Interval Estimation of MTBF Based on Minimal Information from a Reliability Demonstration Test

Reliability program managers are often asked to compute statistical confidence limits on mean time between failures (MTBF) based upon the results of a reliability demonstration test. The raw test data are vital in solving this problem efficiently. All too often (eg, as a result of bureaucratic errors) test data are not available or are not known, and the only information available is the test plan parameters (viz, producer and consumer risks, and the upper and lower test MTBFs) and whether the test was passed or failed. This paper gives 1- and 2-sided statistical confidence intervals on MTBF in this situation and the statistical confidence coefficients. The 2-sided intervals always lead to a non-trivial interval no matter what test outcome is observed and are recommended over the 1-sided intervals. Situations involving more than minimal data are not addressed in this paper since the type and amount of data available are variable. However the methods derived in this paper are not intended to replace a more comprehensive analysis when more complete test data are available.