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.

Many real-world processes generate autocorrelated and/or Weibull data. In such cases, the independence and/or normality assumptions underlying the Shewhart and EWMA control charts are invalid. Although data transformations exist, such tools would not normally be understood or employed by naive practitioners. Thus, the question arises, “What are the effects on robustness whenever these charts are used in such applications?” Consequently, this paper examines and compares the performance of these two control charts when the problem (the model) is subjected to autocorrelated and/or Weibull data. A variety of conditions are investigated related to the magnitudes of various parameters related to the process shift, the autocorrelation coefficient and the Weibull shape parameter. Results indicate that the EWMA chart outperforms the Shewhart in 62% of the cases, particularly those cases with low to moderate autocorrelation effects. The Shewhart chart outperforms the EWMA chart in 35% of the cases, particularly those cases with high autocorrelation and zero or high process shift effects.