Information Technology Reference
In-Depth Information
Fig. 1. Reliability of rails with respect to all defects, grindable defects and non
grindable defects
The estimates of the propagation velocity will thus be multiplied by the
factor 0.2204.
Impact of grinding on the reliability
Let's now identify the hypothetical curve corresponding to the distribu-
tion of all de-fects under preventive grinding from two reliability functions
corresponding to grindable and non grindable defects. We use the follow-
ing relation between the distribution functions:
R
global
(
t
)
=
R
grindable
(
t
)
·
R
nongrindable
(
t
)
This relation is valid whenever a defect is either grindable
or non grindable, and if the random variables describing the occurrence of
this two defects are independent. It is supposed that grinding can extend the
lifetime of the rail. A total renewal of the rail is needed if a given cumulated
length has been replaced. Thus, as the end of life for the rail is defined by a
fixed number of removals carried out, we can state that grinding “rejuvenates”
the rail. This effect is used for the modelling, the formula for the virtual age
function
fvirtualage
(
t
)
has the following form:
fvirtualage
(
ti
)=
qgrindable
((1
−
p
)
·
[
Fgrindable
(
fvirtualage
(
t
i
))
−
Fgrindable
(
fvirtualage
(
t
i
−
1))] +
Fgrindable
(
fvirtualage
(
t
i
−
1)))