Phase II monitoring of auto-correlated linear profiles using linear mixed model
محورهای موضوعی : Mathematical OptimizationA Narvand 1 , P Soleimani 2 , Sadigh Raissi 3
1 - School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
2 - School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
3 - Modeling and Optimization Research Centre in Engineering and Science, Sepahbod Gharani St., No. 165, Tehran, Iran
کلید واژه: autocorrelation, Average run length, Profile monitoring, linear mixed model, MCUSUM, MEWMA, Hotelling’s T2,
چکیده مقاله :
In many circumstances, the quality of a process or product is best characterized by a given mathematical function between a response variable and one or more explanatory variables that is typically referred to as profile. There are some investigations to monitor auto-correlated linear and nonlinear profiles in recent years. In the present paper, we use the linear mixed models to account autocorrelation within observations which is gathered on phase II of the monitoring process. We undertake that the structure of correlated linear profiles simultaneously has both random and fixed effects. The work enhanced a Hotelling’sT2statistic, a multivariate exponential weighted moving average (MEWMA), and a multivariate cumulative sum (MCUSUM) control charts to monitor process. We also compared their performances, in terms of average run length criterion, and designated that the proposed control charts schemes could effectively act in detecting shifts in process parameters. Finally, the results are applied on a real case study in an agricultural field.
