ACTUAL AND PROBABLE LIFE
per year, one-twentieth each year, the last going out of service
in the twentieth year. Or (c) there might be no failures at all
for a number of years, as, for example, during the first half of
the probable life term, and thereafter a uniform or an irregular
rate of failures until some time after the end of the probable
life term. Or (d) there might be a gradually increasing number
of failures per year from the beginning to the end of the term
of the probable life, and thereafter a gradually decreasing num-
ber of failures.
Of these various possible distributions of failures to a series
of years the most probable one is unquestionably (d). For the
sake of a definite basis for calculation it has been assumed that
the increase in the number of annual failures up to the maxi-
mum and thereafter the decrease in the number of annual
failures is uniform; that annual increase before the maximum
and annual decrease thereafter are the same and that the maxi-
mum rate is one-tenth of the whole number and occurs in the
tenth year. On these assumptions studies have been made to
determine the expectancy of any article which has reached any
age with rather interesting results. These are presented not
only as an improvement in the method of estimating probable
remaining life or expectancy of any article which is no longer
new, though still in good condition, but also to encourage further
study along these lines, in order that, where necessary, closer
approximation of the actual accrued and annual depreciation
can be made than has heretofore been attempted.
It should be stated that other hypotheses in the matter of the
rate of failures were tried, but that no other gave results that
appeared as reasonable as those based on the hypothesis as
just stated. Thus, for example, the assumption was tried that
3 per cent of all articles of ten-year life fail in the first year,
13 per cent in the second year, and so on, 93 per cent in the
tenth, 97 per cent in the eleventh, 81 per cent in the twelfth,
etc., and 3 per cent in the twentieth, but with less satisfactory
results for application in estimating remaining value and re-
placement requirements.
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