Replacement first and last for a parallel system with constant and random units

This paper observes optimal replacement times for a parallel system with n units, when it is operating for successive jobs with a random working cycle. The classical approach of “whichever occurs first” and the newly proposed approach of “whichever occurs last” are respectively employed for replacements scheduled at time T and at working cycle Y , whose policies are called replacement first and replacement last. Two cases when the number of units for this parallel system is a given constant value and a random variable with estimated distribution are considered into modelings. We obtain their expected replacement cost rates and optimal solutions analytically. Further, comparisons of replacement first and replacement last are described in detail to determine which policy could save more replacement cost rate.