Reliability & Confidence for Serially Connected Systems

In most test programs component test results are available. It is in general a fairly easy task to find lower one-side confidence limits on the probability of failure of a chosen component. Either variable data or attribute (success-failure) data can be used. From a statistical point of view it is most often more desirable to use variable data (like pressure, temperature or specific impulse, etc.). From that information, upper one-sided confidence limits on the reliability of the component can be secured. It is true, in general, that different components are tested under varied conditions with an unequal sample size. A long-standing problem of interest to both the engineer and statistician is: How can the component reliabilities at different or identical confidence levels be combined to find the system reliability at a chosen confidence level