Duncan's model for X-control charts: sensitivity analysis to input parameters

Duncan’s model is a well-known procedure to build a control chart with specific reference to the production process it has to be applied to. Although many papers report true applications proving the procedure’s noteworthy economic advantages over control charts set purely on the basis of standard statistical criteria, this method is often perceived only as an academic exercise. Perhaps the greater barrier preventing its practical application stems from the difficulty in making cost items explicit. In this paper a sensitivity analysis is proposed for misspecification in the cost parameters for optimal solutions of Duncan’s model. While similar contributions published in the literature perform sensitivity analyses with a one-factor-at-a-time scheme, the original contribution of this paper is represented by the focus given on interactions among changes in values of different cost parameters. The results obtained here denote that all factors significantly affect optimal solutions through quite complicated interactions. This should not, in our opinion, discourage the implementation of Duncan’s model, pointing conversely to its robust versions, already available in the current literature.