A GLR Chart for Monitoring a Proportion with Autocorrelation

• Activity Number: 426
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Ning Wang*+ and Marion Reynolds
• Companies: Virginia Tech and Virginia Tech
• Keywords: Binary data ; Markov Chain ; Loss function ; Maximum likelihood estimates

Abstract

When monitoring a proportion p, it is usually assumed that the binary observations are independent. This paper investigates the problem of monitoring p when the binary observations follow a two-state Markov chain model with first-order dependence. A Markov Binary GLR (MBGLR) chart is proposed based on a likelihood ratio statistic with an upper bound for the MLE of p. The MBGLR chart is used to monitor a continuous stream of auto-correlated binary observations. The MBGLR chart with a relatively large upper bound has good overall performance over a wide range of shifts. The extra number of defectives (END) is defined to measure the loss associated with control charts for monitoring p . The MBGLR chart is optimized over a range of upper bounds. The numerical results show that the optimized MBGLR chart has a smaller END than the optimized Markov binary CUSUM chart, which can detect a shift in p much faster than a traditional Shewhart-type chart.