Quality control charts for short or long runs without a training phase. Part 2. Performances in the presence of a persistent systematic error and simultaneous small shifts in the mean and the variance

Abstract

Sometimes, analytical laboratories receive requests with a small number of determinations and/or samples or outside the typical scope of analytical services. As a result, they may not have historical data on the performance of the required analytical procedures and/or appropriate reference materials. Under these conditions, it is difficult or uneconomical to use traditional quality control charts. This is the so-called start-up problem of these charts. Quesenberry’s Q charts are appropriate in these situations because they do not require a prior training phase. In the first part of this series of publications, the fundamentals and the algebraic expressions of the Q charts were presented for the individual measurements for the mean (four cases) and for the variance (two cases). This experimental study was carried out with data from quality control of mass fractions of Co in a serpentinite CRM and SiO₂ in a laterite CRM, by ICP-OES. The performance of Q charts is discussed in two situations: when the analytical process showed a clear systematic error from the beginning and when small shifts in mean and variance occurred simultaneously. In the first situation, performances of Q charts for the mean depended on the case: two of them were very sensitive even in the short run and the other two were insensitive and useless. In the second situation, the Q charts showed delayed alarms, but with a comparable behavior to the chart for individual measurements and the moving range of two. EWMA charts associated to Q charts were an excellent complement.