Your material handling system serves as oxygen of your business, so you want to do everything in your disposal to minimize downtime. The best way to increase system uptime is with a good preventative maintenance plan. As an engineer, you may have come across maintenance/performing repairs on Material Handling Systems such as Autonomous Vehicles, Industrial Robots, Conveyor Belts, or Machine Cells. Additionally, you probably have randomly generated demand, created inter-arrival rate of shipments, or simulated processing time in different machines etc. In this simulation study, I am going to estimate reliability of a material handling module of a warehouse over a period of time relevant to the system. The Weibull distribution is most commonly employed to determine reliability function.
Estimate System Reliability From Monte Carlo Simulation
A continuous distribution to plot a model fit from the failure rate of the system is created from a Monte Carlo simulation of 7000 trials. The idea behind Monte Carlo simulation is the generation of random events in a computer model, and this generation is repeated many times and counted for occurrence of a specific condition. The Monte Carlo simulation allows us to consider various aspects of system characteristics which cannot be easily captured by analytical methods such as K-out-of-N systems, redundancies, fault trees, repair and maintenance for components.
Furthermore, the reliability analysis from the Weibull distribution provides the information needed for identifying failures, troubleshooting, scheduling periodic maintenance and inspections. The restrictive modeling assumptions that had to be introduced to fit the models to available solutions, is thus avoided.
A series-parallel system of machines is considered here, each working in parallel and connected serially. To determine failure or Mean Time To Failure (MTTF) to be precise, consider each machine type to have k out of n system. Given that there are n machines in a machine type, the entire system fails when k of those n machines fail at any time. The simulation demonstrated here has 2 Warehouse Management Servers (k1), 3 Autonomous Guided Vehicles (k2), and 2 Robotic Palletizers.
Reliability Block Diagram
WMS – 2 Warehouse Management Servers in parallel
AGV – 3 Autonomous Guided Vehicles in parallel
RP – 2 Robotic Palletizers in parallel
MC – Machining Cell
As you can see in the block diagram, all individual have some sort of redundancy. The failure rate of the AGV depends on the failure of WMS components, similar dependency applies to two Palletizers and Machine Cell.
The failure rate of the above components was formulated as:
- manufacturer provided reliability data. As evident, the failure rate almost doubles every 180 days from WMS.
The failure test runs for each day for 600 days. Each sub-system (components) should operate until it fails. Once it fails, it remains in failed status. The time that each component fails is recorded in the spreadsheet.
The cut sets are as follows:
- {WMS1, WMS2}
- {AGV1, AGV2, AGV3}
- {RP1, RP2}
- {MC}
Monte Carlo simulation of the system was conducted using Excel and the number of failures during 7000 trials was 990. The mean time to failure or MTTF of the system was 563 days. Look at the chart below, the probability of failure of the system converged to 14.15% after 7000 trials and it can be reasonably assumed that it will remain around 14.15% over a long period of time. The probability of failure is 0.1415 and was accurate within 3% after 1600 trials.
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