Award Date

August 2022

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

First Committee Member

Chih-Hsiang Ho

Second Committee Member

Amei Amei

Third Committee Member

Malwane Ananda

Fourth Committee Member

Jee Woong Park

Number of Pages



To a practitioner who chooses to be on the safe side, we offer an option between a cocktail of tests and a solo one-size-fits-all test as a needed antidote to power asymmetries. Two bidirectional tests are first established to empower a basic pair of tests as asymmetrical performances. Unsurprisingly, we’ve seen either bidirectional device championing in one alternative setting, but also being turned against the very setting altered with just one of the composed elements. Progressing by filtering out the bad and enhancing the good, we assemble a hybrid from the empowered pair to restore power symmetries that are thought to be automatic and required for quality assurance. Data elaborated by the maximum power-deficits certify that the hybrid, termed as the dual bidirectional test, is robust with essential quality assurance in addition to a user-friendly version for the practitioners conducting the work. To further substantiate the applicability of a p-value induced dual bidirectional test, we challenge the legendary Laplace test to a duel. The outcomes reveal some elaborate concerns associated with the defending champion while supporting the challenger as an all-purpose test and a safe bet for practitioners doing the applicable real-world case studies. We extend the statistical process control architecture to an all-in-one panel of coherent bidirectional control charts fit for group sequential testing and multisystem. The charting tools start with a basic pair of tests that are more complementary than competitive, and are bound together with a common set of control limits. Another unified control limits, partners of an empowered pair of tests, form a second bidirectional control chart. And, a series of novel group sequential control charts, centering on a hybrid of the empowered pair, characterize the test as the only tool possessing the unique feature of having proxies that are free of the system sample size and the sampling schemes. It is, therefore, capable of producing a one-size-fits-all control chart, to be considered in equipment performance assessments of repairable systems and, by extension, other applications. Moreover, we start the development by showing a simple dot-plot that cumulates all the dot-jumps up to each time-point of occurrences and leaves us an often mysterious but meaningful footprint to shed any light on. Its mystery lies in the sequence of the slopes and/or curvature associated with each corresponding hill edging up. We then launch elaborated graphics panels to gain a broad perspective on the data analysis to exchange information, support one another, share findings of reliability trends and the change-point(s) from both directions, and even interconnected with power asymmetries. A cocktail of bidirectional tests is a social lubricant in the saga of absorbing graphics to make it easier to collaborate on new and/or improved technologies in reliability engineering and, by extension, other applications.


Change-point; Maximum power-deficit; Power asymmetries; Power law process; Reliability graphics; Simulation


Statistics and Probability

Degree Grantor

University of Nevada, Las Vegas




IN COPYRIGHT. For more information about this rights statement, please visit