The Economic Performance of a CUSUM<i>t</i>Control Chart for Monitoring Short Production Runs

Abstract

At the start of a production run, the parameters of the distribution of a quality characteristic are frequently unknown. If the quality characteristic should by monitored on-line by means of a control chart and the production run length is too short, then it is impossible to get a sufficient Phase I number of samples allowing for the correct estimation of parameters and the evaluation of the chart’s tentative limits. To overcome this problem, in this paper the economic design of a CUSUM t control chart that is able to monitor short production runs without the need of Phase I samples is proposed. A numerical analysis aimed at comparing the economic performance of the CUSUM t chart vs. the CUSUM X̄ chart with known parameters has been performed on a benchmark of scenarios available from literature. The obtained results show that the expected economic loss associated to the implementation of the CUSUM t chart is quite negligible with respect to the control chart with known parameters. An illustrative example is provided to show the CUSUM t chart’s implementation.