Dual multivariate CUSUM charts with auxiliary information for process mean

Self Cite

Memory-type auxiliary-information-based (AIB) control charts are very effective in detecting small-to-moderate shifts in the process mean. In this study, we first develop a unique uniformly minimum variance unbiased estimator of the process mean that requires information on the study variable as well as on several correlated auxiliary variables. Then, based on this estimator, adaptive and nonadaptive CUSUM and EWMA charts are developed with either fixed or variable sampling interval for monitoring the process mean, namely, the multiple AIB (MAIB) charts. The proposed charts encompass existing charts with or without the auxiliary information. The run length characteristics of the proposed charts are computed with the Monte Carlo simulations when sampling from a multivariate normal distribution. Based on the run length comparisons, it is found that the MAIB charts are uniformly and substantially more sensitive than the AIB charts when monitoring the process mean. Real datasets are also considered to explain the implementation of the MAIB charts.

“…Suppose that the interest lies in monitoring a single variable of study and

p \in {2, 3, 4, 5}

correlated auxiliary variables are employed for the proposed memory‐type MAIB charts. On the lines of Haq and Khoo,19 Haq,20 following choices of the mean vector

μ_{Z}

and variance–covariance matrix

Σ_{Z}

are considered in the performance analyses:

{bold-italicμ}_{bold-italicZ} = {((), \begin{matrix} δ & 0 & 0 & 0 & 0 & 0 \end{matrix})}^{'} and {boldΣ}_{bold-italicZ} = [\begin{matrix} 1.0 & 0.7 & 0.9 & 0.3 & 0.2 & 0.3 \\ 0.7 & 1.0 & 0.8 & 0.1 & 0.4 & 0.2 \\ 0.9 & 0.8 & 1.0 & 0.1 & 0.2 & 0.1 \\ 0.3 & 0.1 & 0.1 & 1.0 & 0.2 & 0.1 \\ 0.2 & 0.4 & 0.2 & 0.2 & 1.0 & 0.1 \\ 0.3 & 0.2 & 0.1 & 0.1 & 0.1 & 1.0 \end{matrix}] .

For example, when

p = 2

{bold-italicμ}_{bold-italicZ} = false(δ, 0, 0 false)

and

{boldΣ}_{bold-italicZ} = false((1.0, 0.7, 0.9), (0.7, 1.0, 0.8

…”

Section: Run Length Computation and Evaluationmentioning

confidence: 99%

“…">2.In order to work with an MAIB chart, the SPC practitioners are required to carefully include those correlated auxiliary variables into

X_{t}

whose mean vector remains unchanged whenever there is a shift in the mean of the study variable

Y_{t}

Section: Run Length Computation and Evaluationmentioning

confidence: 99%

See 1 more Smart Citation

Memory‐type control charts with multiple auxiliary information for process mean

Haq

Khoo

2021

Self Cite

“…For more recent works on the multivariate charts, we refer to Refs. 12–22, and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Directionally sensitive MCUSUM mean charts

Haq

Sohrab

2021

Self Cite

In the context of a disease outbreak detection, a prime interest is to only detect increases in the process mean. It is thus desirable to have a directionally sensitive multivariate chart that can effectively detect either increases or decreases in the process mean vector. In this paper, with a suitable transformation that truncates multivariate observations either above or below the process mean vector, we propose one‐sided and two one‐sided MCUSUM charts for monitoring the mean of a multivariate normal process. Among the proposed charts, the one‐sided MCUSUM charts are directionally sensitive, while the two one‐sided MCUSUM charts are directionally insensitive. In addition, the fast initial response feature is also incorporated into the proposed charts to enhance their sensitivities against initial process shifts. The run length characteristics of these control charts are computed with the Monte Carlo simulation. Based on the run length comparisons, it is found that the proposed charts are more sensitive than the existing charts when detecting moderate‐to‐large shifts in the process mean. The proposed charts are also applied on real datasets to support the theory.

“…Multivariate statistical process control is an efficient tool for assessing the product quality through the monitoring of industrial processes. Numerous researchers have recently investigated the aspects and applications of multivariate control chart, such as Bersimis and Sachlas, 2 Xiang et al, 3 Turkoz et al, 4 and Haq et al 5 Krupskii et al 6 developed new copula‐based multivariate monitoring techniques for possibly autocorrelated, non‐Gaussian data. In other study, Pascual and Akhundjanov 7 investigated an attribute control chart to monitor correlated multivariate Poisson processes by using copula models.…”

Section: Introductionmentioning

confidence: 99%

Robust T² control chart using median‐based estimators

Maleki

Mehri

Aghaie

et al. 2020

One of the most widely used multivariate control charts is the Hotelling T 2. In order to construct a Hotelling T 2 control chart, the mean vector (μ) and the variance-covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T 2 control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T 2 control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance-covariance matrix. The proposed robust estimators of the mean vector and the variance-covariance matrix are compared with the sample mean vector and the sample variance-covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T 2 control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T 2 control chart has much better performance than the traditional Hotelling T 2 and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.