Smooth empirical Bayes estimation with application to the Weibull distribution

The type of decision problem to be considered in this dissertation can best be illustrated by an example. Consider the development program for a particular solid propellant- rocket engine which must "burn" for a specified time. In this program, certain points exist at which progress is monitored. For instance, the Pre-Plight Rating Test program would be one such point at the culmination of the initial R&D program, demonstrating the ability of a sample of engines to perform for a specified length of time. After this phase a new phase is entered in which flight and static tests are performed, and if needed, a more refined system configuration is developed. Finally, design is frozen, and a Qualification Test program is undertaken to demonstrate the suitability of the engine system. During this period in the program, several groups of engines are test-fired, and due to stringent reliability requirements, a large sample of engines is required.