Modeling a System of Softwares Under Imperfect Debugging Marcus A. Agustin * Ma. Zenia N. Agustin † Abstract This paper considers a series system of p softwares where the failure of a software follows a modified Jelinski-Moranda model. In this model, the debugging scheme of a software is imperfect in the sense that the number of bugs introduced to the software that caused system failure is a random variable. Moreover, tasks are assigned to the system with the task completion times assumed to be random. The main interest is to estimate the parameters that describe the failure process of each software as well as the system reliability. Finally, the finite-sample properties of these estimators are investigated via a simulation. Key Words and Phrases: Competing risks, repairable system, software reliability. AMS Subject Classification: Primary: 62N05 Secondary: 49M15, 62F10, 62N02 1. Introduction A typical assumption in software reliability is the ‘perfect debugging’ of a software. This means that in the process of removing the bug(s) that caused software failure, no new bugs are introduced. One of the earliest papers in software reliability is by Jelinski and Moranda (1972) where software failure rate is assumed to be proportional to the residual number of bugs, and each bug has a constant failure rate contribution. In addition, the number of bugs decreases by one after each software failure to indicate a perfect removal of the bug that caused software failure. The finite-sample properties of the estimators in the Jelinski-Moranda model were established in van Pul (1992). Several other models have been proposed for software reliability as evidenced by the papers of Goel and Okumoto (1979), Littlewood (1980), van Pul (1993), Barendregt and van Pul (1995), Goseva-Popstojanova and Trivedi (2000), and Jeske and Pham (2001), among others. Goel and Okumoto (1979) extended the Jelinski-Moranda model by using a * M. Agustin is Associate Professor in the Department of Mathematics and Statistics, Southern Illinois Uni- versity Edwardsville, Edwardsville, IL 62026. † Z. Agustin is Associate Professor in the Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026. 1