Optimizing Shewhart Charts in Parallel Production Lines

Abstract

I describe a methodology for optimizing n Shewhart x-charts operating on parallel production lines in a factory. The goal is to maximize the factory-wide probability of detecting an out-of-control condition subject to a constraint on the expected number of false signals. I use non-linear programming to appropriately set the x-charts’ control limits incorporating information about the probability of each production line going out-of-control. Using this approach, factories can set their quality control systems to optimally detect out-of-control conditions. Given some distributional assumptions, I also present a one-dimensional optimization methodology that allows for the efficient optimization of very large factories.