Very interesting exercise about combinatorial theory and Binomial of Newton
Hello to all my friends of steemit, after a while away for reasons of study I'm back and I want to show you a very interesting exercise that I did a while ago, here I go:
Consider a k-out-of-n parallel system having a linear hazard rate st for each component. Find a minimum number N(> 32) of components so that minimum reliability R = 0.86 will be reached for t = 100 hours and s = 0:0007 failures per hour. Explain your steps in writing and give the formula for the reliability functions RS(n; t) under relevant parameters. Then compute N using R-programming.
Solution:
To calculate we can use an R-program
and we get R = 0:8607474 and N = 1260 is the minimum number of components needed to sustain the reliability of at least 0.86 within 100 hours.
I think it is more of a probability type problem with the choose notation in the binomial formula.
Regardless, it is interesting and R helps with the computations.
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