Variation Drivers Analysis with Arbitrary Lags

• Activity Number: 477
• Type: Contributed
• Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Michael A. Wincek*+
• Companies: General Motors R&D
• Keywords: variance decomposition ; model identification ; Cholesky decomposition ; QR decomposition ; autoregressive

Abstract

The univariate Variation Drivers Analysis, proposed by Lawless, Mackay, and Robinson (1994), is a variance decomposition technique that determines for each stage in a sequence, as in an assembly line, the variation transmitted to a stage from previous stages as well as the variation that is uniquely added to that stage. The underlying lag one model states that the observation at any stage depends the observation at the previous stage plus random noise. The model describes the data as multiple observations of a short, time-varying, lag-one autoregressive process. This work generalizes that model to an arbitrary lag and provides a technique for identifying the lag structure. The identification technique examines the maximum lag at each stage. It uses a Cholesky decomposition of the sample variance matrix or a QR decomposition of the centered data matrix. The resulting variance decomposition is displayed as a segmented bar chart. An example using dimensional data from an automobile assembly line illustrates the technique and the effect of incorrect model order identification on the variance decomposition. Such an error can direct variance reduction efforts to the wrong station.