A New Chart for Monitoring the Covariance Matrix of Bivariate Processes

Antônio Fernando Branco Costa · Marcela Aparecida Guerreiro Machado

28 citations0/0 files storedCommunications in Statistics - Simulation and Computation

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Management Systems and Quality Improvement

Abstract

In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance | S | chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance | S | chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.

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References

1992Introduction to Statistical Quality Control 2005Introduction to Statistical Quality Control 1988$\overline{X}$ Charts with Variable Sampling Intervals 1994XCharts with Variable Sample Size 1993X¯ chart with adaptive sample sizes 1997X Chart with Variable Sample Size and Sampling Intervals 1999X Charts with Variable Parameters 2013Multivariate Quality Control

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