Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

Bourguignon, Marcelo; Ho, Linda Lee; Fernandes, Fidel Henrique

doi:10.1002/qre.2632

Cited by 14 publications

(7 citation statements)

References 15 publications

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“…The result showed the outperformance of the proposition chart for the distribution analysis. Bourguignon et al 52 . have introduced a control chart to observe the Birnbaum‐Saunders median parameter, which was based on three estimators.…”

Section: Introductionmentioning

confidence: 99%

“…The result showed the outperformance of the proposition chart for the distribution analysis. Bourguignon et al 52 have introduced a control chart to observe the Birnbaum-Saunders median parameter, which was based on three estimators. By utilizing the proposed procedures, the practitioner can detect any upcoming problems, using a small sample size of data or products.…”

Section: Introductionmentioning

confidence: 99%

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A hybrid method based on P and P′ control chart for identifying hotspots

Jahan

Abbaspour

Safakhah

2021

Quality & Reliability Eng

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The terms “hotspots,” “blackspot,” or “high‐risk” are normally used for an area on a road where the number of car accidents are far beyond the normal level and, more importantly, the causes of the incident always link to one or many specific reasons. Identifying these spots is helpful and may assist people in authority to implement corrective actions. To do the aforementioned, some decision‐support tools could be useful since they enable us to monitor the indicators that may lead to a car accident, same as the procedure engineers use to control production lines in factories. In this regard, control charts are utilized to identify blackspots. Although the method is low cost, and provides quick detection and statistical reliability level and, more importantly, uses online applications; however, it advised that the rate quality control method could be used on roads with the same geometry and traffic conditions. This research develops a hybrid method, based on accident type, for improving rate quality control method to overcome the shortcomings. Furthermore, the suggested framework considers crash severity and traffic volume that have not been taken into account in the rate quality control method yet. The case study evaluates how this framework is successful to identify blackspots, and based on the result in the real environment, it reveals that the proposed method could detect and identify the hotspots.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A hybrid method based on P and P′ control chart for identifying hotspots

Jahan

Abbaspour

Safakhah

2021

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…A detailed review of the BS distribution including methodologies under the classical and Bayesian approaches was presented in [20]. Recently, guidelines about the minimum sample size for monitoring the BS median in quality control under a classical statistical approach were presented in [21]. Although diverse methodologies related to the BS distribution have been proposed, the problem of determining an optimal sample size when estimating the BS mean has not yet been studied.…”

Section: Introductionmentioning

confidence: 99%

Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions

2021

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The fatigue-life or Birnbaum–Saunders distribution is an asymmetrical model that has been widely applied in several areas of science and mainly in reliability. Although diverse methodologies related to this distribution have been proposed, the problem of determining the optimal sample size when estimating its mean has not yet been studied. In this paper, we derive a methodology to determine the optimal sample size under a decision-theoretic approach. In this approach, we consider symmetric and asymmetric loss functions for point and interval inference. Computational tools in the R language were implemented to use this methodology in practice. An illustrative example with real data is also provided to show potential applications.

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“…Consequently, at least a couple of hundred papers and a single research monograph have already appeared describing all properties and developments of this distribution; see, for example, the comprehensive review by Balakrishnan and Kundu [5] in this connection. Examples of recent applications of the BS distribution are such as Bourguignon et al [6], Hassani et al [7], and Kannan et al [8], among others. The BS distribution belongs to a generalized family of distributions called the generalized BS distribution [9].…”

Section: Introductionmentioning

confidence: 99%

On Modeling Concrete Compressive Strength Data Using Laplace Birnbaum-Saunders Distribution Assuming Contaminated Information

Alam

Nassar

2021

Crystals

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Compressive strength is a well-known measurement to evaluate the endurance of a given concrete mixture to stress factors, such as compressive loads. A suggested approach to assess compressive strength of concrete is to assume that it follows a probability model from which its reliability is calculated. In reliability analysis, a probability distribution’s reliability function is used to calculate the probability of a specimen surviving to a certain threshold without damage. To approximate the reliability of a subject of interest, one must estimate the corresponding parameters of the probability model. Researchers typically formulate an optimization problem, which is often nonlinear, based on the maximum likelihood theory to obtain estimates for the targeted parameters and then estimate the reliability. Nevertheless, there are additional nonlinear optimization problems in practice from which different estimators for the model parameters are obtained once they are solved numerically. Under normal circumstances, these estimators may perform similarly. However, some might become more robust under irregular situations, such as in the case of data contamination. In this paper, nine frequentist estimators are derived for the parameters of the Laplace Birnbaum-Saunders distribution and then applied to a simulated data set and a real data set. Afterwards, they are compared numerically via Monte Carlo comparative simulation study. The resulting estimates for the reliability based on these estimators are also assessed in the latter study.

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Control charts for monitoring the median parameter of Birnbaum‐Saunders distribution

Cited by 14 publications

References 15 publications

A hybrid method based on P and P′ control chart for identifying hotspots

A hybrid method based on P and P′ control chart for identifying hotspots

Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions

On Modeling Concrete Compressive Strength Data Using Laplace Birnbaum-Saunders Distribution Assuming Contaminated Information

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