A study of stress-strength reliability using a generalization of power transformed half-logistic distribution

Xavier, Thomas; Jose, Joby K.

doi:10.1080/03610926.2020.1716250

Cited by 18 publications

(12 citation statements)

References 15 publications

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“…Motivated by the importance of halflogistic distribution in reliability analysis and the importance of having a model to study a bathtub-shaped failure rate, the authors here discuss an additive power transformed half-logistic distribution. Jose and Manoharan, 19 Jose et al , 20 Xavier and Jose 21,22 developed generalizations of half-logistic distribution and studied their applications in reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…The power transformed half-logistic distribution (PTHL) discussed by Krishnarani 23 and Xavier and Jose 21 has the survival function as…”

Section: Introductionmentioning

confidence: 99%

“…with ℜ(𝑎) > 0 and Γ(𝑏) = ∫ ∞ 0 𝑤 𝑏−1 e −𝑤 d𝑤 is called the gamma function with ℜ(𝑎) > 0. Xavier and Jose 21 illustrated that when 𝛾 < 1, the failure rate function in (2) can have a decreasing shape and when 𝛾 > 1, the failure rate function can have an increasing shape. When 𝛿 = 1, 𝛾 = 1, the failure rate slightly increases and then remains constant.…”

Section: Introductionmentioning

confidence: 99%

“…Jose and Manoharan, 19 Jose et al. , 20 Xavier and Jose 21,22 developed generalizations of half‐logistic distribution and studied their applications in reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

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An additive power‐transformed half‐logistic model and its applications in reliability

Xavier

Jose

Nadarajah

2022

Quality & Reliability Eng

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An additive power‐transformed half‐logistic distribution is proposed to model lifetime data having bathtub‐shaped hazard rate function. The model is derived as the sum of hazard rates of two independently distributed power transformed half‐logistic distributions. Some properties of the model like shapes of hazard function, quantile function, mean time between failure (MTBF), probability of failure due to early birth defect and due to ageing are discussed. The graphical estimation technique based on probability plotting procedure is demonstrated to be useful in estimating the parameters of this model. The method of maximum likelihood estimation is discussed for estimating the model parameters and simulation study is considered to show the performance of the estimates. Finally the usefulness of the developed distribution is illustrated by applying it to two real life datasets from engineering reliability.

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Section: Introductionmentioning

confidence: 99%

“…The power transformed half-logistic distribution (PTHL) discussed by Krishnarani 23 and Xavier and Jose 21 has the survival function as…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Jose and Manoharan, 19 Jose et al. , 20 Xavier and Jose 21,22 developed generalizations of half‐logistic distribution and studied their applications in reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An additive power‐transformed half‐logistic model and its applications in reliability

Xavier

Jose

Nadarajah

2022

Quality & Reliability Eng

Self Cite

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“…The HLo model is a random distribution reported by folding at zero the logistic (Lo) distribution centered around the origin. Due to the flexibility of the HLo model, several authors aimed to propose and study many extensions and generalizations for this model with its applications in various fields, for instance, Balakrishnan [1], Balakrishnan and Wong [2], Torabi and Bagheri [3], Olapade [4][5][6], Kantam et al [7], Jose and Manoharan [8], Krishnarani [9], Oliveira et al [10], Usman et al [11], Cordeiro et al [12], Muhammad and Liu [13], Samuel and Kehinde [14], Xavier and Jose [15], Eliwa et al [16] and El-Morshedy et al [17], among others. Among all these generalizations, we take in our consideration the HLo model with two parameters (see Hashempour,[18]).…”

Section: Introductionmentioning

confidence: 99%

A Probability Mass Function for Various Shapes of the Failure Rates, Asymmetric and Dispersed Data with Applications to Coronavirus and Kidney Dysmorphogenesis

et al. 2021

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In this article, a discrete analogue of an extension to a two-parameter half-logistic model is proposed for modeling count data. The probability mass function of the new model can be expressed as a mixture representation of a geometric model. Some of its statistical properties, including hazard rate function, moments, moment generating function, conditional moments, stress-strength analysis, residual entropy, cumulative residual entropy and order statistics with its moments, are derived. It is found that the new distribution can be utilized to model positive skewed data, and it can be used for analyzing equi- and over-dispersed data. Furthermore, the hazard rate function can be either decreasing, increasing or bathtub. The parameter estimation through the classical point of view has been performed using the method of maximum likelihood. A detailed simulation study is carried out to examine the outcomes of the estimators. Finally, two distinctive real data sets are analyzed to prove the flexibility of the proposed discrete distribution.

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Exponentiated half‐logistic Weibull distribution with reliability inference

El‐Awady,

El‐Monsef,

Elbaz

2024

Quality & Reliability Eng

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This paper presents an in‐depth analysis of the exponentiated half‐logistic Weibull (EHLW) distribution, investigating its fundamental statistical properties and exploring parameters estimation using both maximum likelihood and Bayesian approaches. Specifically, our focus centers on the analysis of stress–strength reliability, denoted as , where the strength variable X follows EHLW distribution, and the stress variable Y follows either Weibull distribution or the EHLW distribution. The estimation of the parameter R is discussed in both scenarios, employing both Maximum Likelihood and Bayesian approaches. Furthermore, we calculate that the asymptotic confidence interval, percentile bootstrap interval, and the highest probability density credible interval are obtained for the stress–strength parameter R. In order to assess the efficiency of these estimation techniques, simulation studies are conducted, providing valuable insights into the performance of each estimation approach. Finally, the proposed reliability model is applied to real datasets, highlighting its practical significance.

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A study of stress-strength reliability using a generalization of power transformed half-logistic distribution

Cited by 18 publications

References 15 publications

An additive power‐transformed half‐logistic model and its applications in reliability

An additive power‐transformed half‐logistic model and its applications in reliability

A Probability Mass Function for Various Shapes of the Failure Rates, Asymmetric and Dispersed Data with Applications to Coronavirus and Kidney Dysmorphogenesis

Exponentiated half‐logistic Weibull distribution with reliability inference

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