Parametric reliability-prediction based on small samples

Reliability prediction is considered for systems that fail due to graceful degradation of operational efficiency to below an acceptable level. The efficiency is represented by a stochastic process, X(t), either scalar or vector. The system reliability with regard to such failures is parametric. It is measured by the probability, R(/spl tau/), that X(t) is within the acceptable limits during the time period, [0,/spl tau/]. To predict parametric reliability, a procedure is proposed to determine the lower confidence bound at confidence-level, q, for R(/spl tau/). Measurement results for small N, e.g., 3-5, of X(t) at times, 0/spl les/t/sub 1//spl les/t/sub 2//spl les/...