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System Lifetimes, The Memoryless Property, Euler’s Constant, and π
Anurag Agarwal, James E. Marengo and Likin Simon Romero
The College Mathematics Journal
Vol. 44, No. 3 (May 2013), pp. 210-219
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.44.3.210
Page Count: 10
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Summary A k-out-of-n system functions as long as at least k of its n components remain operational. Assuming that component failure times are independent and identically distributed exponential random variables, we find the distribution of system failure time. After some examples, we find the limiting distribution of system life when n approaches infinity, and apply these results to evaluate two challenging integrals.
Copyright the Mathematical Association of America 2013