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)
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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Question
Q3.29

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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