**1. Introduction**

The two salient tools of statistical process control (SPC) are memory and memory-less control charts. The memory-less control charts are most suitable for large shift, while the memory-control charts are used to monitor moderate and small shifts. The prominent form of memory-less control chart for location monitoring is the Shewhart *X* control chart. In general, control charts-irrespective of the magnitude they measure-operate in two phases: phase-I, the prospective stage from which the control limits are obtained; phase-II, where we monitor the process and correct the unnatural causes of variation whenever they occur (cf. [1]). In phase-I we estimate the control limits using the parameters of the process under study which, in reality, are seldom known. The amount of data employed in phase-I for estimating process parameters varies from one practitioner to the other. As a result, this variability affects the chart performance in the monitoring stage i.e., phase-II. (see for example [2–6]).

Furthermore, the amount of data employed in estimating the process parameters does a ffect the accuracy of the chart, as well as its limits. As we all know, the larger the sample size, the closer we are

to the parameter. Therefore, increasing the sample size used for estimating the parameters should be the remedy to this shortcoming, but there is a limit to which we can increase sample sizes in real-life situations. As a result, the Shewhart chart, like any other chart, loses its performance and credibility. The depth of the loss depends on the e fficacy of the parameter estimation and sample size employed in phase-I.

The presence of outlying/extreme values in the phase-I dataset can a ffect the performance of the control chart. The insu fficiency of the phase-I estimates could be a result of extreme sample points in the sample, and not necessarily the size of the sample (see [5,7]). The easiest remedy for the extreme values is to drop such a sample and pick another one, but this is not appropriate for small sample data. Therefore, there is a need to screen the extreme values to improve the overall performance of the control chart.

Over the years, researchers have studied di fferent types of robust outlier detection models in a series of control charts to enhance their performance. Examples include [8–12]. These outlier detectors require the data to be from normal distribution such as the Student-type and Grubbs-type detectors. However, for a non-normal dataset, the Tukey's and median absolute deviation (MAD) outlier detection models are more accurate and robust since they are independent of mean and standard deviation. (see [13–19]). SPC is widely applied and implemented in various sectors; health, industrial, manufacturing and every service-rendering sector. Control charts, however, are most applied in manufacturing industry, with semiconductors as a case study. Semiconductor manufacturing processes are prone to high chances of assignable cause of variations, due to machine breakdown, multiple products, re-entrant flows, batching processes etc. [20]. Researchers have employed SPC in solving these recurring challenges in this industry (see [21–24]). The proposed charts in this study are applied in photolithography, a semiconductor manufacturing process.

In this article, we study the effects of parameter estimation on the Shewhart *X* chart for normal and non-normal environments. We also study the effect of outliers on the reliability of the control charts and the process parameters are estimated. Furthermore, we propose non-parametric outlier detectors, namely: the robust Tukey and MAD outlier detection models in designing the basic control chart structure. A fair comparison between the two-outlier detection models is also made. We achieve all of these using average run length (ARL) and standard deviation run length (SDRL) as the performance measures.

The remainder of this article is as follows: the next Section entails the methodologies employed for the study; briefing the overview of the Shewhart *X* control chart when the parameters are known and unknown, alongside the performance measure properties adopted in this study; the variability in Shewhart chart performance due to phase-I estimation; a scenario for the presence of outliers in the design structure of Shewhart chart, and its e ffect; incorporating the Turkey and MAD outlier detection models in the design structure of the Shewhart chart as remedies for rectifying the presence of outliers; Section 3 gives a concise and precise description of the simulation results. In Section 4, a detailed comparison of the results is presented; while Section 5 provides an illustrative example with a real life dataset; finally a concluding remark and future recommendations are given in Section 6.
