The use of length-biased distributions in statistical monitoring

Statistical process monitoring (SPM) has been used extensively recently in order to assure the quality of the output of industrial processes. Techniques of SPM have been efficiently applied during the last two decades in non‐industrial processes. A field of application with great interest is public health monitoring, where a pitfall with which we have to deal is the fact that available samples are not random in all cases. In the majority of cases, we monitor measurements derived from patient admissions to a hospital against control limits that were calculated using a sample of data taken from an epidemiological survey. In this work, we bridge the gap of a change in the sampling scheme from Phase I to Phase II, studying the case where the sampling during Phase II is biased. We present the appropriate methodology and then apply extensive numerical simulation in order to explore the performance of the proposed methodology, for measurements following various asymmetrical distributions. As the simulations show, the proposed methodology has a significantly better performance than the standard procedure.