Template:Parametric recurrence data analysis

Parametric Recurrence Data Analysis
Weibull++'s Parametric RDA Specialized Folio is a tool to model recurrent event data. It can capture the trend, estimate the rate and predict the total number of recurrences. The failure and repair data of a repairable system can be treated as one type of recurrence data. Past and current repairs may affect the future failure process. For most recurrence events, time (distance, cycles, etc.) is a key factor. With the time, the recurrence rate may keep constant, increase or decrease. For other recurrence events, not only the time, but also the number of events can affect the recurrence process, e.g. the debugging process in software development. The parametric analysis approach utilizes the General Renewal Process (GRP) model [28]. In this model, the repair time is assumed to be negligible so that the processes can be viewed as point processes. This model provides a way to describe the rate of occurrence of events over time such as in the case of data obtained from a repairable system. This model is particularly useful in modeling the failure behavior of a specific system and understanding the effects of the repairs on the age of that system. For example, consider a system that is repaired after a failure, where the repair does not bring the system to an as-good-as-new or an as-bad-as-old condition.

In other words, the system is partially rejuvenated after the repair. Traditionally in as-bad-as-old repairs, also known as minimal repairs, the failure data from such a system would have been modeled using a homogeneous or non-homogeneous Poisson process (NHPP). On rare occasions, a Weibull distribution has been used as well, in cases where the system is almost as-good-as-new after the repair, also known as perfect renewal process (PRP). However, for the intermediate states after the repair, there has not been a commercially available model, even though many models have been proposed in literature. In Weibull++, the GRP model provides the capability of modeling such systems with partial renewal (general repair or imperfect repair/maintenance) and allows for a variety of predictions such as reliability, expected failures, etc.