Abstract
Control charts are commonly used tools that deal with monitoring of process parameters in an efficient manner. Multivariate control charts are more practical and are of greater importance for timely detection of assignable causes in multiple quality characteristics. This study deals with multivariate memory control charts to address smaller shifts in process mean vector. By adopting a new homogeneous weighting scheme, we have designed an efficient structure for multivariate process monitoring. We have also investigated the effect of an estimated variance covariance matrix on the proposed chart by considering different numbers and sizes of subgroups. We have evaluated the performance of the newly proposed multivariate chart under different numbers of quality characteristics and varying sample sizes. The performance measures used in this study include average run length, standard deviation run length, extra quadratic loss, and relative average run length. The performance analysis revealed that the proposed control chart outperforms the usual scheme under both known and estimated parameters. An application of the study proposal is also presented using a data set related to Olympic archery, for the monitoring of the location of arrows over the concentric rings on the archery board.
Highlights
Statistical process control (SPC) is a collection of useful tools that handle the variations occurring in process parameters
Where h5 and λ are set based on the in-control average run length (ARL), and ΣHt refers to the variance–covariance matrix defined as follows:
Performance Comparison Index (PCI) evaluates the performance of control charts based on the extra quadratic loss (EQL)
Summary
Statistical process control (SPC) is a collection of useful tools that handle the variations occurring in process parameters. We come across different quality characteristics of interest that need our attention in a process This leads us to simultaneous handling of such variables in a multivariate set up, named multivariate SPC. The multivariate control charts are very important tools in timely identification of any changes in multiple quality characteristics of interest in a process. The multivariate CUSUM chart converts the related characteristics into scalar quantity, and formulates the structure of the control chart, while the second CUSUM procedure forms a CUSUM vector directly from the observations. The work of [11] extended the idea of [12] for related quality characteristics, and proposed a multivariate exponential weighted moving average (MEWMA) control chart. The remaining part of the article is arranged as follows: Section 2 describes the preliminaries and some existing multivariate control charts available; Section 3 provides the charring structure of proposed multivariate control chart; Section 4 provides performance measures and evaluation of the proposed chart and estimation effects, along with a comparative analysis with some existing charts; Section 5 provides an illustrative example that demonstrates the implementation of the proposal; and Section 6 concludes the study and provides some future recommendations
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