AbstractIn Phase I analysis, data are used retrospectively to check process stability and to establish limits that will be later used in Phase II for the prospective monitoring. It is clear that the results of Phase I analysis are of crucial importance for the right interpretation of control chart during Phase II. Many of recent papers devoted to Phase I analysis discuss the accuracy of limits found from Phase I data and the impact of these limits' accuracy on the probability of Type I or II errors. Although this is an interesting issue, we think that its importance is overestimated because there is another problem that escapes the attention of many researchers. This is the problem of the order of points in Phase I or the problem of data randomness. We review the role of data succession on right application of simple Shewhart control chart and hope to draw the attention of the statistical community to this problem because it may affect not only Phase I issues but also many other sides of statistical process control. Besides, we suggest a new test for data randomness and give a preliminary estimate of how it works. We also state our thoughts about the possible causes of neglecting the data order and suppose ideas about future researches.