Bivariate Dispersion Control Charts for Monitoring Non‐Normal Processes

In the present article, two semiparametric bivariate control charts are presented, which use order statistics and are effective in jointly monitoring of possible shifts in the process mean and/or variance. To achieve that both the median location (or more generally the location of a specific order statistic) and the number of specific observations of the test sample lying between the control limits are taken into account. The false alarm rate and the in‐control average run length are not affected by the marginal distributions, while the effect of the dependence structure on them is negligible; therefore, they can be used as fully nonparametric charts. A performance‐comparison study is carried out, and an illustrative example is provided using a real‐world data set.

Section: Performance and Comparison Studymentioning

confidence: 99%

Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

Koutras

Sofikitou

2019

“…Also, Saghir 20 compared the efficiency of the |G| chart with the |S| chart using several bivariate distributions. Osei-Aning et al 21 compared a set of Shewhart type bivariate charts based on several dispersion statistics to monitor changes in the covariance matrix under various bivariate processes.…”

Section: Introductionmentioning

confidence: 99%

Efficient bivariate EWMA charts for monitoring process dispersion

Osei-Aning

2019

Self Cite

To ensure high quality standards of a process, the application of control charts to monitor process performance has become a regular routine. Multivariate charts are a preferred choice in the presence of more than one process variable.In this article, we proposed a set of bivariate exponentially weighted moving average (EWMA) charts for monitoring the process dispersion. These charts are formulated based on a variety of dispersion statistics considering normal and non-normal bivariate parent distributions. The performance of the different bivariate EWMA dispersion charts is evaluated and compared using the average run length and extra quadratic loss criteria. For the bivariate normal process, the comparisons revealed that the EWMA chart based on the maximum standard deviation (SMAX E ) was the most efficient chart when the shift occurred in one quality variable. It also performed well when the sample size is small and the shift occurred in both quality variables. The EWMA chart based on the maximum average absolute deviation from median (MDMAX E ) performed better than the other charts in most situations when the shift occurred in the covariance matrix for the bivariate non-normal processes. An illustrative example is also presented to show the working of the charts.

“…During the last decade, more and more attention has been paid to the control of bivariate processes. The majority of works dedicated to this subject deal mainly with the monitoring of the mean vector, 1,2 the covariance matrix, [3][4][5][6] and autocorrelated observations. [7][8][9][10] The idea of using attribute charts to control the mean vector of bivariate processes has been already explored (see, for example, Ho and Costa 11 and Melo et al 12 ; however, we cannot say the same regarding the covariance matrix.…”

Section: Introductionmentioning

confidence: 99%

Attribute control charts for monitoring the covariance matrix of bivariate processes

Machado

Ho²,

Costa

2018

In this article, we consider the use of 3 attribute charts-the np xy , the np w and the Max D charts-to control the covariance matrix of bivariate processes. In comparison with the generalized variance |S| chart, the 3 attribute charts signal faster, with smaller samples, all kind of disturbances, except when the 2 variables are highly correlated. To compete with the VMAX chart, the Max D chart needs larger samples, but no more than twice bigger. An example illustrates the monitoring of the covariance matrix using the Max D and np w .