Statistical inference for component lifetime distribution from coherent system lifetimes under a proportional reversed hazard model

Fallah, A.; Asgharzadeh, A.; Ng, Hon Keung Tony

doi:10.1080/03610926.2020.1824275

Cited by 9 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An interesting representation of the system lifetime T of a coherent system with n components in terms of order statistics has been obtained by Samaniego (1985) (see also Kochar et al, 1999; Navarro et al, 2008; Samaniego, 2007), that is,

P ((), T \leq t) goodbreak= \sum_{j = 1}^{n} s_{j} F_{j : n} ((), t), t \in normalℝ,

where,

s_{1}, \dots, s_{n}

form a pmf on

({},,, 1, \dots, n)

, the so‐called signature. Inferential results have been established by, for example, Bhattacharya and Samaniego (2010), Balakrishnan et al (2012, 2011), Yang et al (2016), and Fallah et al (2020). An application of progressive censoring in this area has been presented in Cramer and Navarro (2016, 2015), Jablonka et al (2019), and Hermanns (2019).…”

Section: Some Supplementary Remarksmentioning

confidence: 90%

“…where, s 1 , …,s n form a pmf on 1,…, n f g, the so-called signature. Inferential results have been established by, for example, Bhattacharya and Samaniego (2010), Balakrishnan et al ( , 2011, Yang et al (2016), andFallah et al (2020). An application of progressive censoring in this area has been presented in Navarro (2016, 2015), Jablonka et al (2019), andHermanns (2019).…”

Section: K-out-of-n Systems: Coherent Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Ordered and censored lifetime data in reliability: An illustrative review

Cramer

2021

WIREs Computational Stats

View full text Add to dashboard Cite

show abstract

P ((), T \leq t) goodbreak= \sum_{j = 1}^{n} s_{j} F_{j : n} ((), t), t \in normalℝ,

where,

s_{1}, \dots, s_{n}

form a pmf on

({},,, 1, \dots, n)

Section: Some Supplementary Remarksmentioning

confidence: 90%

Section: K-out-of-n Systems: Coherent Systemsmentioning

confidence: 99%

Ordered and censored lifetime data in reliability: An illustrative review

Cramer

2021

WIREs Computational Stats

View full text Add to dashboard Cite

show abstract

“…Wang et al (2015) developed estimation methodology for the confidence intervals of the family of PRHR distributions based on lower record values. A proportional causespecific reversed hazards model was introduced by Sankaran and Anjana (2016) and Fallah et al (2021) proposed statistical inference for component lifetime distribution from coherent system lifetimes under a PRHR model. Baratnia and Doostparast (2021) proposed a new statistical method for one-way classification which is based on the RHR function of the response variable and Khan et al (2021) Kalbfleisch and Lawless (1991) or Andersen et al (2012).…”

Section: Proposed Modelmentioning

confidence: 99%

Resilience family of receiver operating characteristic curves

Khan¹

2022

Preprint

View full text Add to dashboard Cite

A new semiparametric model of the ROC curve based on the resilience family or proportional reversed hazard family is proposed which is an alternative to the existing models. The resulting ROC curve and its summary indices (such as area under the curve (AUC) and Youden index) have simple analytic forms. The partial likelihood method is applied to estimate the ROC curve. Moreover, the estimation methodologies of the resilience family of the ROC curve have been developed based on AUC estimators exploiting Mann-Whitney statistics and the Rojo approach. A simulation study has been carried out to assess the performance of all considered estimators. Real data from the American National Health and Nutrition Examination Survey (NHANES) has been analysed in detail based on the proposed model and the usual binormal model prevalent in the literature. Real data in the context of brain injury-related biomarkers is also analysed in order to compare our model with the Lehmann family of the ROC curves. Finally, we show that the proposed model may be applicable in the misspecification scenario through a Ducheme muscular dystrophy data.

show abstract

“…Several results for this kind of data have been obtained in the literature under different assumptions/models. For example, in [8], a parametric proportional reversed hazard rate model is assumed for the common distribution of the components while a proportional hazard rate model is assumed in [16]. A load-sharing model with active redundancy is analyzed in [10].…”

Section: Introductionmentioning

confidence: 99%

Method-of-moments estimators of a scale parameter based on samples from a coherent system

Macci

Navarro

2023

Prob. Eng. Inf. Sci.

View full text Add to dashboard Cite

In this paper, we study the estimation of a scale parameter from a sample of lifetimes of coherent systems with a fixed structure. We assume that the components are independent and identically distributed having a common distribution which belongs to a scale parameter family. Some results are obtained as well for dependent (exchangeable) components. To this end, we will use the representations for the distribution function of a coherent system based on signatures. We prove that the efficiency of the estimators depends on the structure of the system and on the scale parameter family. In the dependence case, it also depends on the baseline copula function.

show abstract

Statistical inference for component lifetime distribution from coherent system lifetimes under a proportional reversed hazard model

Cited by 9 publications

References 21 publications

Ordered and censored lifetime data in reliability: An illustrative review

Ordered and censored lifetime data in reliability: An illustrative review

Resilience family of receiver operating characteristic curves

Method-of-moments estimators of a scale parameter based on samples from a coherent system

Contact Info

Product

Resources

About