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the redundancy? What is the MTTF? What is the reliability over 100 A parking lot has 10 floodlights consisting of 100-watt metal halide bulbs sitting atop 20-foot poles. The failure distribution of the bulbs is best modeled with the two-parameter exponential distribution having a guaranteed lifetime of 1000 hours and a failure rate of .002 failures per day. The floodlights operate for 10 hours per day. Because of the cost to send a crew to replace bulbs, a scheduled replacement interval must be established. (a) Determine a replacement interval in days so that the average number of failed bulbs equals 2 (20 percent). (b) The parking lot is considered unsafe if half or more of the floodlights are inoper- able. Given the replacement interval in (a), what is the probability of more than 4 bulbs having failed before replacement? 3.28 A mean of 0.074 demands per day is observed for components that can be repaired. Repair takes 30 days. How many spare components are needed to meet demands generated during a repair cycle with a probability of 0.98? 3.29 SUPPLEMENTARY EXERCISES 3.30 A more general exponential reliability model may be defined by R(A) = a bt where a > 1 b>0 3Da and a and b are parameters to be determined. Find the hazard rate function, and show how this model is equivalent to R(t) = e ". tigl distribution that the residual mean life is 1/1 regardless

the redundancy? What is the MTTF? What is the reliability over 100 A parking lot has 10 floodlights consisting of 100-watt metal halide bulbs sitting atop 20-foot poles. The failure distribution of the bulbs is best modeled with the two-parameter exponential distribution having a guaranteed lifetime of 1000 hours and a failure rate of .002 failures per day. The floodlights operate for 10 hours per day. Because of the cost to send a crew to replace bulbs, a scheduled replacement interval must be established. (a) Determine a replacement interval in days so that the average number of failed bulbs equals 2 (20 percent). (b) The parking lot is considered unsafe if half or more of the floodlights are inoper- able. Given the replacement interval in (a), what is the probability of more than 4 bulbs having failed before replacement? 3.28 A mean of 0.074 demands per day is observed for components that can be repaired. Repair takes 30 days. How many spare components are needed to meet demands generated during a repair cycle with a probability of 0.98? 3.29 SUPPLEMENTARY EXERCISES 3.30 A more general exponential reliability model may be defined by R(A) = a bt where a > 1 b>0 3Da and a and b are parameters to be determined. Find the hazard rate function, and show how this model is equivalent to R(t) = e ". tigl distribution that the residual mean life is 1/1 regardless

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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the redundancy? What is the MTTF? What is the reliability over 100 A parking lot has 10 floodlights consisting of 100-watt metal halide bulbs sitting atop 20-foot poles. The failure distribution of the bulbs is best modeled with the two-parameter exponential distribution having a guaranteed lifetime of 1000 hours and a failure rate of .002 failures per day. The floodlights operate for 10 hours per day. Because of the cost to send a crew to replace bulbs, a scheduled replacement interval must be established. (a) Determine a replacement interval in days so that the average number of failed bulbs equals 2 (20 percent). (b) The parking lot is considered unsafe if half or more of the floodlights are inoper- able. Given the replacement interval in (a), what is the probability of more than 4 bulbs having failed before replacement? 3.28 A mean of 0.074 demands per day is observed for components that can be repaired. Repair takes 30 days. How many spare components are needed to meet demands generated during a repair cycle with a probability of 0.98? 3.29 SUPPLEMENTARY EXERCISES 3.30 A more general exponential reliability model may be defined by R(A) = a bt where a > 1 b>0 3Da and a and b are parameters to be determined. Find the hazard rate function, and show how this model is equivalent to R(t) = e ". tigl distribution that the residual mean life is 1/1 regardless
Transcribed Image Text:the redundancy? What is the MTTF? What is the reliability over 100 A parking lot has 10 floodlights consisting of 100-watt metal halide bulbs sitting atop 20-foot poles. The failure distribution of the bulbs is best modeled with the two-parameter exponential distribution having a guaranteed lifetime of 1000 hours and a failure rate of .002 failures per day. The floodlights operate for 10 hours per day. Because of the cost to send a crew to replace bulbs, a scheduled replacement interval must be established. (a) Determine a replacement interval in days so that the average number of failed bulbs equals 2 (20 percent). (b) The parking lot is considered unsafe if half or more of the floodlights are inoper- able. Given the replacement interval in (a), what is the probability of more than 4 bulbs having failed before replacement? 3.28 A mean of 0.074 demands per day is observed for components that can be repaired. Repair takes 30 days. How many spare components are needed to meet demands generated during a repair cycle with a probability of 0.98? 3.29 SUPPLEMENTARY EXERCISES 3.30 A more general exponential reliability model may be defined by R(A) = a bt where a > 1 b>0 3Da and a and b are parameters to be determined. Find the hazard rate function, and show how this model is equivalent to R(t) = e ". tigl distribution that the residual mean life is 1/1 regardless
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