Sensitivity study of the CUSUM control chart with an economic model

Economic control chart designs have not been universally implemented in industry for several reasons. For example, the parameters are too numerous and are often difficult to estimate accurately. A possible solution to these problems involves performing a sensitivity analysis of the inputs to determine which parameters are significant and how parameter misspecification impacts the results. Using two-level fractional factorial designs, the authors identify highly significant parameters in the Lorenzen and Vance economic control chart model under a Cumulative Sum condition. The response variables examined include the expected cost per time unit and the decision variables sample size, sampling interval, control chart decision interval and reference value. Verification and misspecification analysis support our conclusions with respect to the expected cost per time unit response variable. The sensitivity study highlights the importance of experiment design in understanding the underlying behavior of the model inputs. Results of testing several scenarios indicate that a small subset of model inputs actually drive the cost response, which should make industrial implementation an easier task. The search for significant inputs can be aided by a study of the relative magnitudes of some factors such as the assignable cause rate and the ratio of out-of-control to in-control quality costs.