Estimating the distribution and variance of time to produce a fixed lot size given deterministic processing times and random downtimes

Managing production throughput variability is necessary to reduce system costs and improve throughput. Critical in this management is predicting how system changes, like reduced repair times, will change throughput variability. Many manufacturing plants produce products in fixed lot sizes to meet production targets which causes system variability to be manifested as variability in the time to produce the lot. We derive analytical approximations of the density function and variance of the time to produce a fixed lotsize on a single workstation with deterministic processing times and random downtimes. These expressions can be applied to larger production systems, by modelling the system as a single workstation with parameters that approximate the system's output. This result quantifies how workstation failures, repair times, and speed affect the density and variance of time to produce a fixed lotsize. The density function also generates a cycle time distribution when the lost size is one. This is useful in discrete event simulation.