Concept explainers
a)
To determine: The probability that the satellite will function for more than 9 years.
Introduction:
Mean time between failures (MTBF):
The mean time between failures is a term which denotes the time that is elapsed between the first failure of a product and the second failure of a product. It is calculated during the normal system operation.
b)
To determine: The probability that the satellite will function for less than 12 years.
Introduction:
Mean time between failures (MTBF):
The mean time between failures is a term which denotes the time that is elapsed between the first failure of a product and the second failure of a product. It is calculated during the normal system operation.
c)
To determine: The probability that the satellite will function for more than 9 years but less than 12 years.
Introduction:
Mean time between failures (MTBF):
The mean time between failures is a term which denotes the time that is elapsed between the first failure of a product and the second failure of a product. It is calculated during the normal system operation.
d)
To determine: The probability that the satellite will function for at least 21 years.
Introduction:
Mean time between failures (MTBF):
The mean time between failures is a term which denotes the time that is elapsed between the first failure of a product and the second failure of a product. It is calculated during the normal system operation.
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OPERATIONS MANAGEMENT -CONNECT
- Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. For example, if a customer switches from brand A, there is probability B/(B + C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 10,000 families for each of the three brands. a. After a year, what will the market share for each firm be? Assume pA = 0.10, pB = 0.15, and pC = 0.20. (Hint: You will need to use the RISKBINOMLAL function to see how many people switch from A and then use the RISKBENOMIAL function again to see how many switch from A to B and from A to C. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the BENOM.INV (or the old CRITBENOM) function to generate binomially distributed random numbers. This takes the form =BINOM.INV (ntrials, psuccess, RAND()).) b. Suppose a 1% increase in market share is worth 10,000 per week to company A. Company A believes that for a cost of 1 million per year it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of pA, pB, and pC as in part a.)arrow_forwardYou now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.arrow_forwardAt the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.arrow_forward
- Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.arrow_forwardAttendance at Orlando's newest Disneylike attraction, Lego World, has been as follows: Guests (in thousands) Quarter Winter Year 1 Spring Year 1 Summer Year 1 Fall Year 1 Winter Year 2 Spring Year 2 63 94 168 75 64 83 Season Quarter Winter Summer Year 2 Fall Year 2 Winter Year 3 Spring Year 3 Summer Year 3 Fall Year 3 Based on the given attendance, the seasonal indices for each of the seasons are (round your responses to three decimal places): Guests (in thousands) Index 124 51 94 151 210 99arrow_forwardA television network earns an average of $25 million each season from a hit program and loses an average of $8 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospec- tive program and issue a report predicting whether the given programwill end up being a hit. If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict the program to be a hit.a. What is the maximum value of C that the network should be willing to pay the market research firm?b. Calculate and interpret EVPI for this decision problem.arrow_forward
- Attendance at Orlando's newest Disneylike attraction, Lego World, has been as follows: Quarter Guests (in thousands) Quarter Guests (in thousands) Winter Year 1 63 Summer Year 2 120 Spring Year 1 99 Fall Year 2 54 Summer Year 1 149 Winter Year 3 94 Fall Year 1 75 Spring Year 3 151 Winter Year 2 64 Summer Year 3 210 Spring Year 2 83 Fall Year 3 99 Part 2 Based on the given attendance, the seasonal indices for each of the seasons are (round your responses to three decimal places): Season Index Winter enter your response herearrow_forwardAttendance at Orlando's newest Disneylike attraction, Lego World, has been as follows: Quarter Winter Year 1 Spring Year 1 Summer Year 11 Fall Year 1 Guests (in thousands) 68 99 149 75 65 84 Quarter Summer Year 2 Fall Year 2 Winter Winter Year 3 Spring Year 3 Summer Year 3 Fall Year 3 Guests (in thousands) 120 51 99 151 Winter Year 2 207 Spring Year 2 97 Based on the given attendance, the seasonal indices for each of the seasons are (round your responses to three decimal places): Season Indexarrow_forward.A 45 kW rated solar power system has its power output and the Solar irradiance on the PV system measured during daylight hours over a day. Based on the following data, create a scatter plot of the power output of the PV system vs the solar irradiance and comment on the relationship between the two. Based on the data, can you tell which season this day was in? Solar Irradiance on the PV system (kW/m²) 0 0.079 0.333 0.571 0.751 0.86 0.914 0.93 0.904 0.803 0.606 0.345 0.054 Power output from the PV system (kW) 0 3.098 12.438 20.124 25.703 28.498 29.587 29.69 28.798 26.264 20.434 12.223 2arrow_forward
- Narrow_forwardAttendance at Orlando's newest Disneylike attraction, Lego World, has been as follows: Quarter Quarter Guests (in thousands) Guests (in thousands) Winter Year 1 68 Summer Year 2 120 Spring Year 1 99 Fall Year 2 51 Summer Year 1 155 Winter Year 3 99 Fall Year 1 75 Winter Year 2 65 Spring Year 3 Summer Year 3 151 207 Spring Year 2 84 Fall Year 3 98 Based on the given attendance, the seasonal indices for each of the seasons are (round your responses to three decimal places): Season Index Winterarrow_forwardIn the given problem, what other probability distributions might accurately describe Oakdale’s weekly usage of glue?arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,