an oversimplification, more realistic versions of this approach can be (and are being) developed using straightforward generalizations of the above model.
One interesting implication of this research is that reliability growth under the assumed circumstances will not necessarily have the general pattern identified by Duane (1964). Consideration of subsystems tested in series with this framework could certainly lead to other patterns of reliability growth.
One possible generalization of this model is to place a Bayesian prior on the ds(0)’s. Doing so would (1) allow the introduction of expert judgment, (2) reduce the assumptions concerning the ds(0)’s to a small number of hyperparameters, and (3) allow some borrowing of information across components. Another generalization that could be explored would be to assume that the θs’s were draws from some distribution, instead of assuming fixed parameters 1-θs. Doing so would (1) help account for overdispersion, (2) reduce the number of parameters to be estimated, and (3) remove the homogeneous failure rate assumption.
Nonhomogeneous Poisson processes (Poisson processes in which the failure rate changes as a function of time) are commonly used for modeling reliability growth. As mentioned above, an extremely popular model is the Duane power law model, a particular nonhomogeneous Poisson process in which the failure rate is assumed to be a power function of time. A chief deficiency of the Duane model is that it is not based on a physical cause-and-effect connection between an observed pattern of system failures and reliability growth (as was noted in the previous section). To address this concern, Fritz Scholz proposed the following model for a system of defect detection and reliability growth. (This idea was originally developed in the context of software testing, but it can be applied to any system that satisfies the cited assumptions. The description provided here is for the continuous case; Scholz, 1986, provides more detail and also addresses the discrete case.)
Assume one wants to measure reliability for a system that is suspected of having a number of design flaws. To measure reliability, the system is subjected to a series of test events. The system is assumed to be a deterministic function of the inputs to the system. A test is the exercising of the system using a selected subset of the set of possible inputs to the system. For a software system, the inputs are user-supplied fields, such as keystrokes