MIXTURE-MODELS FOR RELIABILITY OF SOFTWARE WITH IMPERFECT DEBUGGING -IDENTIFIABILITY OF PARAMETERS

A class of software-reliability mixture-type models is introduced in w hich individual bugs come with i.i.d. random failure-causation rates l ambda, and have conditional hazard function phi(t\lambda) for software failure times, The models allow the possibility of imperfect debuggin g, in that at each failure a new bug (possibly with another rate-param eter lambda) is introduced, statistically independently of the past, w ith probability p. For phi(t\lambda)=lambda, it is shown that the unkn own parameters p, n(0) (the initial number of bugs), and G (the Cdf fo r lambda) are uniquely determined from the probability law of the fail ure-count function (N(t), 0 t less than or equal to delta), for arbitr ary delta > 0. The parameters (n(0),G are also uniquely determined by the mean failure-count function E{N(t)} when p is known leg, is assume d to be 0), but not when p is unknown. For special parametric classes of G, the parameters (n(0),p,G) are uniquely determined by (E{N(t)}, 0 less than or equal to t less than or equal to delta).