The economic performance of the Shewhart t chart

In the production of small batches of customized parts, high flexibility and frequent switching of production fromone product variant to another could not allow for the implementation of a control chart to monitor the process.In fact, when a short-run production should be started, the distribution parameters of the quality characteristicsto be monitored are frequently unknown and the production run is too short to get sufficient Phase I samples. Toovercome this problem, the statistical properties of Shewhart t charts monitoring a short production run have beenrecently discussed in literature. In this paper, we investigate their economic performance: the SPC inspection costoptimization is constrained by the manufacturing and the inspection activities configuration. The decision variablesof the problem include the chart design parameters and the size of batches of parts to be worked and released tothe local inspection area. A numerical analysis aimed at evaluating the economic performance of the Shewhart t chartvs the Shewhart ¯X chart with known parameters has been performed. The expected economic loss associated withthe implementation of the Shewhart t chart is acceptable with respect to the ‘ideal’ condition of the control chartwith known parameters when the cost optimization is achieved without a statistical constraint limiting the numberof expected false alarms. Finally, the effect of an erroneous initial set-up on the correctness of the inspection costestimation has been investigated.