Inverse Gaussian Control Charts for Monitoring Process Variability

Sim, C. H.

doi:10.1081/sac-120013123

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…Inverse Gaussian (IG) distributions have been employed to describe positively skewed data arising in various scientific fields such as stochastic hydrology (Hathhorn and Charbeneau, 1994), materials science (Durham and Padgett, 1997), internet science (Huberman et al, 1998), reliability and life testing (Economou and Caroni, 2005;Onar and Padgett, 2000;Yang, 1999), and quality control (Moghadam and Eskandari, 2006;Sim, 2003). The statistical properties of the IG, that make it a useful and competitive model to the gamma, lognormal and Weibull distributions, are presented in the monographs of Chhikara and Folks (1989) and Seshadri (1993).…”

Section: Introductionmentioning

confidence: 98%

Percentile Estimation in Inverse Gaussian Distributions

Kallioras

Koutrouvelis

2013

Communications in Statistics - Simulation and Computation

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This paper presents procedures for percentile estimation in the three-parameter inverse Gaussian (IG3) and the two-parameter inverse Gaussian (IG2) distributions. All procedures require first the estimation of distribution parameters and second the computation of the desired quantile at the estimated parameters. Parameter estimation is accomplished by maximum likelihood (ML) or a mixed moments (MXM) method. A Newton-Rahpson (NR) procedure is used for inverting the CDF. Simulation and asymp-totic results are given for the resulting estimators. Two sets of real data are used to illustrate the procedures.

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Section: Introductionmentioning

confidence: 98%

Percentile Estimation in Inverse Gaussian Distributions

Kallioras

Koutrouvelis

2013

Communications in Statistics - Simulation and Computation

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“…The family of two-parameter inverse Gaussian distribution (IG2) is one of the basic models for describing positively skewed data which arise in a variety of applications, such as repair times of an airborne communication transceiver [1], the number of visited pages per user within an internet site [2] and quality characteristics [3,4]. Most applications of IG2 are justified on the fact that the IG2 is the distribution of the first passage time in Brownian motion with positive drift.…”

Section: Introductionmentioning

confidence: 99%

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

Koutrouvelis

Karagrigoriou

2012

Journal of Statistical Computation and Simulation

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This paper uses a standardized version of the logarithm of the empirical moment generating function in order to construct plots for assessing the appropriateness of the inverse Gaussian distribution. Variability is added to the plots by utilizing asymptotic and finite-sample results. The plots have linear scales and do not rely on the use of tables or special functions. In addition, they are equivalent to a goodness-of-fit test whose critical values are obtained from fitted equations involving the sample size and the estimated shape parameter of the inverse Gaussian distribution. Three data sets are used to illustrate the plots. A similar test is also proposed whose critical values are found through parametric bootstrap. An extensive simulation study shows that the new tests maintain good stability in level and high power across a wider range of distributions and sample sizes than other tests.

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“…The sampling distributions of IG location and scale parameter were easy to derive. Therefore, control charts for the parameters of IG distribution have been proposed in several articles (cf Edgeman, Edgeman, Edgeman, Hawkins and Olwell, and Sim).…”

Section: Introductionmentioning

confidence: 99%

GLM‐based control charts for the inverse Gaussian distributed response variable

Kinat

Amin

Mahmood

2019

Quality & Reliability Eng

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In the modern era of digitalization, manufacturing industries needed monitoring methods to timely detect an abrupt change in the process. Control charts are widely used online monitoring method and used in several sectors for the surveillance of the process. Usually, control charts are developed for a single study variable, but there exists auxiliary information along with the study variable. Because of the linear relation between the study variable and auxiliary variable, several control chart studies are designed based on the simple linear regression model, but they are restricted to the normally distributed response variable. When the response variable follows an exponential family distribution, then the generalized linear modeling (GLM) approach provides better estimates. Hence, this study is designed to propose GLM‐based control charts when the response variable follows the inverse Gaussian (IG) distribution. In GLM‐based control charts, deviance and Pearson residuals of the IG regression are considered as plotting statistics. For the evaluation purpose, a simulation study is designed, and the performance of the proposed methods is compared with existing counterparts in terms of the run length properties. Moreover, run‐rules are also implemented to gain the efficiency of the Shewhart type GLM‐based control charts under small‐to‐moderate shifts. Finally, an example related to the yarn manufacturing industry is also used to highlight the importance of the stated proposal.

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Inverse Gaussian Control Charts for Monitoring Process Variability

Cited by 10 publications

References 12 publications

Percentile Estimation in Inverse Gaussian Distributions

Percentile Estimation in Inverse Gaussian Distributions

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

GLM‐based control charts for the inverse Gaussian distributed response variable

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