Control charts are among the indispensable tools for monitoring process performance in various industries. When parameter estimation is needed to design these charts, their performance is affected due to parameter estimation errors. To overcome this problem, in the past, researchers have evaluated the performance of control charts and designed them in terms of the expectation of the realized in-control (IC) average run length (𝐶𝐴𝑅𝐿0). But, as pointed recently, this solution does not account for what is known as the practitioner-to-practitioner variability (i.e., the variability of 𝐶𝐴𝑅𝐿0). So, a recent idea emerged where control chart performance is measured by the probability of the 𝐶𝐴𝑅𝐿0 being greater than a specified value - which must be close to the nominal desired one. This is called the Exceedance Probability Criterion (EPC). To apply the EPC, the cumulative distribution function (c.d.f.) of the 𝐶𝐴𝑅𝐿0 is required. However, for the most well-known control chart, named the two-sided Shewhart Xbar (or simply X) Chart (under normality assumption), the mathematical c.d.f. expression of the 𝐶𝐴𝑅𝐿0 is not available in the literature. As a contribution in this respect, the present work presents the derivation of the exact c.d.f. expression of the 𝐶𝐴𝑅𝐿0 for three cases of parameters estimation: (1) when both the process mean and standard deviation are unknown, (2) when only the mean is unknown and (3) when only the standard deviation is unknown. Using these key results, it was possible to calculate the exact minimum number of initial (Phase I) samples (m) that guarantees a desired in-control performance in terms of the EPC. These results show that m can be prohibitively large (such as 3.000 samples). As a solution to this problem, two new equations are derived here to adjust the control limits to guarantee a desired in-control performance in terms of the EPC for any given value of m. The advantage of these equations (compared to the existing adjustments methods) is that one provides exact results and the other one does not require too many computational resources to perform the calculations. A further study about the impact of these adjustments on the out-of-control (OOC) performance provides useful tables to decide the appropriate amount of data and the adjustments that corresponds to a user preferred tradeoff between the IC and OOC performances of the chart. Practical recommendations for using these findings are also provided in this research work.