A New Rank-based Multivariate CUSUM Approach for Monitoring the Process Mean

A New Rank-based Multivariate CUSUM Approach for Monitoring the Process Mean

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Article ID: iaor2016962
Volume: 32
Issue: 3
Start Page Number: 1167
End Page Number: 1178
Publication Date: Apr 2016
Journal: Quality and Reliability Engineering International
Authors:
Keywords: control, decision theory: multiple criteria, production
Abstract:

In many cases, data do not follow a specific probability distribution in practice. As a result, a variety of distribution‐free control charts have been developed to monitor changes in the processes. An existing rank‐based multivariate cumulative sum (CUSUM) procedure based on the antirank vector does not quickly detect the large shift levels of the process mean. In this paper, we explore and develop an improved version of the existing rank‐based multivariate CUSUM procedure in order to overcome the difficulty. The numerical experiments show that the proposed approach dramatically outperforms the existing rank‐based multivariate CUSUM procedure in terms of the out‐of‐control average run length. In addition, the proposed approach particularly resolves the critical problem of the original approach, which occurs in the simultaneous shifts whose components are all the same but not 0. We believe that the proposed approach can be utilized for monitoring real data.

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