Multivariate charts with two-stage sampling and with special decision rule

• Grant number: 06/00284-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2006
• End date: May 31, 2007
• Field of knowledge: Engineering - Production Engineering - Production Management
• Principal Investigator: Antonio Fernando Branco Costa
• Grantee: Carlos Henrique Lucato Sigolo
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

In this project, we intend to study the properties of the multivariate charts used to control processes where the inspection of the items takes into account more than one quality characteristics. These quality characteristics are measurable, and associated to each item there is an X vector whose components are the quality characteristic values. For instance, if the process is producing shafts, their diameters and their weight might be the quality characteristics to be inspected. In this project, we propose the use of the two stage samplings. During the first stage, the first sample item is inspected; if each component of its X vector is not far from the “target” value specified to the corresponding quality characteristic the sampling is interrupted; otherwise the sampling goes on to the second stage. During the second stage all sample items are inspected and the values from their X vectors are used to obtain the Hotelling T2 statistic. This point is plotted on the T2 chart. The use of the two stage sampling aims to minimize the effort with inspection, once the number of times the sampling goes on to the second stage is reduced. The traditional multivariate chart signals an out-of-control condition always when a point falls beyond the control limits. Alternatively, we consider here a different criteria where the signal is give only after the occurrence of a second point in the action region, and under the condition that these two point beyond the control limits are not far from each other. In the literature, the charts based on the two points rule are called Synthetic Control Charts. These charts were designed to attend the user, once he does not feel secure in stopping the process just after the occurrence of the first point in the action region. By simulation, we intend to study the performance of the multivariate charts in detecting process disturbances, when the two stage sampling and the two points rule are adopted.