Nonparametric inference for sequential k-out-of-n systems

Abstract:The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k-out-of-n systems. In particular, we show that they are not necessarily hazard rate ordered.

show abstract

“…General properties and other practical applications of SOS models can be found in Refs. [1,4,[10][11][12]16,19] and in the references therein.…”

Section: Introductionmentioning

confidence: 99%

Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

View full text Add to dashboard Cite

show abstract

“…For further details on sequential order statistics, in particular concerning statistical inference, we refer to, e.g., Kamps (2006), Cramer and Kamps (1996, 2001a,b, 2003, Balakrishnan, Beutner and Kamps (2008), Beutner (2008Beutner ( , 2010, Kamps (2009), Burkschat (2009), Burkschat andLenz (2009), Bedbur (2010), Bedbur, Beutner and Kamps (2012), Burkschat, Kamps and Kateri (2010), and Balakrishnan, Kamps and Kateri (2012).…”

Section: Statistical Model and Preliminariesmentioning

confidence: 99%

Estimating scale parameters under an order statistics prior

Burkschat

Kamps

Kateri

2013

Statistics &Amp; Risk Modeling

View full text Add to dashboard Cite

show abstract

“…Nonparametric estimation of the cumulative hazard rate function, the reliability function and the quantile function of progressively Type II censored order statistics as well as homogeneity tests for two distribution functions in a sampling situation different from that one considered in Alvarez-Andrade and Bordes (2004), Alvarez-Andrade et al (2007), and Bordes (2004) can be found in Beutner (2007a).…”

Section: Nonparametricsmentioning

confidence: 99%

Comments on: Progressive censoring methodology: an appraisal

Kamps

Cramer

2007

TEST

View full text Add to dashboard Cite

Since the mid-90s, when Dr. Balakrishnan together with coauthors Sandhu 1995, 1996; Viveros and Balakrishnan 1994) revisited progressive censoring, a huge number of papers were published dealing with both theoretical and practical aspects. It is one of Dr. Balakrishnan's major scientific merits to reconsider the model of progressive censoring, to see the potential in it, and to advance the methods and properties. His contributions illustrate that progressively Type II censored order statistics are a very useful and powerful model. They lead to a toolbox of properties and statistical procedures, which make the model really applicable. His monograph (Balakrishnan and Aggarwala 2000) on this topic jointly written with R. Aggarwala clearly remains a basic reference work. Now Dr. Balakrishnan provides us with an excellent up-to-date survey on progressive censoring. It impressively illustrates, what has been established in the last decade. We are very pleased to comment on selected topics and to supplement this work, which, of course, can not be exhaustive in some 40 pages. We refer to Dr. Balakrishnan's paper by [B], throughout. Model and distribution theoryThe author points out that progressively Type II censored order statistics are a particular case of generalized order statistics (see Kamps 1995) choosing γ r = k + m − r + m−1 j =r R j , 1 ≤ r ≤ m and k = R m + 1. Hence, the distribution of any choice of progressively Type II censored order statistics can be viewed as a marginal distribution of respective generalized order statistics (see, e.g., (2) in [B]). Thus, the results This comment refers to the invited paper available at: http://dx.

show abstract

Nonparametric inference for sequential k-out-of-n systems

Abstract: Sequential k-out-of-n systems, Nonparametric estimation, Nonparametric hypothesis testing, Nelson–Aalen estimator, Martingale methods,

Cited by 33 publications

References 15 publications

Coherent systems based on sequential order statistics

Coherent systems based on sequential order statistics

Estimating scale parameters under an order statistics prior

Comments on: Progressive censoring methodology: an appraisal

Contact Info

Product

Resources

About