A new synthetic control chart for monitoring process mean using auxiliary information

In this paper, we provide an overview of a class of control charts called the synthetic charts. Synthetic charts are a combination of a traditional chart (such as a Shewhart, CUSUM, or EWMA chart) and a conforming run‐length (CRL) chart. These charts have been considered in order to maintain the simplicity and improve the performance of small and medium‐sized shift detection of the traditional Shewhart charts. We distinguish between different types of synthetic‐type charts currently available in the literature and highlight how each is designed and implemented in practice. More than 100 publications on univariate and multivariate synthetic‐type charts are reviewed here. We end with some concluding remarks and a list of some future research ideas.

Section: Literature Reviewmentioning

confidence: 99%

An overview of synthetic‐type control charts: Techniques and methodology

Rakitzis

Chakraborti

Shongwe

et al. 2019

“…Let the under study process be in in‐control condition. Then, following Haq and Khoo, the difference estimator of μ x is given by

D_{x, t} = \overset{X_{t}}{true} + ρ ((), \frac{σ_{x}}{σ_{w}}) ((), μ_{w} - \overset{W_{t}}{true})

with mean

E ((), D_{x, t}) = μ_{x}

and variance

italicVar ((), D_{x, t}) = \frac{σ_{x}^{2} ((), 1 - ρ^{2})}{n} .

Now applying the following transformation on D x , t

A_{x, t} = \frac{D_{x, t} - μ_{x}}{\sqrt{\frac{σ_{x}^{2} ((), 1 - ρ^{2})}{n}}}

A x , t is the standard normal random variable. In order to monitor the process cv, we normalize the sampling distribution of sample cv for variables X and W .…”

Section: An Aib‐max Ewmaqt Chart For Joint Monitoring Of Process Meanmentioning

confidence: 99%

“…where Q X , t and Q W , t are standard normal random variables, that is Q X , t ∼ N (0,1) and Q W , t ∼ N (0,1). Haq and Khoo suggested difference estimator for monitoring changes in the process variance

σ_{X, t}^{2}

. We use the estimator for estimating cv, ie,

D_{x, t}^{″} = Q_{X, t} - ρ^{* *} Q_{W, t},

where ρ ** is the correlation between Q X , t and Q W , t .…”

Section: An Aib‐max Ewmaqt Chart For Joint Monitoring Of Process Meanmentioning

confidence: 99%

Control charts for simultaneously monitoring of process mean and coefficient of variation with and without auxiliary information

Noor‐ul‐Amin

Tariq

Hanif

2019

A control chart is very useful to control assignable causes which detect the shifted process parameters (eg, mean and dispersion). Simultaneous monitoring of the process parameters is a well‐known approach utilized for the bilateral processes. In the current study, we proposed the blended control chart that monitors the process mean and process coefficient of variation simultaneously. Further, the sensitivity of control chart is enhanced by incorporating an auxiliary variable. We have utilized the concept of EWMA chart and also the log transformation to transform the distribution of sample coefficient of variation to the normal distribution for structuring a joint monitoring control chart. The performance comparison among proposed control charts is presented. On the basis of ARLs and SDRLs, several advantages of the proposed control charts are diagnosed. The empirical evidence is also provided to support proposed control chart with a real‐life dataset.

“…Here, it can be shown that

\overset{X}{true} \sim N_{p} false(μ_{X}, Σ_{\overset{X}{true}} false)

, (cf Johnson and Wichern). In addition, with q = 2 and p = 1, the estimator

\overset{X}{true}

reduces to the difference estimator of the process mean μ X , considered by Riaz and Haq and Khoo() to name a few. Moreover, when X and Y are independent, then

bold-italicX = \overset{X}{true}

.…”

Section: The Proposed Multivariate Chartsmentioning

confidence: 99%

“…Abbas et al integrated the concept of using auxiliary information with the EWMA chart (AIB‐EWMA) and showed that the proposed chart surpasses its existing counterparts. Additionally, Haq and Khoo designed a synthetic chart based on auxiliary information (AIB‐Syn) that surpasses the classical synthetic chart for the process mean shift monitoring in terms of zero‐state and steady‐state average run length (ARL) performances. Furthermore, Sanusi et al developed the AIB‐CUSUM chart that outperforms the classical CUSUM and EWMA charts.…”

Section: Introductionmentioning

confidence: 99%

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

Haq

Khoo

2018

Self Cite

In statistical process control, it is a common practice to increase the sensitivity of a control chart with the help of an efficient estimator of the underlying process parameter. In this paper, we consider an efficient estimator that requires information on several study variables along with one or more auxiliary variables when estimating the mean of a multivariate normally distributed process. Using this auxiliary‐information‐based (AIB) process mean estimator, we propose new multivariate EWMA (MEWMA), double MEWMA (DMEWMA), and multivariate CUSUM (MCUSUM) charts for monitoring the process mean, denoted by the AIB‐MEWMA, AIB‐DMEWMA, and AIB‐MCUSUM charts, respectively. The run length characteristics of the proposed multivariate charts are computed using Monte Carlo simulations. The proposed charts are compared with their existing counterparts in terms of the run length characteristics. It turns out that the AIB‐MEWMA, AIB‐DMEWMA, and AIB‐MCUSUM charts are uniformly and substantially better than the MEWMA, DMEWMA, and MCUSUM charts, respectively, when detecting different shifts in the process mean. A real dataset is considered to explain the implementation of the proposed and existing multivariate control charts.