Inflated beta control chart for monitoring double bounded processes

Lima-Filho, Luiz Medeiros de Araujo; Pereira, Tarciana Liberal; Souza, Tatiene Correia de; Bayer, Fábio M.

doi:10.1016/j.cie.2019.07.017

Cited by 14 publications

(17 citation statements)

References 33 publications

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“…This section presents a Monte Carlo simulation study to evaluate the estimators of the introduced inflated beta regression model with varying dispersion and the performance of the IBRCC. The performance of the proposed control chart is compared with some alternatives in literature, namely: the usual linear regression control chart (RCC) [ 1 ], the beta regression control chart (BRCC) [ 6 ], and the inflated beta control chart (IBCC) [ 30 ]. Note that the RCC is a classical regression control chart that works under Gaussian assumptions.…”

Section: Simulation Studymentioning

confidence: 99%

“…We compared the proposed IBRCC with the standard RCC [ 1 ], and the state-of-the-art charts, namely BRCC [ 6 ] and IBCC [ 30 ]. Since the BRCC does not consider values equal to zero or one, we replaced zeros by 0.0001 and ones by 0.9999 for its application.…”

Section: Simulation Studymentioning

confidence: 99%

“…Since the BRCC does not consider values equal to zero or one, we replaced zeros by 0.0001 and ones by 0.9999 for its application. For all considered control charts, we examined two aspects of evaluation: in-control ( , , ) and out-of-control ( , where β is the type II error probability) [ 30 , 35 ]. For brevity, we do not present the MRL and SDRL results for the out-of-control process.…”

Section: Simulation Studymentioning

confidence: 99%

“…To ensure that the comparisons between ARL 1 occur between control charts of same ARL 0 , we adjusted the chart limits to obtain ARL 0 equal to the specified nominal values of 100 and 370. This control chart calibration is suggested in the literature [ 30 , 37 – 39 ]. After ARL 0 calibration, a δ change was induced in the mean and precision regression structures to generate out-of-control processes as the following: logit( γ t ) = δ + β 0 + β 1 x t and .…”

Section: Simulation Studymentioning

confidence: 99%

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Process monitoring using inflated beta regression control chart

et al. 2020

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This paper provides a general framework for controlling quality characteristics related to control variables and limited to the intervals (0, 1], [0, 1), or [0, 1]. The proposed control chart is based on the inflated beta regression model considering a reparametrization of the inflated beta distribution indexed by the response mean, which is useful for modeling fractions and proportions. The contribution of the paper is twofold. First, we extend the inflated beta regression model by allowing a regression structure for the precision parameter. We also present closed-form expressions for the score vector and Fisher’s information matrix. Second, based on the proposed regression model, we introduce a new model-based control chart. The control limits are obtained considering the estimates of the inflated beta regression model parameters. We conduct a Monte Carlo simulation study to evaluate the performance of the proposed regression model estimators, and the performance of the proposed control chart is evaluated in terms of run length distribution. Finally, we present and discuss an empirical application to show the applicability of the proposed regression control chart.

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Section: Simulation Studymentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

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Process monitoring using inflated beta regression control chart

et al. 2020

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“…For quality characteristics following simplex and unitgamma distributions, Ho et al 6 have studied the consequences in terms of speed to sign shifts on the rates when control charts built for beta distribution are equivocally used to monitor simplex (or unit-gamma) quality characteristics (and vice versa). These contributions [4][5][6] were considered monitoring the average rate or proportion after a reparameterization of the probability density functions.…”

Section: Introductionmentioning

confidence: 99%

Median control charts for monitoring asymmetric quality characteristics double bounded

Lima-Filho

Bourguignon

et al. 2020

Quality & Reliability Eng

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In many practical situations, the quality characteristics of interest assume values in the range (0,1), like rates and proportions (but they are not results from Bernoulli experiments). Most control charts built for these quality characteristics rely on monitoring parameters of their probability distribution functions or on their averages after some reparameterization of their density probability function. However, for highly asymmetric distributions, the median is a more appropriate location parameter than the average. In this paper, we propose Shewhart-type control charts for monitoring the median of observations taken from quality characteristics double bounded after reparameterization of two probability density functions: Kumaraswamy and unit Weibull. The performance of the control charts is evaluated and compared in terms of run length (RL) analysis considering three estimators for the median. Finally, we also carry out two applications to demonstrate the applicability of these control charts.

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Control chart to monitor circular data

Lima-Filho

Bayer

Silva

2020

Quality & Reliability Eng

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This paper proposes a new Shewhart‐type control chart for circular or directional data. This type of data is found in several fields and applications, such as wind direction, the arrival time of a patient in a hospital, and the route of animals. The proposal is based on the Jones–Pewsey distribution, which is a very flexible three‐parameter distribution for modeling processes that can be represented as points on the circumference of the unit circle. We conduct an extensive Monte Carlo simulation study to evaluate and compare the performance of the proposed control chart with some competitors considering individual measurements and the mean direction (nonindividual observations). The results show that the Jones–Pewsey control chart outperforms the competitors in terms of run length distribution analysis. Finally, we present and discuss two applications based on actual datasets to show the applicability of the proposed control chart.

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Inflated beta control chart for monitoring double bounded processes

Cited by 14 publications

References 33 publications

Process monitoring using inflated beta regression control chart

Process monitoring using inflated beta regression control chart

Median control charts for monitoring asymmetric quality characteristics double bounded

Control chart to monitor circular data

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