Abstract: In industrial experiments for improving reliability, censored data are often observed because of cost and time constraints. Associated with censoring are estimability problems, however. We expose these problems in the industrial context by presenting some striking examples which show that it is difficult to tell, just by looking at the data, whether the estimates exist or not. Thus, in practice, there is a potential danger of using meaningless results when the estimates do not exist. Estimability is easily characterized for small two level factorial experiments such as 4 and 8 run designs. Because characterization becomes difficult for larger experiments, using a linear programming (LP) algorithm to check the estimability conditions is recommended. For industrial experiments whose run sizes are typically small, we propose a simple alternative LP problem that can be solved directly by a standard LP algorithm. These results apply to popular reliability models including the Weibull, lognormal and exponential regression models.
Key words and phrases: Maximum likelihood estimation, fractional factorial design, linear programming, lognormal, Weibull and exponential distributions.