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Theoretical Explanation of Observed Decreasing Failure Rate

Frank Proschan
Technometrics
Vol. 5, No. 3 (Aug., 1963), pp. 375-383
DOI: 10.2307/1266340
Stable URL: http://www.jstor.org/stable/1266340
Page Count: 9
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Theoretical Explanation of Observed Decreasing Failure Rate
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Abstract

Pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate. More refined analysis showed that the failure distribution for each airplane separately was exponential, but with a different failure rate. Using the theorem that a mixture of distributions each having a non-increasing failure rate (e. g., a mixture of exponential distributions) itself has a non-increasing failure rate, the apparent decreasing failure rate of the pooled air-conditioning life distribution was satisfactorily explained. The present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters.

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