Methodology

There are several different version of compute life tables for identifying and studying bridge maintenance patterns:

Data

Item	Description	Version 1 (O'Brien Chin)	Version 2
Study window	To observe the behavior of the bridges as they pass through this window	Established as five year study window 2013 - 2017	Established as five year multiple study windows from 1992 to 2020, with an option of overlapping study windows
$leave(x)$	The number of bridges that leave the study at age $x$	Computed similar to the described definition, similar to mortality rate	New approach use the concept of conditional probability of dying instead of mortality rate, change in notation used as $D_x$
$exposures(x)$	The number of bridges in the study at age $x$	Assumes that a bridge be a part of the study for the entire year for it to contribute ot the exposure for that year	Exposures are computed similar to the previous method
Hazard rate $h(x)$	Hazard rate age $x$. See equation 1	Computed as $leaves(x) \over exposure(x)$	$D_x \over P_x + (0.5 * D_x)$
$S(x)$	Survival rate age $x$. See equation 2	Computed as $S(x) = 1 - h(x)$	Computed as $P_x = 1 - Q_x$
$F(x)$	The mortality rate (or cumulative probability of failure) of bridges exposed at age 1 before reaching age $x$	$1 - P_x$	Conditional probability of death $q_x = (D_x / (P_x + (0.5 * D_x)))$
$_yP_1$	Probability of survival at age $y$ for the next year. See Equation 5	This version can compute the probability of survival for next 5 years.	Although, this method is so far not implemented, the version can implement next 5 years of probability