ACTUAL AND PROBABLE LIFE 1
If the reasonableness of the assumption on which Table 3 Is
based be admitted, or if it should be possible to prove by actual
records of failures that these assumptions are near enough to
the truth to be accepted as giving results substantially correct,
then a further analysis will show that the actual replacement
requirements under various conditions of investment will be
as shown in Tables 4 to 6. In the preparation of these tables
account has been taken of the failures that will occur among
the replacements as well as among the units of the original
installations.
Diagrammatic Illustration of the Assumed Rate of Failures. —
The basis for the results in Table 3 for articles with a probable
life of ten years is shown diagrammatically in Fig. 1. The
expectancy is found by dividing the remaining service years at
any time by the corresponding number of surviving units. The
reversed curve marked “Articles remaining in service ” clearly
indicates the hypothesis of failures on which the table is based.
It is to be noted that under this hypothesis there is no serious
departure from the results that were obtained by assuming that
the law of probabilities would apply.
Tabular Presentation of Replacement Requirements for
Groups of Articles. — The replacement requirements, as shown
in Table 5, for numerous articles which when new have a
probable life of ten years, if failures occur substantially as as-
sumed, and if each failing article be at once replaced, would
increase from $1 in the first year to about $10 in the ninth
year for $100 of original investment, fluctuating thereafter be-
tween $9 and nearly $12 per year and gradually settling down
to $10 per year. For an annual investment of $100 per year
(i.e., for a growing plant), the replacement requirements would
gradually increase from $1 per year in the first year to $463 in
the fiftieth year, or from $1 per $100 of investment in the first
year to $6.01 in the tenth year to $8.16 in the twentieth and to
$9.27 in the fiftieth year.
In practical application, in other words, the annual replace-
ment requirement in the case of a plant of full growth all parts
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