DESIGNING ADAPTIVE CONTROL CHARTS WITH ADDITIONAL SAMPLING BETWEEN FIXED TIMES USING MARKOV CHAIN APPROACH

Many industrial products are produced by several different process steps and not just one process step. In each step, one or more quality characteristics of interest may be monitored according to their operation sequences. It implies that in multistage processes consisting of serial value-added manufacturing operations, a parameter shift in any process variable may affect some or all of the measures in the downstream stages but none of the measures preceding it. This property of multistage processes is referred to as the cascade. Cause-selecting control charts are effectively applied to multistage processes for monitoring and detecting shifts. Due to the existence of cascade property, the underlying relationship among stages should be considered and the outgoing quality characteristic must be monitored only after the effect of incoming quality variables has been fully removed. In this paper, an adaptive monitoring procedure for a two-stage process is proposed. In the proposed control charts, extra samples are taken in addition to the samples taken regularly at fixed sampling intervals. These additional samples are taken in case the process is prone to out-of-control situations. The adjusted average time to signal, calculated with the aid of Markov chain approach with 16 transient states, is used as the performance criterion to assess the detect-ability of the proposed control charts. The results clearly reveal that the proposed monitoring scheme outperforms both the control chart with fixed sampling interval and the one with variable sampling interval while detecting various shifts is under consideration. The superiority is of paramount importance and it is strongly recommended to apply the proposed monitoring schemes instead of its existing counterparts in the literature. Finally, the proper statistical design of the proposed control charts has been thoroughly addressed and discussed which helps engineers to identify shifts more quickly and implement corrective actions in a timely manner.