On the implementation of the Shewhart sign control chart for low-volume production

Today, many companies use job production to produce small batches of work output according to customised specifications required by customers. With job production, the quantity of parts to be produced is finite and can be limited to a few thousands or hundreds (low-volume production). Usually, job production requires high-quality standards. When 100% sampling is not possible, online monitoring is a viable solution to immediately start process quality control. However, knowledge about the process distribution is frequently unavailable. Recently, it has been shown that the distribution-free Shewhart sign control chart is an efficient means to monitor processes performing high-volume production within a finite production horizon. In this paper, we reconsider the definition of the Shewhart sign chart statistic when the population size is small and we propose an approach that extends its implementation to finite batch sizes of work to be produced. Tables presenting the statistical properties of the Shewhart sign control chart for low-volume production are shown and commented. An illustrative example is discussed on a simulated data-set.