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(τ), that X(t) is within the acceptable limits during the time period, [0,τ]. To predict parametric reliability, a procedure is proposed to determine the lower confidence bound at confidence-level, q, for R(τ). Measurement results for small N, e.g., 3-5, of X(t) at times, 0⩽t₁⩽t₂⩽…i ⩽τ are taken as initial data along with stated assumptions on the nature of X(t) variations. The small-sample feasibility is due to the prior selection of the failure-model (on the basis of the system-analogue observation) while the test results are used to estimate the model parameters