The variable sample size t control chart for monitoring short production runs

Starting the online monitoring of a quality characteristic by means of a control chart at the beginning of a short production run is often a challenging issue for quality practitioners: in fact, the frequent absence of preliminary information prevents from getting a precise estimate of the characteristic mean and standard deviation. Furthermore, for short runs having a finite rolling horizon, the number of inspections scheduled within the run can be too small to get sufficient samples allowing the phase I implementation of the chart to be completed. Recently, t control charts have been proposed as efficient means to overcome this problem because they do not need any phase I tentative control limits definition or preliminary process knowledge. In this paper, a variable sample size (VSS) version of the t chart is proposed. Adaptive control charts have been implemented with success in long runs: here, the performance of the variable sample size strategy is investigated for a chart used in a short run. The statistical performance of the VSS t chart is compared with the one of the fixed-parameter (FP) t chart for both scenarios of fixed and unknown shift size, with the latter situation being frequent in short-run manufacturing environments. An extensive numerical investigation reveals the potential benefits of the proposed chart. When the statistical design is optimized with respect to a fixed value of the shift size delta, the VSS t chart has a better statistical performance than the FP t chart for moderate to large values of delta. Conversely, for the unknown shift size condition, the VSS t chart always outperforms the FP t chart for in-control average sample sizes ASS(0) > 7. An illustrative example shows the implementation of the VSS during the production of a finite lot of mechanical parts.