Optimum Maintenance Intervals in RCM++
Preventive maintenance can yield significant cost
benefits by increasing the availability of a system and
reducing the total maintenance costs. The question of how often the task
should be
performed, however, is important to consider. If the preventive maintenance interval is too
short, then the maintenance costs associated with
preventive maintenance can be too high. If, on the other
hand, the interval is too long, then the costs
associated with corrective maintenance can be too high.
RCM++ provides
calculations to help determine the
optimum maintenance interval, based on the
probability of occurrence of a failure event and the
costs of performing different types of maintenance. In
this article we will provide the theory behind this
utility
and give an example that illustrates its application
in the software.
Introduction
In order for preventive maintenance to be beneficial,
the failure rate of the
system must increase over time and the cost of the
planned preventive maintenance must be less than the
cost of the unplanned corrective maintenance. If both of
those conditions are met, then the preventive maintenance
should be performed. However, the time interval for
performing preventive maintenance should be such that
the total maintenance costs are minimized, as shown in Figure 1. In order to do that, the time interval
that minimizes the maintenance cost function must be
found.
Figure 1: Cost vs. Time
The maintenance cost per unit time function is given
by:
where:
 R(t) is the reliability at time
t.
 C_{P} is the preventive maintenance
cost per incident (planned maintenance).
 C_{U} is the corrective maintenance
cost per incident (unplanned maintenance).
The optimum replacement time interval, t, is the
time that minimizes CPUT(t). This can be found by solving for
t such that:
or by solving for a time, t,
that satisfies:
For more information on the
maintenance cost per unit time equation you can read
Preventive Maintenance and the Cost Per Unit Time
Equation from Issue 96 of the Reliability HotWire.
Application
Imagine that we are engineers in an automotive
company and we are responsible for the maintenance of
the assembly line. Recently, we’ve focused our efforts on
the induction hardening process for drive shafts. Figure 2 shows the FMEA
for this
process.
Figure
2: FMEA of Induction Hardening Process
One
of the controls that we have identified is a preventive
maintenance task on the induction hardening machines. Using past data, we have determined that
the machine's probability of
failure follows a Weibull distribution
with a beta of 3 and an eta of 800 hours, as shown in Figure 3.
Figure 3: Probability of
Failure of the
Hardening Machine
Figure 4 shows the
maintenance costs associated with the corrective
maintenance of the machine. The typical task duration
for repairing the machine is 5 hours. However, given that when the machine
fails unexpectedly there is a delay for the repair crew
to arrive and the spare parts to be obtained, there is a total downtime of
7.7 hours per incident. Since the cost per hour of downtime is
$1,000, this translates to a cost of downtime of $7,700
per unexpected failure. With the other cost inputs,
including the materials cost of $200 per incident and
the calculated total labor cost of $250 (5 hours for the
task multiplied by the labor rate of $50 per hour), the
total cost per corrective maintenance incident is equal
to $8,150.00.
Figure
4: Corrective Maintenance Costs
Using the probability of failure of the machine and
the associated corrective maintenance costs, we can run
a simulation to determine the average availability of the
machine for one year of operation (or 4,160 hours, given
that the machine operates for 16 hours a day, 5 days
a week) with a "run to failure" maintenance strategy . The
average availability is 99.01% and the total operating
cost is $43,463.95, as shown in Figure 5. These figures
reflect the availability and cost
assuming that no preventive maintenance is performed.
Figure 5: Calculated Average
Availability and Total Operating Cost for Corrective
Maintenance Only (no Preventive Maintenance)
As mentioned above, we have determined that preventive
maintenance should be performed on the hardening
machine. We now need to decide how often the preventive maintenance
should be
scheduled. As we’ve seen, given the corrective and
preventive maintenance costs and the probability of
failure, we can find a time interval that minimizes the
total cost function. This task can be performed
easily in RCM++.
Figure 6 shows the costs associated
with the preventive maintenance. Since
preventive maintenance is a planned task, the total
duration of the incident is considerably lower compared
to the corrective maintenance task. As a result, the
downtime cost and the total cost per incident will also be lower.
Figure 6: Preventive Maintenance
Costs
Now that we have determined the
maintenance costs, we can calculate the optimum interval
for performing the preventive maintenance.
Figure 7 shows that the optimum interval is found to be
468.984 hours. RCM++ gives us the option to set this as
the assigned interval and use it in our calculations,
set it as a proposed interval in order to keep it as a
record without using it, or not use it at all. In this
case, we will set it as the proposed interval.
Figure 7: Calculation of
Optimum Maintenance Interval
For the actual assigned interval, we choose to round
the calculated figure to 470 hours. Using this maintenance interval, we can run a simulation
again to calculate the average availability and total
operating cost for a year of operation. As we can see in
Figure 8, the average availability from implementing the
preventive maintenance strategy is calculated as
99.36% and the total operating cost $29,390.25. So we
can see that by using the optimum maintenance interval
to perform preventive maintenance, the availability is
increased (99.36% compared to 99.01%) and the operating
cost is reduced ($29,390.25 compared to $43,463.95).
Figure 8: Calculated
Average
Availability and Total Operating Cost for Preventive
Maintenance Strategy with Optimum Maintenance Interval
