Concept explainers
a
Interpretation:
Indifference value of the item with a free replacement warranty.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
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.
b
Interpretation:
Whether the value of warranty larger or smaller than in exponential case.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
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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Production and Operations Analysis, Seventh Edition
- TenTen Company manufactures video recorders. It is so certain of its quality control that it is offering a complete replacement warranty if the set fails within two years. Based upon compiled data, the company has a need that only 1% of its recorders fail during the first year and 5% fail during the second year. The warranty does not cover replaced recorders. a) Formulate this problem as a Markov chain and determine the transition matrix. b) Find the probability that the manufacturer will have to honor the warranty.arrow_forwardA producer of pocket calculators estimates that the calculators fail at a rate of oneevery five years. The calculators are sold for $25 each with a one-year freereplacement warranty but can be purchased from an unregistered mail-ordersource for $18.50 without the warranty. Is it worth purchasing the calculator withthe warranty? For Problem 37, what length of period of the warranty equates the replacementcosts of the calculator with and without the warranty?arrow_forwardLarge-scale integrated (LSI) circuit chips are made in one department of an electronics firm. These chips are incorporated into analog devices that are then encased in epoxy. The yield is not particularly good for LSI manufacture, so the AQL specified by that department is 9% while the LTPD acceptable by the assembly department is 44%. Assume the company is willing to accept a consumer's risk of 10 percent and a producer's risk of 5 percent. (Use Exhibit 10.16.) (pictured below) A. Find the sample size. (Round up your answer to the next whole number.) B.How would you tell someone to do the test? Randomly sample LSI using the sample size from part a, reject the lot if more than _____ defective.arrow_forward
- Large-scale integrated (LSI) circuit chips are made in one department of an electronics firm. These chips are incorporated into analog devices that are then encased in epoxy. The yield is not particularly good for LSI manufacture, so the AQL specified by that department is 0.15 while the LTPD acceptable by the assembly department is 0.40. Assume the company is willing to accept a consumer's risk of 10 percent and a producer's risk of 5 percent. Find the sample size. Use Exhibit 10.16. Note: if the exact value of the computed LTPD ÷ AOQ ratio does not appear in Exhibit 10.16, use the next higher ratio. Note: Round up your answer to the next whole number. How would you tell someone to do the test?arrow_forwardIf events X and Y are mutually exclusive then A- P(X)P(Y) = 0 B- they are independent events C- their joint probability is zero D- P(X)P(Y) = P(X | Y)arrow_forwardZemansky’s sells tires with a pro rata warranty. The tires are warranted to deliver50,000 miles with the rebate based on the remaining tread on the tire. The tires failon the average after 35,000 miles of wear. Suppose the tires sell for $50 each withthe warranty. If failures occur completely at random, what would be a consistentprice for the tires if no warranty were offered?arrow_forward
- A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of the four possible states: State Condition Good as new Operable-minimum deterioration Operable-major deterioration Inoperable 2 3 The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by 1 7 1 - 16 8 16 3 1 1 P = 8. 4 8. 1 1 2 a. Determine the expected life of a new machine if it is replaced when it is "Inoperable". b. Determine the expected life of a new machine if it is replaced when it is either "Operable-major deterioration" or "Inoperable". c. According to the replacement rule in b., what is the percentage of machines that are replaced when they are inoperable?arrow_forwardA producer of pocket calculators estimates that the calculators fail at a rate of oneevery five years. The calculators are sold for $25 each with a one-year freereplacement warranty but can be purchased from an unregistered mail-ordersource for $18.50 without the warranty. Is it worth purchasing the calculator withthe warranty?arrow_forwardExpected monetary value is most appropriate for problem solving that takes place: O under conditions of uncertainty O when conditions are average O when all states of nature are equally likely O when all alternatives are equally likely under conditions of risk MacBook Air 000 DD 000 F6 F5 V 7. 00 *arrow_forward
- A 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_forward84 Large-scale integrated (LSI) circuit chips are made in one department of an electronics firm. These chips are incorporated into analog devices that are then encased in epoxy. The yield is not particularly good for LSI manufacture, so the AQL specified by that department is 12% while the LTPD acceptable by the assembly department is 35%. Assume the company is willing to accept a consumer's risk of 10 percent and a producer's risk of 5 percent. a. Find the sample size. Use Exhibit 10.16. Note: if the exact value of the computed LTPD/AOQ ratio does not appear in Exhibit 10.16, use the next higher ratio Note: Round up your answer to the next whole number.arrow_forwardConsider a product that is "settled in." Its MTBF distribution has been found to be normal with a mean of 10,000 hours and a standard deviation of 100 hours. Answer the following questions: (a) Calculate the probability of a breakdown before 8,000 hours? (b) Calculate the probability of a breakdown before 9,000 hours? (c) Would you prefer a policy of “preventive maintenance” or a policy of “breakdown maintenance” on this product? Explain your choice.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,