The combined effect of serial dependency and measurement errors is known to negatively affect the statistical efficiency of any monitoring scheme. However, for the recently proposed homogenously weighted moving average (HWMA) scheme, the research that exists concerns independent and identically distributed observations and measurement errors only. Thus, in this paper, the HWMA scheme for monitoring the process mean under the effect of within-sample serial dependence with measurement errors is proposed for both constant and linearly increasing measurement system variance. Monte Carlo simulation is used to evaluate the run-length distribution of the proposed HWMA scheme. A mixed-s&m sampling strategy is incorporated to the HWMA scheme to reduce the negative effect of serial dependence and measurement errors and its performance is compared to the existing Shewhart scheme. An example is given to illustrate how to implement the proposed HWMA scheme for use in real-life applications.

Autocorrelation and measurement errors have a negative effect on the performance of any monitoring scheme; therefore, more efficient monitoring schemes are required to monitor such special processes. Hence, in this paper, the use of improved synthetic and runs-rules X̅ schemes with an embedded variable sample size and sampling interval (VSSI) approach to efficiently monitor the mean of a process under the combined effect of autocorrelation and measurement errors is proposed. These new monitoring schemes incorporate a linearly covariate error model with a constant standard deviation and a first-order autoregressive model to the variability of this special process in order to account for measurement errors and autocorrelation, respectively. Moreover, in order to evaluate the zero- and steady-state run-length properties of the proposed monitoring schemes, a dedicated Markov chain matrix that takes into account the following is constructed: (i) VSSI approach, (ii) improved charting regions design of the synthetic and runs-rules X̅ schemes, and (iii) the combined effect of autocorrelation and measurement errors. Also, the probability elements of the Markov chain matrix incorporate two special sampling methods that aid in the reduction of the negative effect of autocorrelation and measurement errors. A real life example is given to illustrate the implementation of the proposed monitoring schemes.

Distribution-free (or nonparametric) monitoring schemes are needed in industrial, chemical and biochemical processes or any other analytical non-industrial process when the assumption of normality fails to hold. The Mann-Whitney (MW) test is one of the most powerful tests used in the design of these types of monitoring schemes. This test is equivalent to the Wilcoxon rank-sum (WRS) test. In this paper, we propose a new distribution-free generally weighted moving average (GWMA) monitoring scheme based on the WRS statistic. The performance of the proposed scheme is investigated using the average run-length, the standard deviation of the run-length, percentile of the run-length and some characteristics of the quality loss function through extensive simulation. The proposed scheme is compared with the existing parametric and nonparametric GWMA monitoring schemes and other well-known control schemes. The effect of the estimated design parameters as well as the effect of the Phase I sample size on the Phase II performance of the new monitoring scheme are also investigated. The results show that the proposed scheme presents better and attractive mean shifts detection properties, and therefore outperforms the existing monitoring schemes in many situations. Moreover, it requires a reasonable number of Phase I observations to guarantee stability and accuracy in the Phase II performance.