Monitoring and Change Point Estimation of AR(1) Autocorrelated Polynomial Profiles

On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

“…with ς j defined in Equation (16) and u j defined in Equation (18), for j=1,2,…,2w−1. It is worth mentioning that Equations (16) to (19), or similar versions, have been done in earlier and recent publications for the i.i.d. and autocorrelated observations scenarios using one-and two-sided schemes; see Page, 38 Champ, 39 Acosta-Mejia, 40 Lim and Cho, 42 Shongwe et al, 26,44 and Shongwe and Malela-Majika.…”

“…45 A number of authors have shown that if a monitoring scheme is designed based on one specific shift size δ, it would perform poorly when it is considerably different from the assumed one; see Reynolds and Lou 50 and Ryu et al 51 This makes the ARL inefficient in assessing the overall performance of a monitoring scheme. Thus, in addition to specific shift measures, ie, Equations (17) and (19), researchers are encouraged to use some overall performance metric, like the expected ARL (EARL) because users tend not to know beforehand what exact shift value(s) is targeted-see, for example, Machado and Costa, 52 Huh, 53(chapter 4) Tran et al, 54 Malela-Majika and Rapoo, 55 You,56,57 Shongwe and Graham, 58 and Rakitzis et al 59 The EARL measures the performance of a monitoring scheme over a range of shift values, ie, δ min to δ max -which are the lower and the upper bound of δ, respectively. Note that the shifts within the interval [δ min , δ max ] usually occur according to a probability density function (p.d.f.)…”

“…Some of these models are known as autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), etc; see Box et al for more thorough discussion on these. In this paper, we only consider the well‐known first‐order AR model (ie, AR(1)) as a starting point (other models will be discussed in upcoming articles) and because according to Alwan and Radson, this is the most commonly used time series model in SPM applications; see also Wardell et al, Runger and Willemain, Claro et al, Kazemzadeh et al, Costa and Machado, Chang and Wu, Keramatpour et al, Franco et al, Hu and Sun, Osei‐Aning et al, Garza‐Venegas et al, Shongwe et al, Ahmad et al, etc, for additional indication that AR(1) is the most used model in SPM due to its simplicity as compared with other stationary time series processes.…”

Change Point Estimation of the Stationary State in Auto Regressive Moving Average Models, Using Maximum Likelihood Estimation and Singular Value Decomposition-based Filtering

“…To remove the autocorrelation impact in phase-ІІ of the monitoring of polynomial auto-correlated profiles, in the case of AR(1), Keramatpour et al [7] introduced the GLT/R diagram .…”

A two-sided Bernoulli-based CUSUM control chart with autocorrelated observations

“…Most of the published works on control charts for autocorrelated binary observations assume that the observations can be modeled as a two-state Markov chain in which the probability of an observation being defective depends on the value of the previous observation (firstorder dependence). In this regard, see, for example, Shepherd et al (2007), Keramatpour et al (2013), Vakilian et al (2015), and Ashuri and Amiri (2015), in which observations are autocorrelated according to first-order dependence. Some additional published works have considered monitoring problems more related to what is studied here.…”