Rockwell Automation Arena Packaging Users Guide - Manual (Page 92)

A RENA P ACKAGING T EMPLATE U SER ’ S G UIDE
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As the simulation run length and number of replications goes to infinity, the failures
generated by the failure stream will cause the equipment to be operational for
approximately the specified percent of total available operational time.
For example, suppose you entered an Expected Uptime of 93% and a Time to Repair of 5
minutes for a conveyor. At runtime, Arena Packaging would create a single random failure
stream for the conveyor. Each failure would have a duration of 5 minutes, and the times
between failures would be sampled from the distribution exponential (5*(93/7)) or expo-
nential (66.43 minutes).
If you ran the above model for a long time period (e.g., 30 days), then the following
equation will approximately be true:
Total Time Running/(Total Time Running + Total Time Failed) = .93
where the total running time is the total time the conveyor’s speed factor was greater than
zero (i.e., its belt was moving).
When a failure occurs, the equipment is stopped and its state is set to Failed. The variable
_FailureNumber for the equipment is set to 1. The downtime duration for each failure is
the Time to Repair. This duration can be adjusted by operator skill factors if repair opera-
tors are used. Refer to the section in Chapter 2 titled “Step 5: Experiment with complex
strategies” for more detail on modeling labor in the system.
Using reliability over a time span
In its strictest definition, reliability is the probability that a piece of equipment will not fail
over some operational time span (e.g., a day’s worth of operations or a month’s worth of
operations). This probability is derived theoretically using the equation
R = e- λt
where
R is the reliability, t is the time span, and λ is the failure rate.
Note that t and λ must be in the same time units (e.g., days and failures/day). Reliability is
a probability between 0 and 1.
E XAMPLE
Company XYZ collected failure data for a filler machine in its bottling line. The time span
for the data collection was six months of total processing time. During that six-month
period, the filler failed 10 times. The average downtime for a failure was 22 minutes.
What is the probability that the filler can run for one month of processing time without
failing?