Robust optimisation for simultaneous process mean, process tolerance and product specification determination

Abstract

Conventionally, process mean determination is performed prior to process tolerance design, independent of product design, such as product specification. In addition, previous studies considered the production costs and quality losses as deterministic values in mean and tolerance decisions. This study foregoes the assumptions of deterministic value and independent determination. For further cost reduction and quality improvement, process mean, process tolerance and product specification are simultaneously determined as controllable factors under the assumption that production costs and quality losses are random variables with given probabilistic distributions. At first, the various levels of mean, tolerance and specification are combined in accordance with the Box–Behnken experimental matrix, and used as inputs for a Monte Carlo simulation to obtain the simulated outputs. Then, these outputs are transferred to the total cost, which includes quality loss, production cost and penalty cost. Mean, tolerance and specification are treated as controllable factors, while total cost is a response value of interest. The design problem is analysed statistically using response surface methodology (RSM) in order to find the response function, which in turn is used as an objective function and optimised through mathematical programming (MP). A bicurve lens design is employed to demonstrate the proposed approach.