A Comparison of the Performance of Phase II Simple Linear Profile Control Charts when Parameters are Estimated

Abstract

The standard deviation of the average run length (SDARL) is an important performance metric in studying the performance of control charts with estimated in-control parameters. Only a few studies in the literature, however, have considered this measure when evaluating control chart performance. The current study aims at comparing the in-control performance of three phase II simple linear profile monitoring approaches; namely, those of Kang and Albin (2000), Kim et al. (2003), and Mahmoud et al. (2010). The comparison is performed under the assumption of estimated parameters using the SDARL metric. In general, the simulation results of the current study show that the method of Kim et al. (2003) has better overall statistical performance than the competing methods in terms of SDARL values. Some of the recommended approaches based solely on the usual average run length properties can have poor SDARL performance.

Keywords:

• Estimation effect
• EWMA
• Phase II analysis
• Profile monitoring
• Standard deviation of average run length
• Statistical process control

Mathematics Subject Classification:

• 62L10
• 62J05