Abstract
Most of the existing research in multi-state systems is focused on modeling techniques and the design of optimal systems from a choice of components. While the assessment of uncertainty during design is essential, variability in system availability is commonly ignored. Unfortunately, unlimited testing which could provide these arbitrarily accurate estimates is not economical. In this paper, we present a statistical approach to quantify the uncertainties inherent in limited testing. The methodology enables the derivation of joint confidence intervals for a system's performance distribution and subsequently provides a hypothesis testing procedure for assessment. This builds on previous research which has only addressed confidence bounds for system reliability. Instead of dividing systems into acceptable and unacceptable, our approach can handle the case when a system exhibits three or more distinct performance levels. Thus, our method does not place restrictions on the flexibility of the underlying multi-state system paradigm. The value of our approach is illustrated using a case study and several experiments. The results indicate that the joint confidence intervals produced by this procedure are accurate for a range of common confidence levels and sample sizes.