This paper studies a renewal reward process with fuzzy random interarrival times and rewards under the >-independence associated with any continuous Archimedean t-norm >. The interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are >-independent fuzzy variables. Under these conditions, some limit theorems in mean...

The present paper is concerned with the eetlmatlon of the transition distributions of a Markov renewal process with finitely many states, which extends and unifies nome aspects of the results in the special cases of discrete and continuous parameter Markov chains. A natural estimator of the transition distribution." is defined and shown to be consistent. Limiting distributions of this estimator...

This paper proves the fundamental theorem of uncertain calculus with respect to both canonical process and renewal process, which gives the differential of an uncertain process in the form of a function of canonical process and renewal process.

After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each oth...

This work is based on a retrospective analysis of a renewal process applied to a very aged, highly degraded software system. Some parts of the results are generalized to define a method for determining the technical and economic qualities of software system components. The work also presents a decision model for identifying the most suitable renewal process to be applied, based on the quality o...

This work is based on a retrospective analysis of a renewal process applied to a very aged, highly degraded software system. Some aspects of the results are generalized to define a method for determining the technical and economic qualities of the components of a software system. The work also presents a decision model for identifying the most suitable renewal process to be applied, on the basi...

The concept of the renewal property is extended to processes indexed by a multidimensional time parameter. The definition given includes not only partial sum processes, but also Poisson processes and many other point processes whose jump points are not totally ordered. A new version of the waiting time paradox is proven for multidimensional Poisson processes, and is shown to imply the renewal p...

We consider parameter estimation in a regression model corresponding to an iid sequence of censored observations of a finite state modulated renewal process. The model assumes a similar form as in Cox regression except that the baseline intensities are functions of the backwards recurrence time of the process and a time dependent covariate. As a result of this it falls outside the class of mult...

This paper considers a point process model with a monotonically decreasing or increasing ROCOF and the underlying distributions from the location-scale family. In terms of repairable system reliability analysis, the process is capable of modeling various restoration types including “better–than–new”, i.e., the one not covered by the popular G-Renewal model (Kijima & Sumita, 1986). The character...