Equivalency of Two Popular Reliability Estimators


Wasserman, Gary S.; Reddy, Isanaka S.   (1992, ASQC)   Wayne State University, Detroit, MI 48202

Annual Quality Congress, Nashville TN    Vol. 46    No. 0
QICID: 9907    May 1992    pp. 863-868
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Article Abstract

The author compares two formulas for estimating failure probabilities of censored life data: Auth's alternative to Johnson's formula and the Kaplan-Meier technique.

Statistical analysis of reliability data is more complicated than analysis of other experimental data due to censoring of life data. Historically, Johnson's formula has been used to calculate adjusted ranks of recorded failures and that data has gone into a median rank estimation equation for failure distribution. The Johnson formula is difficult to use and Auth has developed an easier alternative. The Auth variation is compared to yet another method: the Kaplan and Meier (KM) product-limit estimator.

The Johnson estimator calculates adjusted ranks based on an analysis of all of the combinatorial arrangements of the possible failure times of censored data items if they had not been censored. The Auth variation also calculates adjusted ranks, but in more direct fashion.

The KM estimator calculates the probability of a component surviving during an interval of time as estimated from the number of units failed in that interval.

In spite of different approaches, Johnson's estimator and the KM estimator are identical with respect to adjusted rank criteria. Although the KM procedure is easier to use than the basic Johnson procedure, the Auth variation on the Johnson procedure is easier still.


Auth formula,Johnson curves,Reliability,Statistics

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