SPCQCharts for Start-Up Processes and Short or Long Runs

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Abstract
Classical control charts are designed for processes where data to estimate the process parameters and compute the control limits are available before a production run. For many processes, especially in a job-shop setting, production runs are not necessarily long and charting techniques are required that do not depend upon knowing the process parameters in advance of the run. It is desirable to begin charting at or very near the beginning of the run in these cases. We present here the needed formulas so that charts for both the process mean and variance can be maintained from the start of production, whether or not prior information for estimating the parameters is available. These Q charts are all plotted in a standardized normal scale, and therefore permit the plotting of different statistics on the same chart. This will sometimes permit savings in the chart management program.