Phase-I monitoring of standard deviations in multistage linear profiles

Abstract

In most modern manufacturing systems, products are often the output of some multistage processes. In these processes, the stages are dependent on each other, where the output quality of each stage depends also on the output quality of the previous stages. This property is called the cascade property. Although there are many studies in multistage process monitoring, there are fewer works on profile monitoring in multistage processes, especially on the variability monitoring of a multistage profile in Phase-I for which no research is found in the literature. In this paper, a new methodology is proposed to monitor the standard deviation involved in a simple linear profile designed in Phase I to monitor multistage processes with the cascade property. To this aim, an autoregressive correlation model between the stages is considered first. Then, the effect of the cascade property on the performances of three types of T 2 control charts in Phase I with shifts in standard deviation is investigated. As we show that this effect is significant, a U statistic is next used to remove the cascade effect, based on which the investigated control charts are modified. Simulation studies reveal good performances of the modified control charts.

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.…”

A new non‐parametric control chart for monitoring general linear profiles based on log‐linear modelling

“…In the literature, lots of charting schemes have been proposed for simple linear profiles monitoring. Refer to the references such as Kang and Albin, 1 Kim, et al, 2 Mahmoud and Woodall, 3 Zou et al, 4 Gupta et al, 5 Mahmoud et al, 6 Zou et al, 7 Xu et al, 8 Amiri et al, 9 Kazemzadeh et al, 10 Khedmati and Niaki, 11 Kalaei et al 12 and so forth. Recently, Abbasi et al 13 suggested a homogeneously weighted moving average chart for monitoring the simple linear profile parameters.…”

Phase II monitoring of multivariate simple linear profiles with estimated parameters

“…As an application of simple linear profiles, Kang and Albin (2000) addressed a calibration problem in semiconductor manufacturing and monitored the relationship between measured pressure (Y) and the amount of flow (X) using profiles. Monitoring and change point estimation of simple linear profiles have been considered by some researchers, including Stover and Brill (1998), Mestek et al (1994), Mahmoud and Woodall (2004), Wang and Tsung (2005), Gupta et al (2006), Mahmoud et al (2007), Zou et al (2007), Noorossana et al (2008), Jensen et al (2008), Narvand et al (2013), Niaki (2015, 2016) and Kalaei et al (2018).…”