Article

Mason, Sterling A. *(1986, ASQC)* *Eastman Kodak Company, Rochester, NY*

*40th Annual Quality Congress, May 1986, Anaheim, CA* Vol. 40 No. 0
- QICID: 3197 May 1986 pp. 307-310
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## Article Abstract

This paper reviews the current estimate of MTBF (mean time between failures) for time truncated tests of repairable devices with constant failure rates. For tests which are terminated at a failure an unbiased estimate of MTBF is available. However, if the test is truncated at some predetermined time, it is shown that the current esimate is biased as much as 38% above the true value.This overestimation of MTBF comes about because the test time between the last failure and the end of the test is not properly accounted for in the estimate.An alternate estimate of MTBF for time truncated data is developed, based on an evaluation of the expected value of the ratio of the test time to the number of failures plus one. This expected value turns out to be a function of the true MTBF, but by a series of approximations, an estimate is developed which is unbiased as long as at least one failure has occurred. The estimate is given byT/Cor(K) = T/[(K+1)(1-exp[-(K+1)[1-exp[-(K+1)[1-...]]]])]where T is the total test time and K is the number of failures which occurred during the test. Since this estimate involves an infinite exponentiation, a table is provided which evaluates the estimate for a range of failures.A simulation was conducted to verify the thesis of this paper. The estimates which were compared wereT/K, T/(K+1), and T/Cor(K)The simulation showed that T/K overestimates the true MTBF by 38%, as previously mentioned. T/(K+1) was found to consistently underestimate the true MTBF while T/Cor(K) provided the best estimate.

## Keywords

Reliability

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