New Bivariate Lifetime Distributions Based on Bath-Tub Shaped Failure Rate

A class of lifetime distributions which has received considerable attention in modelling and analysis of lifetime data is the class of lifetime distributions with bath-tub shaped failure rate functions because of their extensive applications. The purpose of this thesis was to introduce a new class of bivariate lifetime distributions with bath-tub shaped failure rates (BTFRFs). In this research, first we reviewed univariate lifetime distributions with bath-tub shaped failure rates, and several multivariate extensions of a univariate failure rate function. Then we introduced a new class of bivariate distributions with bath-tub shaped failure rates (hazard gradients). Specifically, the new class of bivariate lifetime distributions were developed using the method of Morgenstern’s method of defining bivariate class of distributions with given marginals. The computer simulations and numerical computations were used to investigate the properties of these distributions.

Synthesis and Characterization of Photochromic Copolymers Containing 3-Indolylfulgides/Indolylfulgimides

Fulgides and fulgimides are important organic photochromic compounds and can switch between the open forms and the closed forms with light. The 3-indolylfulgides and 3-indolylfulgimides exhibit promising photochromic properties and have great potential in optical memory devices, optical switches and biosensors. Copolymers containing 3-indolylfulgides/indolylfulgimides synthesized via free radical polymerizations increase conformation changes and allow the photochromic compounds to be uniformly distributed in the polymer matrix. A trifluoromethyl 3-indolylfulgide and two trifluoromethyl 3-indolylfulgimides with one or two polymerizable N-stryryl group(s) were prepared. Copolymerization with methyl methacrylate provided two linear copolymers or a cross-linked copolymer. The properties of the monomeric fulgide/fulgimides and copolymers in toluene or as thin films were characterized. In general, the photochromic monomers and copolymers revealed similar photochromic properties and exhibited good thermal and photochemical stability. All compounds absorb visible light in both open forms and closed forms. The closed form copolymers were more stable than the open form copolymers and showed little or no degradation after 400 h. The photochemical degradation rate was less than 0.03% per cycle. In films, conformational restrictions were observed for the open forms suggesting that the preparation of films from the closed forms is advantageous. Two novel methyl 3-indolylfulgimides with one or two polymerizable N-stryryl group(s) were prepared. Copolymerization of acrylamide with the methyl indolylfulgimides or the trifluoromethyl indolylfulgimides yielded two aqueous soluble linear copolymers and two photochromic hydrogels. The closed form copolymers containing trifluoromethyl indolylfulgimides were hydrolyzed in aqueous solution by replacing the trifluoromethyl group with a carboxylic acid group. The resulting carboxylic copolymers were also photochromic. The copolymers containing methyl fulgimides were stable in aqueous solutions and did not hydrolyze. Both methyl and carboxylic copolymers exhibited good stability in aqueous solutions. In general, the open form copolymers were more stable than the closed form copolymers, and the copolymers revealed better stability in acidic solution than neutral solution. The linear copolymers displayed better photochemical stability in neutral solution and degraded up to 22% after 105 cycles. In contrast, the hydrogels showed enhanced fatigue resistance in acidic condition and underwent up to 60 cycles before degrading 24%.