Quality control charts for short or long runs without a training phase. Part 1. Performances in state of control and in the presence of outliers

Sometimes analytical laboratories receive requests with a small number of determinations and/or a small number of samples, or outside the typical scope of analytical services. As a result, they may not have historical data on the performance of analytical processes and/or appropriate reference materials. Under these conditions it is difficult or uneconomical to use traditional or classic quality control charts. This is the so-called start-up problem of these charts. The Q charts seem appropriate charts under these conditions because they do not need any prior training or study phase. The fundamentals and the algebraic expressions of Q charts for the mean (four cases) and for the variance (two cases) are offered. This experimental study of Q charts for individual measurements was done with data from quality control for the evaluation of mass fraction of Ni and Al₂O₃ in a laterite CRM by ICP-OES. The performance of these Q charts is discussed where the analytical process is in the state of statistical control and in the presence of outliers at the start-up. In the first situation performance of Q charts are quite satisfactory and they behave properly. When outliers are collected at the beginning, the deformation of some charts is evident or the charts become useless. Severe outliers will corrupt the parameter estimates and the subsequent plotted points, or the charts will become insensitive and useless. The practitioner should take extreme care to assure that the initial values are obtained in the state of statistical control to have adequate sensitivity to detect parameter shifts.