component ins eries what is the probabbility that a single component lives
Added by Stephanie M.
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Components are connected in series, meaning the entire system works only if every single component works. Show more…
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A system consists of five components is connected in series as shown below. As soon as one component fails, the entire system will fail. Assume that the components fail independently of one another. (a) Suppose that each of the first two components have lifetimes that are exponentially distributed with mean 98 weeks, and that each of the last three components have lifetimes that are exponentially distributed with mean 127 weeks. Find the probability that the system lasts at least 60 weeks. (b) Now suppose that each component has a lifetime that is exponentially distributed with the same mean. What must that mean be (in years) so that 86% of all such systems lasts at least one year? Answer in years, correct to 2 decimals.
Supreeta N.
The lifetime of a component is distributed exponentially with a mean lifetime 10^3 hours. a) Find the probability that the component will last longer than its double expected lifetime. b) If the component is working at time 10^3 hours, find the probability that it will not fail during next 10^3 hours. c) A system consists of two such components connected in series (i.e., if a component fails, the system fails). The components fail independently. Find the probability that the lifetime of the system will exceed 2 · 10^3 hours. (10)
Kumar A.
The behavior of series of components plays a huge role in scientific and engineering reliability problems. The reliability of the entire system is certainly no better than that of the weakest component in the series. In a series system, the components operate independently of each other. In a particular system containing three components, the probabilities of meeting specifications for components $1,2,$ and $3,$ respectively, are $0.95,0.99,$ and $0.9 .$ What is the probability that the entire system works?
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