Modeling Dynamic Conveyor Buffer Sizes before Capital Expenditure Commitments
Dynamic conveyor buffer sizing uses empirical breakdown distributions in discrete event models to establish capital allocation bounds before hardware purchase.
Stochastic Failure Distribution
Meaning
A statistical model describes the variable times between equipment breakdowns and the duration of those interruptions using probability distributions rather than fixed values. Incorporating a stochastic failure distribution into line simulations allows designers to create more realistic models of production behavior. This approach accounts for the fact that machine breakdowns are not scheduled and can occur in clusters, which is essential for sizing line buffers.
Mathematical Fit
The distribution is typically modeled using exponential, Weibull, or log-normal functions based on historical maintenance data from similar equipment. While an exponential model assumes a constant failure rate, a Weibull distribution can account for the higher failure rates that occur during a machine’s start-up phase or as it approaches the end of its wear life.
Operational Value
Using this statistical approach helps prevent the under-sizing of accumulation systems that occurs when designers rely on average up-time figures. If a line is designed based only on the average time between failures, it will frequently experience starvation or blockage because it cannot handle the long-duration breakdowns that the stochastic failure distribution predicts, leaving the plant unable to meet its daily targets.
Validation Method
Validating the failure model requires comparing the simulated line output with the actual data collected during a multi-week production run. If the actual failure patterns are different from the distribution used in the model, the simulation will either over-predict or under-predict the line’s capacity. Ensuring that the failure model matches reality is a prerequisite for using the simulation to justify major capital expenditures.