Performance of Processes with Multiple Variables

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Amitava Mitra*+
• Companies: Auburn University
• Keywords: Multivariate process ; loss function ; process deviation from target ; process variance

Abstract

Performance of processes typically involve the satisfaction of customer requirements for several quality characteristics. These characteristics may not be independent of each other. Processes usually have a target value for each variable along with some specifications. The degree of shift of the process mean from the target along with the variability of the characteristic may influence the associated costs to reduce product proportion nonconforming. Further, the unit costs associated with reduction of the process bias from the target and reduction of the process variance are usually different. A loss function is developed that incorporates these two components. The loss function integrates the relationship between the process variables through the variance-covariance matrix. In this paper, we develop a model to determine adjustments associated with each quality characteristic, through shifting of the mean or the reduction of the variability of the characteristic. The objective is to minimize expected loss. Resource availability may impose constraints on the process variables. Hence, a constrained optimization approach may be warranted.