Template:Recurrent events data analysis

Recurrent Events Data Analysis, also called Recurrence Data Analysis (RDA), can be used in various applied fields such as reliability, medicine, social sciences, economics, business and criminology.

Whereas in life data analysis (LDA) it was assumed that events (failures) were independent and identically distributed (iid), there are many cases where events are dependent and not identically distributed (such as repairable system data) or where the analyst is interested in modeling the number of occurrences of events over time rather than the length of time prior to the first event, as in LDA.

Weibull++ provides both parametric and non-parametric approaches to analyze such data.


 * •	The non-parametric approach is based on the well-known Mean Cumulative Function (MCF). The Weibull++ module for this type of analysis builds upon the work of Dr. Wayne Nelson, who has written extensively on the calculation and applications of MCF [31].
 * •	The parametric approach is based on the General Renewal Process (GRP) model, which is particularly useful in understanding the effects of the repairs on the age of a system. Traditionally, the commonly used models for analyzing repairable systems data are perfect renewal processes (PRP), corresponding to perfect repairs, and nonhomogeneous Poisson processes (NHPP), corresponding to minimal repairs. However, most repair activities may realistically not result in such extreme situations but in a complicated intermediate one (general repair or imperfect repair/maintenance), which are well treated with the GRP model.

Introduction
Non-parametric recurrence data analysis provides a nonparametric graphical estimate of the mean cumulative number or cost of recurrence per unit versus age. In the reliability field, the Mean Cumulative Function (MCF) can be used to: [31]


 * •	Evaluate whether the population repair (or cost) rate increases or decreases with age (this is useful for product retirement and burn-in decisions).
 * •	Estimate the average number or cost of repairs per unit during warranty or some time period.
 * •	Compare two or more sets of data from different designs, production periods, maintenance policies, environments, operating conditions, etc.
 * •	Predict future numbers and costs of repairs, such as, the next month, quarter, or year.
 * •	Reveal unexpected information and insight.