The new synthetic and runs-rules schemes to monitor the process mean of autocorrelated observations with measurement errors

The use of the 2-of-(H + 1) runs-rules and synthetic schemes to improve the performance of the currently available X¯ schemes in monitoring the process mean under the combined effect of measurement errors and autocorrelation is proposed. To maximize the detection ability of the 2-of-(H + 1) runs-rules and synthetic schemes, we implement the modified side-sensitive (MSS) design approach for the charting regions as we show it yields the best possible performance out of all the available designs. These new monitoring schemes incorporate the additive model with a constant standard deviation and a first-order autoregressive model to the computation of the control limits in order to account for measurement errors and autocorrelation, respectively. Moreover, to construct a dedicated Markov chain matrix, the abovementioned models and some sampling methods are incorporated into the values of probability elements which are then used to derive closed-form expressions for the zero- and steady-state run-length distribution. A real life example is used to illustrate the practical implementation of the proposed schemes.