Copula-Based Bivariate ZIP Control Chart for Monitoring Rare Events

Models and monitoring of zero‐inflated processes: The past and current trends

“…Fatahi et al proposed a methodology based on copula function, used to generate a joint distribution of two correlated ZIP variables. This bivariate ZIP (BZIP) method was compared with the combined univariate ZIP control charts to detect a change in λ while the parameter p remained unchange in the whole study.…”

“…Leong and Tan 65 Polio Rakitzis et al, 79 Rakitzis et al 80 Read and write Xie and Goh, 15 Chang and Gan, 19 Xie et al, 38 Xie et al, 39 Yang et al, 44 15 Xie et al, 38 Xie et al, 39 He et al, 40 Sim and Lim, 42 Yang et al, 44 Li et al, 45 Fatahi et al, 46 Katemee and Mayureesawan, 48 Katemee and Mayureesawan, 49 Rakitzis and Castagliola, 51 Rakitzis et al 72 Fatahi et al, 56 Areepong, 62 Leong and Tan 65 He et al, 54 He et al, 55 He et al, 61 Rakitzis et al, 64 Sukparungsee, 70 Rakitzis et al, 72 Huh et al 73 Areepong and Sukparungsee, 58 Sukparungsee, 59 Areepong 60…”

Control Charts for Monitoring Correlated Poisson Counts with an Excessive Number of Zeros

“…351–356) has been considered by several authors as an appropriate model for that kind of processes. Control charts for controlling ZIP processes have been proposed and studied by Xie and Goh, Xie et al , Chen et al , Sim and Lim, Fatahi et al , and He et al Applications of the ZIP distribution from several fields of applied research can be found in Bohning …”

“…351-356) has been considered by several authors as an appropriate model for that kind of processes. Control charts for controlling ZIP processes have been proposed and studied by Xie and Goh, 7 Xie et al, 8,9 Chen et al, 10 Sim and Lim, 5 Fatahi et al, 11,12 and He et al 13,14 Applications of the ZIP distribution from several fields of applied research can be found in Bohning. 15 Although independence of observations is a key assumption concerning control charts, observations on a process will be autocorrelated when the sampling rate is very high, which, in turn, commonly happens due to the technological progress in automated sampling.…”

Copula modelling for multivariate statistical process control: a review

“…Copulas create a link between multivariate joint distributions and univariate marginal distributions; they have been widely studied and applied in areas concerned with the problem of dependence relations. Many researchers have developed the copula for use with control charts (Dokouhaki and Noorossana, 2013;Fatahi et al, 2011Fatahi et al, , 2012Hryniewicz, 2012;Hryniewicz and Szediw, 2010;Kuvattana et al, 2016;Verdier, 2013). Time is used to represent some attibutes or variable measures in the manufacturing processes.…”