The Performance of Phase II Simple Linear Profile Approaches when Parameters Are Estimated

Abstract

Previous studies of statistical performance of Phase II simple linear profile approaches were reported only for the case of known profile parameters assumption. The main objective of this article is to evaluate and compare the performance of these approaches when the profile parameters are estimated from an in-control Phase I profile data set. Simulations establish that the performance of these approaches is strongly affected when the parameters are estimated compared to the known parameters case. The in-control performance of the competing approaches significantly deteriorates if estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. The results show also that some profile monitoring approaches need much larger number of Phase I profiles than other approaches to achieve the expected statistical performance. They also show that the profile monitoring approach proposed by Mahmoud et al. (2010) has generally better out-of-control run length performance than the competing approaches when the estimated parameters are used in the charts design.

Keywords:

• Average run length
• Estimation effect
• EWMA
• Phase II analysis
• Profile monitoring
• Statistical process control

Mathematics Subject Classification:

• 62P30
• 62J05

Acknowledgment

The authors greatly appreciate the helpful comments of the anonymous referee. His/her comments contributed substantively in the evolution of this article.