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4 bulbs having failed before replacement: 9 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?

4 bulbs having failed before replacement: 9 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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Q3.29

. A parking lot has 10 floodlights consisting of 100-watt metal halide bulbs sitting 20-foot poles. The failure distribution of the bulbs is best modeled with the atop 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 day. interval must be established. (a) Determine a replacement interval in days so that the average number of failed bulbs equals 2 (20 percent). ) 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? 3.29 Amean of 0.074 demands per day is observed for Repair takes 30 days. How many spare components are needed to meet demands generated during a repair cycle with a probability of 0.98? components that can be repaired. SUPPLEMENTARY EXERCISES 3.30 A more general exponential reliability model may be defined by R(t) = a bt where a> 1 6>0 and a and D are parameters to be determined. Find the hazard rate function, and show how this model is equivalent to R(t) = e. %3D 3De 1 the residual mean life is 1/ regardless of
Transcribed Image Text:. A parking lot has 10 floodlights consisting of 100-watt metal halide bulbs sitting 20-foot poles. The failure distribution of the bulbs is best modeled with the atop 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 day. interval must be established. (a) Determine a replacement interval in days so that the average number of failed bulbs equals 2 (20 percent). ) 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? 3.29 Amean of 0.074 demands per day is observed for Repair takes 30 days. How many spare components are needed to meet demands generated during a repair cycle with a probability of 0.98? components that can be repaired. SUPPLEMENTARY EXERCISES 3.30 A more general exponential reliability model may be defined by R(t) = a bt where a> 1 6>0 and a and D are parameters to be determined. Find the hazard rate function, and show how this model is equivalent to R(t) = e. %3D 3De 1 the residual mean life is 1/ regardless of
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