Modeling Complex Systems and Their Variability

The Monte Carlo approach relies on data that describe the variation of elements within the system. It also connects the elements such that the result is an estimate of performance. For reliability modeling this is easiest to imagine for a series system.

For a system with two elements in series, a very simple reliability block diagram multiplies the expected reliability for each block to determine the system reliability value. Yet, it is possible to have both elements at the low end of the range of possible reliability values, or at the high end, or a mix. That is the value of the Monte Carlo approach.

For a simple series model with two elements, we can describe the reliability as a function of time for both elements using the Weibull function plus the range of uncertainty for the Weibull model. So, for example, at one year the reliability of the first element may range from 90% to 95% with a mean of 93%. Then we can randomly select a reliability value for each element from their respective distributions and then multiply to find the system reliability value.

Of course, the mean values provide an estimate of the estimated mean system value. If that is all you need then you do not need to use the Monte Carlo approach. If you want to estimate the range of system values that the system is likely to produce, or the distribution of possible system reliability values, then you can use the Monte Carlo approach.

When to Use Monte Carlo Techniques for Modeling

For two elements in a system it is possible to determine the system reliability mathematically by combining the two distributions, yet for a complex system with many variables impacting the system reliability of any one system, than a Monte Carlo approach may be an efficient solution.

A clear case in which the Monte Carlo approach works well is when there is a combination of environmental, user or usage, and component variables that impact the system performance. For example, if a portion of your products were to be in dry cold environment then they would exhibit a very different rate of corrosion-related failures then those in hot moist environments. Even if you only have rough percentages of units in different environments, that would allow the model to improve its ability to estimate the overall system reliability expectations.

Why to Use Monte Carlo Techniques

You need accurate system reliability information to make decisions. The Monte Carlo approach takes more data and a bit of work to create, yet it can provide the necessary accuracy when estimating system performance.

An added benefit of the approach is the need to gather and understand the variability that affects the system reliability performance. The initial model may have only crude estimates of the necessary variables, like using just hot and cold for temperature. Yet, it highlights the need to understand the temperature variability and its relation to system reliability though its impact on failure mechanisms. Thus, the team gathers two kinds of information: environmental temperature data that describe the distribution pattern of temperature in different regions plus the failure mechanism models that relate time to failure to a given temperature. Both help improve the overall system model.

Another benefit is the ability for the team to conduct ‘what if’ analysis at a finer granularity. Like a sensitivity analysis the model can help the team understand which set of variables and sources of variation has the greatest impact on system reliability. This is handy when working to achieve a consistent system reliability performance.

Bio:

Fred Schenkelberg is an experienced reliability engineering and management consultant with his firm FMS Reliability. His passion is working with teams to create cost-effective reliability programs that solve problems, create durable and reliable products, increase customer satisfaction, and reduce warranty costs. If you enjoyed this articles consider subscribing to the ongoing series at Accendo Reliability.