Analysis of sodium valve reliability data at CREDO. [LMFBR] Page: 4 of 13
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The operating and failure (event) history of each valve was recorded
in as much detail as was available. The accuracy of the operating and
event data is extremely difficult to assess. However, for most of the
sites, the reported operating hours and the occurrence of failures were
taken directly from or verified by log books and other periodic reports.
Some approximations and assumptions were necessary, but mis-estimation of
operating hours or number of failures is not felt to be a major source of
error, particularly when there are more than a few actual failures within
a data set. Estimates of cycling rates could usually be verified only by
discussion with operating personnel, and are generally less precise.
Many valves, especially at the test loops, were replaced or taken out
of service for any of a number of reasons without failing; others were
completely repaired and reinstalled after failure. Sets of data such as
these can be analyzed by treating them as progressively censored life tests.
First, a point estimate of the failure rate was calculated under the frequently
made assumption of exponentiality. The maximum likelihood estimator (MLE)
x for the failure rate x for progressively censored samples having an
exponential distribution is given by:8
where n = number of failed items;
x. = failure time for ith failed item;
1 J_ L.
T. = j n lifetime (censoring time) for unfailed items;
r. = number of items censored at time T-;
k = number of unfailed items.
An approximate two-sided 90% confidence-interval estimator for x is given by:
(X2;2n)/2T < X < (x2 ;2n+2)/2T, (2)
5 — — 95
where T = £ x. + l T-.
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Bott, T F & Haas, P M. Analysis of sodium valve reliability data at CREDO. [LMFBR], article, January 1, 1979; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc1100705/m1/4/: accessed March 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.