A Nazari - School of Information Technology and Mathematical Sciences, University of Ballarat, Australia
S Ahmad - School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia
M Abdollahian - School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia
P Zeephongsekul - School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, Australia

Today’s manufacturing and service industries are using quantitative measures such as proportion of nonconforming products/services for quality assessment and continuous improvement endeavors. In any industry there is a great deal of interest in quantitative measures of process performance for multiple quality characteristics. It is well known that production processes very often produce products with quality characteristics that do not follow normal distribution. In some cases fitting a known non-normal distribution to these quality characteristics would be an impossible task. Furthermore, there is always more than one quality characteristics of interest in process outcomes and very often these quality characteristics are correlated with each other. In this paper we will use the geometric distance approach to reduce the dimension of the correlated non-normal multivariate data and then fit Burr distribution to the geometric distance variable. . The optimal parameters of the fitted Burr distribution are estimated using Compass search method and Secant methods. The proportion of nonconformance (PNC) for process measurements is then obtained by using the fitted Burr distributions based on the two methods. To assess the efficacy of the two methods in estimating Burr parameters, the PNC results are then compared with the exact proportion of nonconformance of the data. Finally, a case study using real data is presented.

Burr distribution, Proportion of nonconformance for skewed process, Burr distribution parameter estimation