Classical monitoring schemes are typically designed under the assumption of known process parameters, perfect measurements and normality. In real-life applications, these assumptions are often violated. Thus, their Phase II performances are negatively affected by both measurement errors and parameter estimation. In this paper, the performance of the homogenously weighted moving average (HWMA) scheme is investigated under the assumption of unknown process parameters with and without measurement errors using the characteristics of the run-length distribution through intensive simulations. The negative effect of measurement errors is reduced using multiple measurements sampling strategy. The effects of the Phase I sample size on the Phase II performance as well as the robustness to non-normality of the HWMA scheme are also investigated. Moreover, it is found that the negative effect of the measurement errors is higher as the smoothing parameter increases and the larger the Phase I sample size, the smaller the effect of measurement errors. Moreover, the Phase II performance of the HWMA ̅ scheme is compared with the corresponding memory-type monitoring schemes under the effect of both parameter estimation and measurement errors. An illustrative example is given to demonstrate the implementation in real-life applications.