Percentile residual life orders

Franco-Pereira, Alba M.; Lillo, Rosa E.; Romo, Juan; Shaked, Moshe

doi:10.1002/asmb.825

Cited by 13 publications

(3 citation statements)

References 18 publications

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“…al. [22] proved that ≤ ℎ if for any ∈ (0, 1) we have ≤ − . Here, we define X to be smaller than Y in the -quantile residual life if order X ≤ − Y, if…”

Section: Multivariate -Quantile Residual Life Ordermentioning

confidence: 99%

Dynamic Multivariate Quantile Residual Life in Reliability Theory

Noughabi

Kayid

Abouammoh

2018

Mathematical Problems in Engineering

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We extend the univariate α-quantile residual life function to multivariate setting preserving its dynamic feature. Principal attributes of this function are derived and their relationship to the dynamic multivariate hazard rate function is discussed. A corresponding ordering, namely, α-quantile residual life order, for random vectors of lifetimes is introduced and studied. Based on the proposed ordering, a notion of positive dependency is presented. Finally, a discussion about conditions characterizing the class of decreasing multivariate α-quantile residual life functions is pointed out.

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“…al. [22] proved that ≤ ℎ if for any ∈ (0, 1) we have ≤ − . Here, we define X to be smaller than Y in the -quantile residual life if order X ≤ − Y, if…”

Section: Multivariate -Quantile Residual Life Ordermentioning

confidence: 99%

Dynamic Multivariate Quantile Residual Life in Reliability Theory

Noughabi

Kayid

Abouammoh

2018

Mathematical Problems in Engineering

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“…Properties of the PRL-p have been explored in a number of studies, e.g. see [16], [17] and [18] among others. The median residual life as a special case of the PRL-p also receives much attention, e.g.…”

Section: Preliminariesmentioning

confidence: 99%

Performance-based Burn-in for products sold with warranty

Tang

Xie

2011

2011 IEEE International Conference on Industrial Engineering and Engineering Management

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To protect users from early failures, manufacturers often use burn-in to screen out weak units and meanwhile providing warranty to customers. Some performance-based burn-in models have been proposed in the literature. However, relations between these indices are not clear. In this study, we look into this problem and reveal the internal relations between these indices. More specifically, we focus on the probability of failure within the warranty period, mean number of failures within the warranty period and the percentile residual life that maximize the warranty period given a specified proportion of field failure. It is found that there are some dual relations between these indices. An illustrative example is used to demonstrate our results.Keywords -Probability of failure, warranty, percentile of the residual life

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“…Haines and Singpurwalla (1974) introduced the α-percentile residual life (α-PRL) function describing the α-percentile or quantile of the remaining life given survival up to a certain time. Afterwards, many authors studied this reliability measure in some details, e.g., Arnold and Brockett (1983), Gupta and Longford (1984), Joe and Proschan (1984), Joe (1985), Song and Cho (1995), Lin (2009), and Franco-Pereira et al (2010a, 2010b, 2010c, 2011. This measure and specially the median residual life function (0.5-PRL function) may be a good alternative for the MRL function particularly when the underlying distribution is skewed, the data are censored, we may have some outliers in the data set, or the statement for the MRL function is very complicated or infinite.…”

Section: Introductionmentioning

confidence: 99%

On the Percentile Residual Lifetime of Parallel Systems

Noughabi

Roknabadi

Borzadaran

2014

Communications in Statistics - Theory and Methods

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In this paper, we consider a parallel system consisting of n components. Then, the percentile residual lifetime of the system given survival of at least n − r + 1, r = 1, 2, . . . , n component(s) has been introduced, and some properties of this measure have been investigated. We show that the system accommodates decreasing percentile residual lifetime function, provided the components have increasing hazard rate functions. Different parallel systems have been compared with each other in terms of the introduced measure. Furthermore, behavior of the percentile residual lifetime of the system and the components have been compared in terms of some reliability notions. Also, a characterization result has been presented.

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Percentile residual life orders

Cited by 13 publications

References 18 publications

Dynamic Multivariate Quantile Residual Life in Reliability Theory

Dynamic Multivariate Quantile Residual Life in Reliability Theory

Performance-based Burn-in for products sold with warranty

On the Percentile Residual Lifetime of Parallel Systems

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