Date of Award


Document Type


Degree Name

Master of Science in Systems Engineering


Department of Systems Engineering and Management

First Advisor

Jason K. Freels, PhD.


The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped hazard functions arise from the existence of multiple competing failure modes which dominate at different periods in a systems lifecycle. The standard method for modeling the infant mortality, useful-life, and end-of-life wear-out failures depicted in a bathtub-curve is the Weibull distribution. However, this will only model one or the other, and not all three at once. The poly-Weibull distribution arises naturally in scenarios of competing risks as it describes the minimum of several independent random variables where each follows a distinct Weibull law. Little is currently known or has been developed for the poly-Weibull distribution. In this report, the poly-Weibull is compared against other goodness-of-fit models to model these completing multimodal failures. An equation to determine the moments for the poly-Weibull is derived leading to the development of properties such as the mean, variance, skewness, and kurtosis using Maximum Likelihood Estimation (MLE) parameters obtained from a data set with known bathtub shaped hazard function.

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DTIC Accession Number