Maintenance Optimization Based on Three-Stage Failure Process under Performance-Based Contracting

Table 2

Notations used in this paper.

Notations	Descriptions
Xn	Random variable representing the duration of the nth stage of the system, n = 1, 2, 3
fXn	Probability density function of Xn, n = 1, 2, 3
FXn	Cumulative distribution function of Xn, n = 1, 2, 3
t	Inspection interval
Tp	Time to preventive replacement
Tf	Time to failure
Cins	Cost per inspection
Cp	Cost per preventive renewal
Cf	Cost per failure renewal
Dp	Downtime per preventive renewal
Df	Downtime per failure renewal
EC	Expected cost in a renewal cycle
Tdown	Expected downtime in a renewal cycle
Tup	Expected uptime in a renewal cycle
EC(t)	Expected cost rate per unit time
A(t)	Expected average availability
ER(t)	Expected revenue rate per unit time
EP(t)	Expected profit rate per unit time
Rmax	The upper limit of revenue