Adaptive Progressive Censoring

Cramer, Erhard; Iliopoulos, George

doi:10.1007/978-3-319-25433-3_5

Cited by 10 publications

(4 citation statements)

References 15 publications

(23 reference statements)

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“…In the above progressive censoring schemes, the censoring plan is in principal prefixed before the start of the life test. General approaches to choose the censoring design dependent on the measurements and the already applied censoring numbers have been proposed in Cramer and Iliopoulos (2010, 2015). Details on the distributional properties as well as basic inferential results can be found in these papers.…”

Section: Censoring Mechanismsmentioning

confidence: 99%

Ordered and censored lifetime data in reliability: An illustrative review

Cramer

2021

WIREs Computational Stats

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Section: Censoring Mechanismsmentioning

confidence: 99%

Ordered and censored lifetime data in reliability: An illustrative review

Cramer

2021

WIREs Computational Stats

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“…[] pointed out that this model is a particular case of APC. For a general account to adaptive progressive censoring, we refer to .…”

Section: Progressive Censoringmentioning

confidence: 99%

ProgressiveType‐II censoring and coherent systems

Cramer

Navarro

2015

Naval Research Logistics

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Abstract:A new connection between the distribution of component failure times of a coherent system and (adaptive) progressively Type-II censored order statistics is established. Utilizing this property, we develop inferential procedures when the data is given by all component failures until system failure in two scenarios: In the case of complete information, we assume that the failed component is also observed whereas in the case of incomplete information, we have only information about the failure times but not about the components which have failed. In the first setting, we show that inferential methods for adaptive progressively Type-II censored data can directly be applied to the problem. For incomplete information, we face the problem that the corresponding censoring plan is not observed and that the available inferential procedures depend on the knowledge of the used censoring plan. To get estimates for distributional parameters, we propose maximum likelihood estimators which can be obtained by solving the likelihood equations directly or via an Expectation-Maximization-algorithm type procedure. For an exponential distribution, we discuss also a linear estimator to estimate the mean. Moreover, we establish exact distributions for some estimators in the exponential case which can be used, for example, to construct exact confidence intervals. The results are illustrated by a five component bridge system.

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“…Therefore, inferential results obtained in the non‐adaptive model can be directly applied in the adaptive model (for more details as well as statistical implications of this property, see Remark 3.2). An extension including also (adaptive) Type‐I progressive censoring has been developed in Cramer and Iliopoulos (2015). Yan et al (2021) proposed a modification of the Ng–Kundu–Chan model called improved adaptive progressive Type‐II censoring scheme (see also Dutta and Kayal (2021)).…”

Section: Introductionmentioning

confidence: 99%

Generalized Ng–Kundu–Chan model of adaptive progressive Type‐II censoring and related inference

Schmiedt,

Cramer

2023

Naval Research Logistics

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The model of adaptive progressive Type‐II censoring introduced by Ng et al. (2009) (referred to as Ng–Kundu–Chan model) is extended to allow switching from a given initial censoring plan to any arbitrary given plan of the same length. In this generalized model, the joint distribution of the failure times and the corresponding likelihood function is derived. It is illustrated that the computation of maximum likelihood and Bayesian estimates are along the same lines as for standard progressive Type‐II censoring. However, the distributional properties of the estimators will usually be different since the censoring plan actually applied in the (generalized) Ng–Kundu–Chan model is random. As already mentioned in Cramer and Iliopoulos (2010), we directly show that the normalized spacings are independent and identically exponentially distributed. However, it turns out that the spacings themselves are generally dependent with mixtures of exponential distributions as marginals. These results are used to study linear estimators. Finally, we propose an algorithm for generating random numbers in the generalized Ng–Kundu–Chan model and present some simulation results. The results obtained also provide new findings in the original Ng–Kundu–Chan model; the corresponding implications are highlighted.

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Adaptive Progressive Censoring

Cited by 10 publications

References 15 publications

Ordered and censored lifetime data in reliability: An illustrative review

Ordered and censored lifetime data in reliability: An illustrative review

ProgressiveType‐II censoring and coherent systems

Generalized Ng–Kundu–Chan model of adaptive progressive Type‐II censoring and related inference

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