Monitoring simple linear profiles in the presence of within‐ and between‐profile autocorrelation

Abstract

The current study investigates the effect of within-profile and between-profile autocorrelations on the performance of four monitoring methods of simple linear profiles in Phase II. To this end, a general correlation model between error terms is considered such that the correlation structure of within-profiles errors and the error terms between consecutive profiles follow an autoregressive (AR) times series model of order one. Extensive simulations have been done to assess the effect of both autocorrelation types and the profile size on the estimations of the model parameters as well as the performance of control charts. The performance of the monitoring schemes is investigated and compared with respect to the average run length (ARL) metric. The simulation study results show that the autocorrelation within and between profiles has a negative impact on the monitoring technique's performance. It reduces the control chart's ability to detect process shifts compared to no or weak autocorrelation cases. Moreover, the performance of all the methods is improved by increasing the profile size. An illustrative example is also provided to demonstrate the use of the proposed methods for monitoring the stability of profiles in the chemical industry.

A novel application of statistical process control charts in financial market surveillance with the idea of profile monitoring

“…Hence, a novel T 2 statistic by considering simultaneous autocorrelation effects is proposed here. The general idea is to combine the proposed approaches in Noorossana, Amiri [ 63 ] and Soleimani, Noorossana [ 64 ] which has been recently done by Ahmadi, Yeganeh [ 65 ].…”

“…To account for both auto-correlation effects in profile model through AutoRegressive time series of order one (AR(1)), Ahmadi, Yeganeh [ 65 ] proposed the following profile structure: where ε ij and a ij are the correlated error terms and u ij are the independently andidentically normally distributed errors with mean zero and standard deviation σ . Furthermore, the explanatory variables BTC ij are assumed to follow a normal distribution with mean μ and variance σ b 2 .…”

Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme

“…These two situations were completely investigated by Noorossana, et al [45] and Soleimani, et al [46], in which the autocorrelation coefficients were denoted by φ and ρ, respectively. Furthermore, sometimes both of them (between and within correlation) may happen at the same time; this scenario has been discussed by Ahmadi, et al [47]. Note that the observations of different lags are possible when studying the autocorrelation effect.…”

“…When there is autocorrelation effect in Phase II, the LMM approach, as well as the proposed statistics by Noorossana, Amiri and Soleimani [45], Soleimani, Noorossana and Amiri [46] and Ahmadi, Yeganeh and Shadman [47] can be utilized to remove the autocorrelation effect; note that this is similar to the Phase I analysis for the T 2 control chart. On the other hand, several researchers, such as Sheu and Lu [53] and Li, et al [54], studied the robustness of EWMA control charts with the effect of autocorrelation in the Phase II analysis so that the MEWMA approach [42] can be directly employed with autocorrelated data.…”

“…It generates some new coefficients for the model and the effect of autocorrelation could be reduced or removed. Another possible approach is to employ the proposed statistics by Noorossana, Amiri and Soleimani [45], Soleimani, Noorossana and Amiri [46] and Ahmadi, Yeganeh and Shadman [47] for Phase I analysis, depending on the type of autocorrelation.…”