Month/Year of Graduation


Degree Name

Bachelor of Science (B.S.)



First Advisor

Dr. Steve From


In reliability theory, a renewal process is a stochastic model for arrival times or events occurring in a certain system. For a renewal process, it is of interest to be able to estimate the number of events that will occur in the time interval (0, t]. The renewal function, M(t), is the expected value of renewals to occur within the system from (0,t]. It is a solution of the renewal equation. Since closed-form solutions of the renewal equation are mostly non-existent, approximation methods are used. Simpler approximation methods than those currently available are presented and are applied to data. The approximations presented are especially useful for time instances less than the mean of the underlying distribution of the process, which suggests application to studies like warranty analysis.