A number-between-events control chart for monitoring finite horizon production processes

In this paper, we present a number-between-events (NBE) control chart for monitoring the fraction nonconforming in finite horizon production (FHP) processes and related specific performance measures. When monitoring fractions nonconforming in FHP processes, the common binomial p$p$-chart has two crucial limitations: the underlying distributional assumptions are violated when dealing with low-volume production and a scarce efficiency in the case of processes characterized by a low fraction nonconforming. Thus, an efficient monitoring of FHP processes requires the selection of the correct underlying statistical model: in this case, a distribution from the hypergeometric family of discrete statistical distributions. An efficient statistical monitoring of processes with low fractions nonconforming can be achieved by means of discrete time-between-events (TBE) control charts, which count the number of units up to the appearance of a fixed number of nonconforming units in the sample. Here, we present a discrete TBE-chart, denoted as NBE-chart, based on the negative hypergeometric distribution that meets numerous requirements of efficient monitoring of FHP processes. The proposed control chart can be conveniently used for both low-volume and mass production in processes with frequent changeovers.