Birth-Death and Bug Counting

Abstract

Many software reliability time-domain bug-counting models are, as fault counters, special cases of the stochastic process known as the death process. Generalization to a nonhomogeneous birth-death process achieves three ends: stochastic fault introduction, the synthesis of a time-dependent failure rate with imperfect debugging and fault introduction, and the mathematical unification of much bug-counting theory. Often, the price for generalization is mathematical intractability. Yet useful and tractable reliability measures with strong intuitive appeal are derived. The paper opens with a brief general discussion of software reliability and a selective review of some bug-counting models. Thereafter, the fundamental concepts and equations of a birth-death process are presented and applied to software reliability modeling. Assumptions for this application are then dealt with at some length. Reliability measures-initial, present, and future - are developed. Finally. the practical application of the model in the reliability assessment of a software package is discussed.