Rockwell Automation Arena Packaging Users Guide - Manual (Page 94)

A RENA P ACKAGING T EMPLATE U SER ’ S G UIDE
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When the simulation begins, Arena Packaging first calculates the theoretical failure rate 8
for the piece of equipment using the values entered for the Time Span and Reliability for
Time Span operands:
R = e- λt
Therefore, λ = -1 *(LN(Reliability for Time Span) / (Time Span)).
Arena Packaging then creates a single random failure stream for the piece of equipment,
whereby the time between failure arrivals is sampled from the stochastic distribution
exponential (1/
λ).
For machines and palletizers, the time between failures is interpreted as the processing
time between failures (i.e., time that the machine or palletizer is running and not starved).
For conveyors, the time between failures is interpreted as the running time between fail-
ures (i.e., time tht the conveoyr’s belt is actually moving).
For the XYZ example, the failure rate 8 of the filler machine would be calculated as λ = -1 *
(LN(.189)/30) = 0.0555 failures/day. Thus, the time between failure arrivals would be
sampled from the distribution exponential (1/0.0555) or exponential (18 days).
When a failure occurs, the equipment is stopped and its state is set to Failed. The down-
time duration for each failure is the Time to Repair. If a random distribution is used, then
the Time to Repair is sampled from that distribution at the beginning of each failure. The
Time to Repair can also be adjusted by operator skill factors if repair operators are used.
Refer to the section “Step 5 • Experiment with complex strategies” on page 15 for more
detail on modeling labor in the system.
Using individual failure streams
The third option for modeling the downtime of a piece of equipment is to specify your
own individual failure streams. This detailed way of describing equipment reliability is
useful when:
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A failure process must be modeled with different arrival rates or downtime distribu-
tions than what are provided in the first two options.
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You have several types of failures for a piece of equipment (e.g., rare, frequent, electri-
cal, mechanical, etc.), and each type has unique failure rate and downtime distributions.
If labor constraints are incorporated into the model, different sets of repair operators
might also be required for the different types.
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You have machine or palletizer failures where the arrival process of the failures is
based on unit counts (i.e., throughput) and not time.
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You have time-based failures where the time between failures needs to be specified as
calendar time, not processing or running time.