Repeated significance tests on accumulating data of repairable systems

Abstract

Data used to track the reliability growth trend of repairable systems occur naturally in a sequential fashion. It is thus desirable to study some basic properties of repeated significance tests on accumulating data of repairable systems. In this paper, we provide side-to-side information for the following two widely used test statistics in this area: (1) the well-known Laplace test (called L test), and (2) the most powerful test for the shape parameter in a Poisson process with Weibull intensity (called Z test). Discussions of major results include: (1) the estimated probability of type I error at or before the nth test in sampling from a simple Poisson distribution at a constant nominal level, (2) performance assessment for abrupt changes (increasing or decreasing in the intensity of the process), (3) the existing support from the well-developed sequential clinical trial designs available in the literature, and (4) an example presents a visual interpretation of the trend in the intensity.

Keywords:

• Poisson processes
• power law processes
• sequential tests