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
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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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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