Most of the existing research in multi-state systems relies on point estimation for modeling and optimization. The assessment of uncertainty during design is essential, yet variability in system performance is commonly ignored. Unfortunately, unlimited testing which could provide these arbitrarily accurate estimates is not economical. This paper describes a statistical inference technique to quantify the uncertainties inherent in limited testing. The methodology enables estimation of joint confidence intervals for both system and component performance distributions and subsequently provides a hypothesis testing procedure to perform objective assessments. This builds on previous research which has only addressed confidence bounds for system reliability. Instead of dichotomizing systems into acceptable and unacceptable classes, our approach can handle the case when a system exhibits three or more distinct performance levels. Thus, the method does not place restrictions on the flexibility of the underlying multi-state system concept. The value of the approach is illustrated using a case study and several experiments. The results indicate that joint confidence intervals produced by this procedure are accurate for a range of common confidence levels and sample sizes. It is also demonstrated how hypothesis testing and uncertainty assessment may be used to objectively measure system readiness.
An Insight of Linear Regression Analysis
