Please see Poisson Process, which is different than Poisson distribution, http://www.randomservices.org/random/poisson/index.html http://www.randomservices.org

Please see Poisson Process, which is different than Poisson distribution, http://www.randomservices.org/random/poisson/index.html http://www.randomservices.org/random/poisson/index.html .. failures are indeed independent.