 - Prob. 51APCh. 13 - Prob. 52APCh. 13 - Prob. 53AP
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- Due to the extreme cost of interrupting production, a firm has two standby machines available in case a particular machine breaks down. The machine in use has a reliability of .94, and the backups have reliabilities of .90 and .80. In the event of a failure, either backup can be pressed into service. If one fails, the other backup can be used. Compute the system reliability.arrow_forwardA garage door opener has three sections, which have reliabilities of .9, .8, and .9. The lowest of these has an identical backup that automatically goes on if the original fails. All three parts must operate to perform its intended function. The system reliability is closest to:arrow_forwardThe reliability of a hard-disk drive is typically described in terms of a quantity called mean time between failures (MTBF). Although this quantity is called a “time,” the MTBF actually is measured in drive-hours per failure. If a system contains 1,000 disk drives, each of which has a 750,000-hour MTBF, which of the following best describes how often a drive failure will occur in that disk farm: once per thousand years, once per century, once per decade, once per year, once per month, once per week, once per day, once per hour, once per minute, or once per second?arrow_forward
- 1. Three hundred identical cathode ray tubes (CRTS) placed into service simultaneously on January 1, 1976, experienced the following numbers of failures through December 31, 1988: 1983 Year Number of failures 1984 1985 1986 1987 1988 13 19 16 34 21 38 Assume that there were no failures before 1983. a. Based on these data, estimate the cumulative distribution function (CDF) of a CRT chosen at random. Using the results of part (a), estimate the probability that a CRT chosen at random 13.1 Reliability of a Single Component 753 b. Lasts more than 5 years. c. Lasts more than 10 years. d. Lasts more than 12 years. e. That has survived for 10 years fails in the 11th year of operation.arrow_forwardA typical retail transaction consists of several smaller steps, which can be considered components subject to failure. A list of such components might include: Let the eight probabilities of success be .92, .94, .99, .99, .98, .97,.95, and .96. What is the reliability of the system; that is, the probabilitythat there will be a satisfied customer? If you were the storemanager, what do you think should be an acceptable value forthis probability? Which components would be good candidatesfor backup, which for redesign?arrow_forwarda bread manufacturer relies on maintenance employees to keep its rather quite old production equipment for their operation. Whenever the equipment breaks down, the maintenance team is able to repair the equipment quickly. However, they are less effective at avoiding these breakdowns and cannot predict when the equipment will break down. The maintenance group has modified the equipment over the years and, in any event, the manufacturer of the equipment is no longer in business. The maintenance employees teach each other how to repair the equipment, but have refused to document any of this information (saying that it is too difficult to document these details). The company owner has thought about firing the maintenance staff unless they document the maintenance procedures, but realizes that there is no one else who can repair the equipment. Discuss or explain the sources or types of power and contingencies (moderator) of power among the maintenance employees in this situation.arrow_forward
- A local military base maintains a variety of different equipment. One of these is a sensitive radardevice that signals incursion of enemy planes into American airspace. Breakdowns of the device occur completely at random at an average rate of three per year. The equipment is generally repaired the same day that it fails. Determine the following:b. The probability that there are exactly five breakdowns in any given year.arrow_forwardA product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a 0.96 probability of functioning, and two have a probability of 0.99. (Leave your answers in 4 decimal places).arrow_forwardPlease Answer Quality Management Question A milling machine has an expected life of 10 years from the time it is installed into a production line. Assume the exponential distribution is appropriate. What is the probability that the machine will fail between 5 and 12 years after being installed into the production line? Suppose the three milling machines were designed in parallel into the production line system. What is the probability that the production line system will survive 10 years?arrow_forward
- Example 13.4 A local manufacturer of copying equipment includes a repair warranty with each copier. Virtu- ally all of his equipment exhibit an increasing failure rate. Based on historical repair data, the failure rate for Model 25cc7 is accurately described by the function r(t) = 2.7786t'3, where t is measured in months of continuous operation. What is the probability that the time between two successive failures of this equipment exceeds two months of operation?arrow_forwardAn operation consists of two steps , the first of which has a reliability of 97% and the second a reliability of 99%. What is the probability that the operation will fail? please I need full explanationarrow_forwardThe 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_forward
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