EWMA Control Chart Performance with Estimated Parameters under Non-normality

Noorossana, Rassoul; Fathizadan, Sepehr; Nayebpour, Mohamad R.

doi:10.1002/qre.1896

Cited by 22 publications

(16 citation statements)

References 25 publications

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“…This implies that non-normality and contaminated data are a major concern when one deals with geometric profiles. As stated in the studies conducted by Borror et al 14 and Noorossana et al, 15,16 t and Gamma distributions provide decent grounds to investigate the effect of non-normality in different applications of SPC. Similar to normal distribution, the t distribution is symmetric around mean but with heavier tails probabilities.…”

Section: Non-normalitymentioning

confidence: 99%

Using independent component analysis to monitor2‐Dgeometric specifications

Fathizadan

Niaki

Noorossana

2017

Quality & Reliability Eng

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Functional data and profiles are characterized by complex relationships between a response and several predictor variables. Fortunately, statistical process control methods provide a solid ground for monitoring the stability of these relationships over time. This study focuses on the monitoring of 2‐dimensional geometric specifications. Although the existing approaches deploy regression models with spatial autoregressive error terms combined with control charts to monitor the parameters, they are designed based on some idealistic assumptions that can be easily violated in practice. In this paper, the independent component analysis (ICA) is used in combination with a statistical process control method as an alternative scheme for phase II monitoring of geometric profiles when non‐normality of the error term is present. The performance of this method is evaluated and compared with a regression‐ and PCA‐based approach through simulation of the average run length criterion. The results reveal that the proposed ICA‐based approach is robust against non‐normality in the in‐control analysis, and its out‐of‐control performance is on par with that of the PCA‐based method in case of normal and near‐normal error terms.

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Section: Non-normalitymentioning

confidence: 99%

Using independent component analysis to monitor2‐Dgeometric specifications

Fathizadan

Niaki

Noorossana

2017

Quality & Reliability Eng

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“…where ARL is calculated by (28). Since the integrals in (24), (25), and (28) are difficult to compute directly, the Gauss-Legendre quadrature (see [47], [48]) is used to obtain an approximation of the integrals.…”

Section: The Run Length Properties Of One-sided Exponential Ewma Chmentioning

confidence: 99%

“…For the lower-sided exponential EWMA chart, [30] showed that RL distributions are generally right skewed, and the shape of the RL distribution is uncertain due to the effect of parameter estimation. In order to assess the interpretation of ARL, the percentiles of the RL distribution and the ARL are calculated for the lower-sided exponential EWMA chart by using (26) and (28) in Section II. In addition, F ARL is also calculated by using (29) to visualize the meaning of the ARL.…”

Section: Interpretation Problems Of the Arl-based Exponential Ewmamentioning

confidence: 99%

Optimal Design of One-Sided Exponential EWMA Charts With Estimated Parameters Based on the Median Run Length

Qiao

Sun

et al. 2019

IEEE Access

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One-sided exponential exponentially weighted moving average (EWMA) charts are useful tools for monitoring high-quality processes. Average run length (ARL) is usually used as the only criterion to evaluate the performance of a control chart. However, the shapes of the run length (RL) distributions of the one-sided exponential EWMA charts are highly skewed, and furthermore, are affected by the number of Phase I samples used to estimate the process parameters. This results in some confusion in the interpretation of control charts based on ARL for practitioners. Fortunately, the median run length (MRL), which is more intuitional for users, could be employed as a good alternative measure. Based on these, the MRL-based one-sided exponential EWMA charts are investigated in this paper, by taking the effect of estimated parameters into account. The performances of control charts are investigated through a Markov chain approach. An optimal design procedure is developed for the one-sided exponential EWMA charts with estimated parameters based on MRL. Finally, an illustrative example is presented to show the implementation of the exponential EWMA chart when process parameters are estimated. INDEX TERMS Control charts, estimation, EWMA, exponential distribution, median run length.

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“…They were also able to use the bootstrap method in multivariate control charts for principal component analysis based on non-normal distributions when subgroup size is one (Phaladiganon, Kim, Chen, & Jiang, 2013). Mostajeran, Iranpanah, and Noorossana (2016) proposed a new bootstrap algorithm to construct Hotelling's T 2 control chart for individual observations (n = 1).…”

Section: Introductionmentioning

confidence: 99%

An explanatory study on the non-parametric multivariate T2 control chart

Mostajeran

Iranpanah

Noorossana

2018

J. Mod. Appl. Stat. Methods

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Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T 2 are correlated, the T 2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling's T 2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling's T 2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production.

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EWMA Control Chart Performance with Estimated Parameters under Non-normality

Cited by 22 publications

References 25 publications

Using independent component analysis to monitor2‐Dgeometric specifications

Using independent component analysis to monitor2‐Dgeometric specifications

Optimal Design of One-Sided Exponential EWMA Charts With Estimated Parameters Based on the Median Run Length

An explanatory study on the non-parametric multivariate T2 control chart

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