Effect of autocorrelation estimators on the performance of the X̄ control chart

Quality & Reliability Eng

Molahloe³

2019

In some industrial or health-related processes, it makes more practical sense to monitor either an increase only or a decrease only in the quality characteristic of interest. Consequently, in this paper, we propose four one-sided Shewhart X charts supplemented with runs-rules to monitor the mean of autocorrelated normally distributed samples using a stationary first-order autoregressive model. To counteract the negative effect of autocorrelation, we implement a sampling strategy which involves sampling of non-neighboring observations to form rational subgroups. The Markov chain technique is used to derive zero-state and steady-state closed-form expressions of the specific shift performance metric, ie, average run-length (ARL). Moreover, we compute the expected ARL metric which evaluates each monitoring scheme based on all specified range of possible values of the shift parameter, or more specifically, from a global point of view and thus gives a different perspective from the specific shift ARL metric. We observed that the steady-state improved w-of-w and the improved 2-of-(H + 1) schemes yield a better overall performance than their corresponding basic counterparts for all different levels of autocorrelation. A real-life example is provided to illustrate the implementation of the monitoring schemes proposed here.

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scheme.…”

Section: Resultsmentioning

confidence: 99%

One‐sided runs‐rules schemes to monitor autocorrelated time series data using a first‐order autoregressive model with skip sampling strategies

Quality & Reliability Eng

Molahloe³

2019

“…Case U) for i.i.d. and observations with measurement errors, respectively, while Garza-Venegas et al (2018) studied the FSSI X ¯ scheme for autocorrelated observations (with no measurement errors); hence, for future research purpose, the performance of the VSSI X ¯ scheme under the combined effect of autocorrelation and measurement errors for Case U need to be investigated. Moreover, similar to Noorossana et al (2015), the proposed VSSI design can be combined with the improved double sampling design proposed in Malela-Majika et al (2019) to monitor the mean under the combined effect of autocorrelation and measurement errors.…”

Section: Resultsmentioning

confidence: 99%

Combined effect of autocorrelation and measurement errors on the adaptive X¯ monitoring schemes

Transactions of the Institute of Measurement and Control

2020

For independent and identically distributed observations, and those with measurement errors only, the adaptive designs (i.e. variable sampling sizes (VSS), variable sampling intervals (VSI) and the latter two combined to form VSSI) have been thoroughly discussed. However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Quality & Reliability Eng

Castagliola

2020

Self Cite

Runs‐rules have been widely used since the 1950s in industrial and nonindustrial process monitoring applications to improve the performance of basic and other traditional monitoring schemes. However, none of the studies on runs‐rules have accounted for a process with a combined effect of measurement errors and autocorrelation. Hence, in this paper, the use of the w‐of‐w runs‐rules to improve the performance of the Shewhart trueX¯ scheme using an additive model with a constant variance and a first‐order autoregressive model is proposed. To reduce the combined negative effect of measurement errors and autocorrelation, we implement a sampling strategy based on rational subgroups in which (a) multiple measurements per item are taken (instead of a standard single measurement) and (b) non‐neighboring observations are gathered. Moreover, the latter sampling strategy is incorporated into the values of probability elements of a Markov chain matrix which is used to derive some closed‐form expressions for the zero‐ and steady‐state run‐length distribution. The main finding of this study is that, with respect to some overall performance measures, the proposed scheme outperforms the existing Shewhart trueX¯ scheme by a significant margin. A real‐life example is used to illustrate the practical implementation of the proposed scheme.