The process of software testing usually involves the correction of a detected bug immediately upon detection. In this article, in contrast, we discuss continuous time testing of a software with periodic debugging in which bugs are corrected, instead of at the instants of their detection, at some pre-specified time points. Under the assumption of renewal distribution for the time between successive occurrence of a bug, maximum-likelihood estimation of the initial number of bugs in the software is considered, when the renewal distribution belongs to any general parametric family or is arbitrary. The asymptotic properties of the estimated model parameters are also discussed. Finally, we investigate the finite sample properties of the estimators, specially that of the number of initial number of bugs, through simulation.

We prove a central limit theorem for linear triangulararrays under weak dependence conditions. Our result is then appliedto dependent random variables sampled by a ${\mathbb Z}$ -valued transient random walk. This extends the resultsobtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics3 (2003) 477–497]. An applicationto parametric estimation by random sampling is also provided.

Dans cet article nous présentons quelques plans d'essais accélérés pour estimer la fiabilité des produits. Les plans étudiés sont basés sur le modèle standard de vie accélérée (SVA) en considérant des estimations paramétrique et non-paramétrique. Des applications sur des trombones, soumis à de la fatigue oligocyclique, sont présentées pour illustrer ces différents plans.

Let {Xn, n ≧ 1} be an i.i.d. sequence of positive random variables with a continuous distribution function having a regularly varying upper tail. Denote by {X(n), n ≧ 1} the corresponding sequence of record values. We introduce two statistics based on the sequence of successive record values and investigate their asymptotic behaviour. We also give some numerical results.