Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment

Zhi Song, Amitava Mukherjee and Jiujun Zhang

European Journal of Operational Research, 2021, vol. 289, issue 1, 177-196

Abstract: In this paper, we develop two adaptive approaches for detecting the signal source in a bivariate process when a shift occurs in the location vector or the scale matrix or both. The proposed method capitalises the notion of Sklar’s principle of expressing any multivariate joint distribution in terms of univariate marginal-distribution functions and a copula, which represents the dependence structure between the variables. Motivated by this, we recommend monitoring the two marginal distributions and the copula function simultaneously using appropriate nonparametric (distribution-free) test statistics. At each stage of Phase-II monitoring, we adopt the permutation method for computing the individual p-values and derive the plotting statistics of our proposed schemes combining suitable transforms of the three p-values of the component testing. We establish the in-control robustness of the proposed surveillance plans and compare them with two competitors in terms of run length properties. Performance of the proposed schemes in detecting a correct out-of-control signal is as good or better than some existing charting schemes for bivariate process monitoring. The novelty of our proposed technique lies in the fact that it indigenously helps in identifying the component(s) responsible for the signal, which is not straightforward with the traditional schemes for surveillance of a bivariate process. Numerical results substantiate that the proposed procedure performs significantly better than its competitors in many cases. Also, we investigate the percentage of correct diagnosis of a signal via the proposed charting schemes. Nowadays, in monitoring and control of smooth service operations, the use of quality monitoring has increased than ever before, but the problem and data structures become more complicated in the Industry 4.0 era. We analyse two real case studies, one in the context of monitoring the response time and service quality in a call centre and the other related to the inspection of product quality, to illustrate the application of the proposed schemes.

Keywords: Quality control; Bivariate process; Copula; p-value; Robust statistic (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221720306275
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:289:y:2021:i:1:p:177-196

DOI: 10.1016/j.ejor.2020.07.016

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().