Analysis of sodium valve reliability data at CREDO. [LMFBR] Page: 6 of 13
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failures did indicate exponential behavior for at least a portion of the
lifetime. However, the majority of the data sets were better represented
over the complete span of operating time by a Weibull model. Columns 5
and 6 list the values of a and e, respectively, estimated from the graphs.
The inverse of the mean-time-between-failure jj for each of the Weibull
distributions is listed in column 7 of Table 2 for comparison to the values
Note that for most of the data sets, the estimated value of s is less
than unity, which suggests a decreasing failure rate (DFR) with time. Two
sets (GPL and LMEC) have e's greater than unity, which suggests an increasing
failure rate (IFR). Barlow and Campo10 have presented a graphical method for
analyzing data which provides (among other things) a means for quantifying
the tendency toward either DFR or IFR. The method applies a derived statistic
called "total-time-on-test" transform. The resulting graphical procedure is
to plot the total-time-on-test transform (designated here Hy) vs. time on
linear paper. If the Hy plot lies entirely below the 45° line, the hypothesis
of an exponential model should be rejected in favor of a DFR model. For a
plot of n failures, the level of significance for the test is If the Hy
plot lies entirely above the 45° line, an IFR is indicated with a significance.
The indication from the Hy plots and the ^ significance levels for
rejecting the exponential hypothesis are listed in the last two columns of
Table 2. For TTL, EBR-II, the MSAR loops and SRE, the indication of DFR
behavior is quite strong. There are a number of reasons that a decreasing
failure rate may be indicated, including the classical "wear-in" behavior.
Maintenance and operating practices may improve with experience, and reduce
the number of failures. This may well have been at EBR-II, where there is a
constant sample size and the number of failures per year did decrease over a
period of years.
Another reason for indicated DFR behavior might be "clustering" of failures,
i.e., a number of failures occurring in a relatively short time after a
relatively long period of failure-free operation. Since the data 1 treatment
assumes all "lifetimes" start simultaneously at t=0, clustering wc^uld appear
as a relatively high frequency of failures early in life, followed! by fewer
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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/m1/6/: accessed March 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.