Group inspection of dependent binary processes

Abstract

We consider serially dependent binary processes, how they occur in several fields of practice. If such a process cannot be monitored continuously, because of process speed for instance, then one can analyze connected segments instead, where two successive segments have a sufficiently large time-lag. Nevertheless, the serial dependence has to be considered at least within the segments, i.e. the distribution of the segment sums is not binomial anymore. We propose the Markov binomial distribution to approximate the true distribution of the segment sums. Based on this distribution, we develop a Markov np chart and a Markov exponentially weighted moving average (EWMA) chart. We show how average run lengths (ARLs) can be computed exactly for both types of chart. Based on such ARL computations, we derive recommendations for chart design and investigate the out-of-control performance. A real-data example illustrates the application of these charts in practice.

EWMA control charts for monitoring binary processes with applications to medical diagnosis data

“…), Knoth and Schmid 24 (AR processes), and by Schipper and Schmid 25 (GARCH processes). EWMA control charts have also been used for monitoring attribute processes, see Gan 26 (binomial counts), Yeh et al 16 (binomial, Bernoulli, and geometric counts), Spliid 17 (geometric counts), Weiß 27 (Markov binomial counts), Gan 28 and Borror et al 29 (Poisson counts), Weiß 30,31 (Poisson INAR(1) processes), or Steiner 32 (k-grouped data). A basic EWMA chart for monitoring serially independent binary processes is proposed in Section 2, where we also investigate its average run length (ARL) performance.…”

One‐ and two‐sided monitoring schemes for BINARCH(1) processes

“…Gan's scheme was applied in the monitoring of serially independent binomial counts. Then, Weiß 23 and Weiß 24 considered Gan's EWMA chart and applied it in the case of a first order integer-valued Poisson autoregressive (PINAR(1)) process whereas Weiß 25 applied this scheme in the monitoring of a Markov binomial process, as well. Also, Weiß 26 proposed a modification on the rounding function by considering the s-rounding which rounds a number to the closest fraction with denominator s. That is, the s − round(x) function is defined as…”