Robust start up stage for beltline moulding process variability monitoring using vector variance

Rohayu Mohd Salleh,Maman A Djauhari

doi:10.11113/mjfas.v6n1.179

Abstract

One of the primary problems encountered in monitoring the variability of beltline moulding process in an automotive industry is the estimation of parameters in the start-up stage. This problem becomes more interesting because the process is in multivariate setting and must be monitored based on individual observations, i.e., the sample size of each subgroup is 1. This paper deals with a robust estimation of location and scale during the start-up stage. For this purpose, we use Mahalanobis distance in data ordering process. But, in data concentration process, we use vector variance (VV). This method is highly robust and computationally efficient. Its advantage in monitoring the variability of beltline moulding process will be compared with the non-robust method.

Highlights

It is known that a successful of monitoring process in Phase II depends on a successful analysis during start up stage (SUS) or Phase I (Jensen et al, 2005)
Jensen et al (2005) discussed the use of robust MSD method based on minimum volume estimate (MVE) and minimum covariance determinant (MCD) criteria in start up stage
Djauhari (2007) introduced a new robust estimator method called as minimum vector variance (MVV)

Summary

INTRODUCTION

It is known that a successful of monitoring process in Phase II depends on a successful analysis during start up stage (SUS) or Phase I (Jensen et al, 2005). We assume that Xi ; i = 1, 2,..., n are independent and follow a multivariate normal distribution These data vectors will be used in start-up stage to obtain an in-control data subset which will be used to estimate the process parameters. Explained by Hadi (1992), outliers do not necessarily have large value of MSD and not all observations with large MSD value are necessarily outliers These problems are known as masking and swamping effect due to the fact that mean vector and covariance matrix are not robust. To handle this problem, the method of robust monitor the process variability right after a future data estimator is applicable as theoretical foundations of the vector or, equivalently, individual observation is available. Djauhari / Journal of Fundamental Sciences Vol 6, No 1 (2010) 67-71

CLASSICAL APPROACH

Classical distance and distribution

ROBUST APPROACH

Data concentration using VV di2

Robust distance and distribution

CONCLUSION