In this paper, optimal bum-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is obtained. When the products with cumulative pro-rata warranty have high failure rate in the early period (infant mortality period), a burn-in procedure is adopted to eliminate early product failures. After burn-in, the posterior product life distribution and the warranty-related cost are dependent on burn-in time; long burn-in period may reduce the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain total mean cost under burn-in and cumulative pro-rata warranty. Property of the optimal burn-in time is analyzed, and numerical examples and sensitivity analysis are studied.

A k-out-of-n standby system is considered where all of its components are s-independent and classified either working or cold standby connected with imperfect switches. The probability density function of the life length for this system is established in closed form, when the underlying components have constant failure rates. Also the reliability function of the system is derived. Finally, the reliability functions for one, two and three out of four systems are deduced for perfect or imperfect switches and identical or non-identical constant failure rates for working and standby components.

Shanmugam(1991) generalized the Poisson distribution to capture a restriction on the incidence rate $\theta$ (i.e. $\theta$ ＜ $\beta$, an unknown upper limit), and named it incidence rate restricted Poisson (IRRP) distribution. Using Neyman's C($\alpha$) concept, Shanmugam then devised a hypothesis testing procedure for $\beta$ when $\theta$ remains unknown nuisance parameter. Shanmugam's C ($\alpha$) based .results involve inverse moments which are not easy tools, This article presents an alternate testing procedure based on likelihood ratio concept. It turns out that likelihood ratio test statistic offers more power than the C($\alpha$) test statistic. Numerical examples are included.

The objective of this paper is to provide a model for effective implementation of costing RAM management in the design and procurement of production facility considering the system cost-performance trade-off. This research proposes a two-step approach of costing RAM design and test of system RAM for production facility. In Step 1, a static model is proposed to find an initial system configuration to meet the required performance based on system RAM and LCC and analyzes the trade-off relationships between various factors of RAM and LCC. In the second Step, we developed time and failure truncated models for system reliability test and analysis. For the computational purpose, we developed computer programs and have shown the sample results. By the sample test run, the proposed model has shown the possibilities to provide a good method to analyze system performance evaluation for both design and operational phase, This model can be applied to a wide variety of systems not only for costing RAM of the production facilities but also for the other kinds of equipment.