Self-starting X-bar control chart based on Six Sigma quality and sometimes pooling procedure

Self-starting control charts have been proposed in the literature to allow process monitoring when only a small amount of relevant data is available. In fact, self-starting charts are useful in monitoring a process quickly, without having to collect a sizable Phase I sample for estimating the in-control process parameters. In this paper, a new self-starting control charting procedure is proposed in which first an effective initial sample is chosen from the perspective of Six Sigma quality, then the successive sample means are either pooled or not pooled (sometimes pooling procedure) for computing next Q-statistics depending upon its signal. It is observed that the sample statistics obtained so from this in-control Phase I situation can serve as more efficient estimators of unknown parameters for Phase II monitoring. An example is considered to illustrate the construction of the proposed chart and to compare its performance with the existing ones.