Mixture models for reliability of software with imperfect debugging: Identifiability of parameters

A class of software-reliability mixture-type models is introduced in which individual bugs come with i.i.d. random failure-causation rates /spl lambda/, and have conditional hazard function /spl phi/(t|/spl lambda/) for software failure times. The models allow the possibility of imperfect debugging, in that at each failure a new bug (possibly with another rate-parameter /spl lambda/) is introduced, statistically independently of the past, with probability p. For /spl phi/(t|/spl lambda/)=/spl lambda/, it is shown that the unknown parameters p, n/sub 0/ (the initial number of bugs), and G (the Cdf for /spl lambda/) are uniquely determined from the probability law of the failure-count function (N(t), 0/spl les/t/spl les/spl delta/), for arbitrary /spl delta/>0. The parameters (n/sub 0/,G) are also uniquely determined by the mean failure-count function E{N(t)} when p is known (e.g., is assumed to be 0), but not when p is unknown. For special parametric classes of G, the parameters (n/sub 0/,p,G) are uniquely determined by (E{N(t)}, 0/spl les/t/spl les/spl delta/).<
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