Phase II monitoring of binary profiles in the presence of within-profile autocorrelation based on Markov Model

ABSTRACT

This paper introduces a Markov model in Phase II profile monitoring with autocorrelated binary response variable. In the proposed approach, a logistic regression model is extended to describe the within-profile autocorrelation. The likelihood function is constructed and then a particle swarm optimization algorithm (PSO) is tuned and utilized to estimate the model parameters. Furthermore, two control charts are extended in which the covariance matrix is derived based on the Fisher information matrix. Simulation studies are conducted to evaluate the detecting capability of the proposed control charts. A numerical example is also given to illustrate the application of the proposed method.

KEYWORDS:

• Average run length (ARL)
• Binary profile
• Markov models
• Particle swarm optimization
• Within-profile autocorrelation

MATHEMATICS SUBJECT CLASSIFCATIONS:

• Primary 62J12
• Secondary 62M10

Acknowledgment

The authors are thankful to respectful reviewers for their valuable comments which led to significant improvement in the paper.