Identifying the time of a step change in AR(1) auto-correlated simple linear profiles

Khedmati, Majid; Niaki, Seyed Taghi Akhavan

doi:10.1007/s40092-015-0114-x

Cited by 5 publications

(1 citation statement)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kazemzadeh et al (2008) applied three methods, namely a change point, F statistics and T 2 , to monitor polynomial profiles in Phase I. Other studies in Phase I include Jensen et al (2008), Noorossana et al (2009), Zou et al (2007) and Khedmati and Niaki (2015a).…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Phase-I monitoring of standard deviations in multistage linear profiles

et al. 2017

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Phase-I monitoring of standard deviations in multistage linear profiles

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

Phase II monitoring of multivariate simple linear profiles with estimated parameters

2019

View full text Add to dashboard Cite

In some applications of statistical process monitoring, a quality characteristic can be characterized by linear regression relationships between several response variables and one explanatory variable, which is referred to as a "multivariate simple linear profile." It is usually assumed that the process parameters are known in Phase II. However, in most applications, this assumption is violated; the parameters are unknown and should be estimated based on historical data sets in Phase I. This study aims to compare the effect of parameter estimation on the performance of three Phase II approaches for monitoring multivariate simple linear profiles, designated as MEWMA, MEWMA_3 and MEWMA∕ 2 . Three metrics are used to accomplish this objective: AARL, SDARL and CVARL. The superior method may be different in terms of the AARL and SDARL metrics. Using the CVARL metric helps practitioners make reliable decisions. The comparisons are carried out under both in-control and out-of-control conditions for all competing approaches. The corrected limits are also obtained by a Monte Carlo simulation in order to decrease the required number of Phase I samples for parameter estimation. The results reveal that parameter estimation strongly affects the in-control and out-of-control performance of monitoring approaches, and a large number of Phase I samples are needed to achieve a parameter estimation that is close to the known parameters. The simulation results show that the MEWMA and MEWMA∕ 2 methods perform better than the MEWMA_3 method in terms of the CVARL metric. However, the superior approach is different in terms of AARL and SDARL.

show abstract