REDEFINING FAILURE RATE FUNCTION FOR DISCRETE DISTRIBUTIONS

By Min Xie, Olivier Gaudoin, Cyril Bracquemond. 2002

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A new discrete probability distribution with integer support on (−∞, ∞) (2016, unknown): “• Second rate of failure (SRF) (see Roy and Gupta, 1992; Xie et al., 2002): rY ∗∗(y; p, μ) = log[S(y)/S(y + 1)] = log[(1 + py−μ+1)/(p (1 + py−μ)]; y ∈ Z, 0 < p < 1; −∞ < μ < ∞ Remark 7.”
The discrete Lindley distribution: properties and applications (2011, unknown): “and the second rate of failure [4,12] is given by r∗∗(x) = log [ S(x) S(x + 1) ] = log [ (2 + x) log λ − 1 λ(3 + x) log λ − 1 ] .”
DISCRETE INVERSE RAYLEIGH DISTRIBUTION (2014, background): “…(2) has some misconception i.e. i) It is bounded i.e. 1. x h  this may add some confusion in industry that failure rate and failure probability are sometimes mixed up (see Xie et al., 2002). ii) Suppose that if we have m discrete component connected independently in series then their failure…”