Fuzzy cause selecting control chart for monitoring multistage processes

Many processes contain several dependent steps. If a change happens in a stage it will affect the successive quality characteristics which referred to as cascade property. Hence, to monitor the quality characteristics in each stage we have to use a procedure to omit the effect of preceding stages. Therefore, cause selecting control charts are suggested for this purpose. To the best of our knowledge, in all of the papers in the area of monitoring multistage processes with control charts, it is assumed that the quality characteristics are crisp. However, in some applications, the quality characteristics may be imprecise and they can be expressed by fuzzy numbers. In this paper, we specifically assume that there is a two-stage process with fuzzy quality characteristic in the second stage. Note that the fuzzy quality characteristic represents two kinds of uncertainty including randomness and fuzziness. Then, we propose a fuzzy cause selecting control chart to monitor the process in phase I. The performance of the proposed method is evaluated using simulation studies in terms of power. The use of the proposed method is shown step by step through a numerical example. The results show the satisfactory performance of the proposed control chart.