Monitoring simple linear profiles in the presence of generalized autoregressive conditional heteroscedasticity

Abstract

In this paper, monitoring of simple linear profiles is investigated in the presence of nonequality of variances or heteroscedasticity, ie, generalized autoregressive conditional heteroscedasticity. In this condition, using of the common methods regardless of the heteroscedasticity leads to the fault interpretations. We consider a simple linear profile and assume that there is a generalized autoregressive conditional heteroscedasticity (GARCH) (1,1) model within the profiles. Here, we particularly focus on Phase II monitoring of simple linear regression. We studied the generalized autoregressive conditional heteroscedasticity effect, briefly GARCH effect, on the average run length criterion. As the remedial measures, the weighted least squares method to estimate the regression parameters and the heteroscedasticity‐consistent approaches to estimate the covariance matrix of regression parameters, are used to extract the GARCH effect. Two control chart methods namely T2 and exponentially weighted moving average 3 are discussed to monitor the simple linear profiles. Their performances are evaluated by using the average run length criterion. Finally, a real case from an industry field is studied.

A new model to monitor very small effects of a polynomial profile

“…Several researchers have studied different profile types like linear regression or more complicated types such as nonlinear and multivariate regressions. Kang and Albin (2000), Mahmoud (2008), Kazemzadeh et al (2008), Soleimani et al (2009), Saghaei et al (2009), Norrossana et al (2011), Amiri et al (2012), Mahmoud (2012), Amiri et al (2013), Soleimani and Norrossana (2014), Aly et al (2015), Niaki et al (2015), Kazemzadeh et al (2016), Amiri et al (2016), Khedmati and Niaki (2016), Kalaei et al , 2018a, b and Hadizadeh and Soleimani (2017) contributed monitoring the linear profile type. Walker and Wright (2002), Ding et al (2006), Moguerza et al (2007), Vaghefi et al (2009), Jensen and Birch (2009), Chicken et al (2009), Shiau et al (2009), Chang and Yadama (2010), Paynabarand Jin (2011), Nikoo and Noorossana (2012), Fan et al (2013), Chou et al (2014), Hadidoust et al (2015), Atashgar et al (2015), Shahriari et al (2016) and Awad et al (2018) focused on nonlinear profile monitoring.…”