Improving multivariate measurement systems assessment.

In manufacturing environment, critical decisions about process and product quality depend on the quality of the measurement systems. Measurement systems analysis (MSA) is a set of statistical techniques used to quantify the uncertainty of the measurement instruments. Burdick et al. (2003) provided a review of gauge repeatability and reproducibility (R&R) methods for assessing the precision of univariate measurement systems. In current manufacturing practice multiple characteristics processes are very common. Accordingly, Majeske (2008) proposed multivariate extensions of three commonly used univariate MSA approval criteria using the volume of constant-density contours to characterize the variability of the measurement system. These multivariate MSA-metrics require a multivariate analysis of variance (MANOVA) for estimating the covariance matrices for one factor and two factors gauge studies. In order to ensure constant flows of reliable data, manufacturers should periodically assess their measurement systems and the costs involved in maintaining well performing measurement systems are normally relevant. This issue motivates the present work. Multivariate measurement systems analysis is usually performed designing suitable gauge R&R experiments ignoring available data generated by the measurement system while used for inspection or process control. In recent literature, the use of these measurements from regular use of the instrument has been suggested for univariate MSA studies (see e.g, Steiner et al. 2013). Here we propose the following approach. Once assessed in the initial set up the multivariate measurement instrument as adequate, its performances are assumed as benchmark. Therefore, using the data from the regular activity of the instrument, the periodic assessments of the measurement device are performed by comparing the present precision with the benchmark through a statistical test. Since the proposed method does not require to perform a multivariate gauge study, our proposal can be a useful tool for reducing the costs of multivariate MSA carried out with a certain frequency. To study the ability of the test for detecting worsening in the measurement instrument performances we design suitable simulation experiments. The experiments allows us to investigate the performances of the test in realistic worsening scenarios of the measurement instrument after a period of use. The results show that the proposed method is effective for reducing the costs of a multivariate MSA performed with a certain frequency and may be a useful tool for improving the overall quality of multivariate measurement systems. Burdick, R.K., Borror, C.M. and Montgomery, D.C. (2003). “A review of methods for measurements systems capability analysis”. Journal of Quality Technology, 35, 4, pp. 342-354. Majeske, K. D. (2008). Approval criteria for multivariate measurement systems. Journal of Quality Technology 40, 140–153. Steiner, S.H., Browne R.P., Stevens, N.T. and MacKay, R.J. (2013). “Gauge R&R Studies that Incorporate Baseline Information”. IIE Transactions, forthcoming