Statistical Properties of a New Bathtub Shaped Failure Rate Model With Applications in Survival and Failure Rate Data

Arshad, Muhammad; Iqbal, Muhammad; Mutairi, Alya Al

doi:10.5539/ijsp.v10n3p49

Cited by 3 publications

(3 citation statements)

References 30 publications

(24 reference statements)

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“…Hjorth 4 proposed three parameters mixed distributions with Increasing Failure Rate giving the possibility that this model can be used for small samples. Arshad et al 5 obtains a three-parameter model based on the modification of the Mustapha Type-I distribution; through the Lehmann-II distribution's general formulation, the extra shape parameter allows better control of the skewness and kurtosis of the density function. Dombi et al 6 proposes the Omega distribution with three parameters formulated from the Lambert W-function; this new distribution has two essential characteristics, it lacks exponential terms, and its domain does not have infinity.…”

Section: Introductionmentioning

confidence: 99%

“…Hjorth 4 proposed three parameters mixed distributions with Increasing Failure Rate giving the possibility that this model can be used for small samples. Arshad et al 5 . obtains a three‐parameter model based on the modification of the Mustapha Type‐I distribution; through the Lehmann‐II distribution's general formulation, the extra shape parameter allows better control of the skewness and kurtosis of the density function.…”

Section: Introductionmentioning

confidence: 99%

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A reliability analysis for electronic devices under an extension of exponentiated perks distribution

Méndez‐González¹,

Rodríguez‐Picón²,

Pérez-Olguín³

et al. 2022

Quality & Reliability Eng

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This paper presents a reliability analysis for electronic devices (ED) with bathtub curve-shaped failure times. An extension of the exponentiated perks distribution (EPD) is proposed for the analysis. The extension of this new distribution is based on the Alpha Power Transformation, so the Alpha Exponentiated Perks Distribution (AEXP) is introduced. The AEXP has three shape parameters and one scale parameter, allowing greater flexibility to represent failure rates in an increasing, decreasing, or bathtub curve form. Some useful properties in the reliability engineering context are presented. AEXP parameters were estimated via the Maximum Likelihood Method. Finally, two case studies focused on ED are used to compare the proposed distribution and other distributions with similar failure rate representation properties. The obtained results show that the AEXP better describes the behavior of ED than the distributions considered in the analysis.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A reliability analysis for electronic devices under an extension of exponentiated perks distribution

Méndez‐González¹,

Rodríguez‐Picón²,

Pérez-Olguín³

et al. 2022

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…In the most recent times, attention towards the generalization of probability distributions has grown phenomenally high. For more insight, see the trustworthy work of Cordeiro and Brito [7], Zaka and Akhter [8], Al Mutairi et al [9], Tahir et al [10], Shahzad et al [11], Ahsan-ul-Haq et al [12], Okorie et al [13], Abdul-Moniem [14], Hassan et al [15], Zaka et al [16], Arshad et al [17], Arshad et al [18,19], Al-Mutairi [20], Alzaatreh et al [21], Gleaton and Lynch [22], Bourguignon et al [23], Afify et al [24], Tahir et al [25], Aldahlan et al [26], Aslam et al [27], Balogun et al [28], Afify et al [29], Mansour et al [30], Mahdavi and Kundu [31], Nassar et al [32], Ijaz et al [33], Klakattawi and Aljuhani [34], Afify et al [35], Alsubie et al [36], Ahmad et al [37], and Nofal et al [38].…”

Section: Introductionmentioning

confidence: 99%

A New Class of the Power Function Distribution: Theory and Inference with an Application to Engineering Data

Mutairi

Iqbal

Arshad

et al. 2022

Journal of Mathematics

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In this study, a new class that generates optimal univariate models called a new exponentiated-G class of distributions is developed. Numerous complementary statistical properties are derived and discussed in detail for the newly exponentiated power function (EPF) distribution. All possible shapes of the probability density and hazard rate functions are sketched for selected values of parameters. Six accredited estimation methods are discussed, and their performance is assessed and compared by a simulation study. The applicability of the new class is evaluated by analyzing the automotive engineering sector data.

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A novel extended Kumaraswamy distribution and its application to COVID‐19 data

Suleiman,

Daud,

Ishaq

et al. 2024

Engineering Reports

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In the field of biomedical research, data characteristics often exhibit significant variability, challenging the applicability of classical probability distributions for biomedical data modeling. In this research, we introduce a novel four‐parameter distribution called the odd beta prime Kumaraswamy (OBPK) distribution, derived from the odd beta prime generalized family of distributions and the Kumaraswamy distribution. This distribution exhibits greater flexibility compared with the traditional Kumaraswamy distribution. Importantly, the OBPK distribution offers symmetrical, right‐skewed, left‐skewed, bathtub, N‐shaped, J‐shaped, and reversed J‐shaped densities, as well as varied hazard functions, including increasing, decreasing, bathtub, increasing‐decreasing, upside‐down bathtub, and N‐shaped forms. These curvature patterns make it particularly useful for modeling biomedical data. We derive some basic properties of the OBPK distribution. Parameters are estimated using the maximum likelihood approach, and the performance of various estimators is assessed via Monte Carlo simulations. Finally, four applications to real data on COVID‐19 mortality rates from different countries are evaluated to demonstrate the importance of the OBPK model over other extended versions of the Kumaraswamy models. The empirical findings suggest that the OBPK model outperforms other extended versions of the Kumaraswamy models in these applications.

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Statistical Properties of a New Bathtub Shaped Failure Rate Model With Applications in Survival and Failure Rate Data

Cited by 3 publications

References 30 publications

A reliability analysis for electronic devices under an extension of exponentiated perks distribution

A reliability analysis for electronic devices under an extension of exponentiated perks distribution

A New Class of the Power Function Distribution: Theory and Inference with an Application to Engineering Data

A novel extended Kumaraswamy distribution and its application to COVID‐19 data

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