Award Date


Degree Type


Degree Name

Master of Science (MS)


Mathematical Sciences

First Committee Member

Chih-Hsiang Ho

Number of Pages



A key parameter, most sought after by the modelers of reliability, is the failure rate of a targeted repairable system. Popular modeling techniques based on a point process such as the Power-law process often are handicapped by the requirement of a monotonic failure rate. In this thesis, we show the potential of building a linking bridge between the traditional homogeneous and nonhomogeneous Poisson processes and the classical time series via a sequence of the empirical recurrence rates, calculated at equally spaced intervals of time. The distinctive signature, marking the unique failure pattern of a repairable system, is displayed with an empirical recurrence rate time-plot, referred as the "fingerprint" or an "ERR-plot" of a targeted system. A major strength of our approach is that we present an interesting extension of advanced time series analysis techniques into the domain of data exploration of point processes, including but not limited to the events associated with repairable systems or natural phenomena (earthquakes and volcanic eruptions), and make new and innovative use of the well-known ARIMA method possible for modeling the recurrence rate of such events ranging from constant recurrence rate to those show cyclic trends; ARIMA time series modeling techniques are well developed. Therefore, the scope of our study is to investigate the merits of the transformation in terms of the diagnostics on the basic plots and some tests of goodness-of-fit via pseudo and real data.


Empirical; Modeling; Rate; Recurrence; Statistical

Controlled Subject


File Format


File Size

665.6 KB

Degree Grantor

University of Nevada, Las Vegas




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