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Debasis Kundu - One of the best experts on this subject based on the ideXlab platform.

  • on the joint type ii progressive Censoring Scheme
    Communications in Statistics-theory and Methods, 2020
    Co-Authors: Shuvashree Mondal, Debasis Kundu
    Abstract:

    Recently the progressive Censoring Scheme has been extended for two or more populations. In this article we consider the joint Type-II progressive Censoring (JPC) Scheme for two populations when th...

  • Exact inference on multiple exponential populations under a joint type-II progressive Censoring Scheme
    Statistics, 2019
    Co-Authors: Shuvashree Mondal, Debasis Kundu
    Abstract:

    ABSTRACTRecently Mondal and Kundu [Mondal S, Kundu D. A new two sample type-II progressive Censoring Scheme. Commun Stat Theory Methods. 2018. doi:10.1080/03610926.2018.1472781] introduced a Type-I...

  • Point and Interval Estimation of Weibull Parameters Based on Joint Progressively Censored Data
    Sankhya B, 2019
    Co-Authors: Shuvashree Mondal, Debasis Kundu
    Abstract:

    The analysis of progressively censored data has received considerable attention in the last few years. In this paper, we consider the joint progressive Censoring Scheme for two populations. It is assumed that the lifetime distribution of the items from the two populations follows Weibull distribution with the same shape but different scale parameters. Based on the joint progressive Censoring Scheme, first, we consider the maximum likelihood estimators of the unknown parameters whenever they exist. We provide the Bayesian inferences of the unknown parameters under a fairly general priors on the shape and scale parameters. The Bayes estimators and the associated credible intervals cannot be obtained in closed form, and we propose to use the importance sampling technique to compute the same. Further, we consider the problem when it is known a priori that the expected lifetime of one population is smaller than the other. We provide the order-restricted classical and Bayesian inferences of the unknown parameters. Monte Carlo simulations are performed to observe the performances of the different estimators and the associated confidence and credible intervals. One real data set has been analyzed for illustrative purpose.

  • On the joint Type-II progressive Censoring Scheme
    Communications in Statistics - Theory and Methods, 2019
    Co-Authors: Shuvashree Mondal, Debasis Kundu
    Abstract:

    AbstractRecently the progressive Censoring Scheme has been extended for two or more populations. In this article we consider the joint Type-II progressive Censoring (JPC) Scheme for two populations...

  • A new two sample type-II progressive Censoring Scheme
    Communications in Statistics - Theory and Methods, 2018
    Co-Authors: Shuvashree Mondal, Debasis Kundu
    Abstract:

    In this paper we introduce a new type-II progressive Censoring Scheme for two samples. It is observed that the proposed Censoring Scheme is analytically more tractable than the existing joint progr...

Narayanaswamy Balakrishnan - One of the best experts on this subject based on the ideXlab platform.

  • Multi-criteria-based optimal life-testing plans under hybrid Censoring Scheme
    TEST, 2019
    Co-Authors: Ritwik Bhattacharya, Graceila González Farías, Baidya Nath Saha, Narayanaswamy Balakrishnan
    Abstract:

    In designing an optimal life-testing experiment under Censoring setup, the design parameters are usually chosen by optimizing a suitable criterion function. The criterion function is chosen by using either a variance-based or a cost-based model, and sometimes a combination of both these factors. However, it is an optimization problem with a single objective function. In this article, a multi-criteria-based optimization problem is considered in the context of hybrid censored life-testing experiment. Both the variance and the cost factors are optimized simultaneously. The exact distribution of the maximum likelihood estimate of the lifetime model parameter is used to construct the optimality criteria. All the proposed methods are illustrated through numerical examples. One dataset is finally analyzed for real-life applications.

  • Hybrid Censoring
    Computational Statistics & Data Analysis, 2013
    Co-Authors: Narayanaswamy Balakrishnan, Debasis Kundu
    Abstract:

    A hybrid Censoring Scheme is a mixture of Type-I and Type-II Censoring Schemes. In this review, we first discuss Type-I and Type-II hybrid Censoring Schemes and associated inferential issues. Next, we present details on developments regarding generalized hybrid Censoring and unified hybrid Censoring Schemes that have been introduced in the literature. Hybrid Censoring Schemes have been adopted in competing risks set-up and in step-stress modeling and these results are outlined next. Recently, two new Censoring Schemes, viz., progressive hybrid Censoring and adaptive progressive Censoring Schemes have been introduced in the literature. We discuss these Censoring Schemes and describe inferential methods based on them, and point out their advantages and disadvantages. Determining an optimal hybrid Censoring Scheme is an important design problem, and we shed some light on this issue as well. Finally, we present some examples to illustrate some of the results described here. Throughout the article, we mention some open problems and suggest some possible future work for the benefit of readers interested in this area of research.

  • A very flexible hybrid Censoring Scheme and its Fisher information
    Journal of Statistical Computation and Simulation, 2012
    Co-Authors: Sangun Park, Narayanaswamy Balakrishnan
    Abstract:

    Various hybrid Censoring Schemes, which are mixtures of Type I and Type II Censoring Schemes, have been suggested for flexibility in termination time and efficiency level. In this paper, we propose a general hybrid Censoring Scheme to be a Censoring Scheme with Type I or Type II bounds which provides more flexible termination time and efficiency level. The Type I hybrid Censoring Scheme can be interpreted as a Type I Censoring Scheme with a Type II upper bound, while the generalized Type I hybrid Censoring can be interpreted as a Type I Censoring Scheme with Type II lower and upper bounds. The bounds involved in the termination can also be a hybrid. We then show that the unified hybrid Censoring Scheme of Balakrishnan et al. [Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution, J. Statist. Comput. Simul. 78 (2008), pp. 475–488] is a special case of the general hybrid Censoring Scheme. Finally, we discuss several new hybrid Censoring Schemes and evaluate ...

  • Pitman closeness as a criterion for the determination of the optimal progressive Censoring Scheme
    Statistical Methodology, 2012
    Co-Authors: William Volterman, Katherine F. Davies, Narayanaswamy Balakrishnan
    Abstract:

    Abstract Selecting the optimal progressive Censoring Scheme for the exponential distribution according to Pitman closeness criterion is discussed. For small sample sizes the Pitman closeness probabilities are calculated explicitly, and it is shown that the optimal progressive Censoring Scheme is the usual Type-II right Censoring case. It is conjectured that this to be the case for all sample sizes. A general algorithm is also presented for the numerical computation of the Pitman closeness probabilities between any two progressive Censoring Schemes of the same size.

  • On simple calculation of the Fisher information in hybrid Censoring Schemes
    Statistics & Probability Letters, 2009
    Co-Authors: Sangun Park, Narayanaswamy Balakrishnan
    Abstract:

    A hybrid Censoring Scheme is a mixture of Type-I and Type-II Censoring Schemes. In this paper, we present two interesting results which are useful in deriving the Fisher information along with the expected Censoring times and expected numbers of failures in hybrid and generalized hybrid Censoring Schemes. We first interpret the Type-II Censoring Scheme in terms of a Type-I Censoring Scheme so that the Censoring time in hybrid Censoring Schemes can be regarded as a mixture of Type-I Censoring times. We then exploit this mixture form to derive the Fisher information in hybrid censored Schemes. We further establish an addition rule underlying Type-I and Type-II hybrid Censoring Schemes and derive the Fisher information in the case of generalized hybrid Censoring Schemes. Finally, we present an example to illustrate the results developed here.

Tsang-yi Wang - One of the best experts on this subject based on the ideXlab platform.

  • A Neyman-Pearson Type Sensor Censoring Scheme for Compressive Distributed Sparse Signal Recovery
    2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2018
    Co-Authors: Jwo-yuh Wu, Ming-hsun Yang, Tsang-yi Wang
    Abstract:

    To strike a balance between energy efficiency and data quality control, this paper proposes a Neyman-Pearson type sensor Censoring Scheme for distributed sparse signal recovery via compressive-sensing based on wireless sensor networks. In the proposed approach, each sensor node employs a sparse sensing vector with known support for data compression, meanwhile enabling making local inference about the unknown support of the sparse signal vector of interest. This naturally leads to a ternary Censoring protocol, whereby each sensor (i) directly transmits the real-valued compressed data if the sensing vector support is detected to be overlapped with the signal support, (ii) sends a one-bit hard decision if empty support overlap is inferred, (iii) keeps silent if the measurement is judged to be uninformative. Our design then aims at minimizing the error probability that empty support overlap is decided but otherwise is true, subject to the constraints on a tolerable false-alarm probability that non-empty support overlap is decided but otherwise is true, and a target Censoring rate. We derive a closed-form formula of the optimal Censoring rule; a low complexity implementation using bi-section search is also developed. Computer simulations are used to illustrate the performance of the proposed Scheme.

  • SAM - A Neyman-Pearson Type Sensor Censoring Scheme for Compressive Distributed Sparse Signal Recovery
    2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM), 2018
    Co-Authors: Ming-hsun Yang, Tsang-yi Wang
    Abstract:

    To strike a balance between energy efficiency and data quality control, this paper proposes a Neyman-Pearson type sensor Censoring Scheme for distributed sparse signal recovery via compressive-sensing based on wireless sensor networks. In the proposed approach, each sensor node employs a sparse sensing vector with known support for data compression, meanwhile enabling making local inference about the unknown support of the sparse signal vector of interest. This naturally leads to a ternary Censoring protocol, whereby each sensor (i) directly transmits the real-valued compressed data if the sensing vector support is detected to be overlapped with the signal support, (ii) sends a one-bit hard decision if empty support overlap is inferred, (iii) keeps silent if the measurement is judged to be uninformative. Our design then aims at minimizing the error probability that empty support overlap is decided but otherwise is true, subject to the constraints on a tolerable false-alarm probability that non-empty support overlap is decided but otherwise is true, and a target Censoring rate. We derive a closed-form formula of the optimal Censoring rule; a low complexity implementation using bi-section search is also developed. Computer simulations are used to illustrate the performance of the proposed Scheme.

  • Performance Analysis of Distributed Decision Fusion Using A Multilevel Censoring Scheme in Wireless Sensor Networks
    IEEE Transactions on Vehicular Technology, 2010
    Co-Authors: Victor W. Cheng, Tsang-yi Wang
    Abstract:

    Sensor-Censoring Schemes have been widely applied to distributed detection to achieve the goal of energy saving in limited-energy wireless sensor networks (WSNs). In the traditional Censoring Scheme, the sensor transmits data to the fusion center (FC) only when the reliability is beyond a specified threshold, and hereby, energy saving is achieved. To further exploit the energy-efficiency capability of the Censoring decision Scheme, this paper proposes a new multilevel sensor-Censoring Scheme. As opposed to our earlier proposed three-region Censoring Scheme, the number of Censoring levels in the proposed Scheme is not restricted. A criterion on computing the reliability of the observation in each region is quantitatively determined, which controls the power of the signal transmitted to the FC. When the observation falls within the region with high reliability, the power of the transmitted signal is high, and vice versa. Both soft- and hard-decision fusion rules under the considered multilevel Censoring strategy are investigated. For a given fusion rule, the main problem of this work is to minimize the error probability of the global decisions made by the FC by obtaining the best region allocation on the observation, which corresponds to the optimum multilevel Censoring regions. The performance of the proposed multilevel Censoring Scheme is examined in terms of both energy saving and error performance. We compare the multilevel Censoring Scheme with the conventional Scheme, which censors no sensor observations. The results show that the multilevel Censoring Scheme not only offers us a more flexible design of the Censoring strategy but consumes much less energy as well, compared with the conventional Scheme when the same error probability constraint is given. In addition, the obtained result shows that the superiority of the multilevel Censoring Scheme becomes more remarkable when the signal strength of the sensor observations is small.

Laurent Bordes - One of the best experts on this subject based on the ideXlab platform.

  • Optimal progressive Type-I interval censored Scheme under step-stress life testing
    Statistics and Its Interface, 2017
    Co-Authors: Xuejing Zhao, Laurent Bordes
    Abstract:

    The parametric estimation and optimal Censoring Scheme are considered under the progressive multi-stage Type-I Censoring Scheme as well as step-stress accelerated lifetime model. Nonparametric estimators, using the information of the observable numbers of failures and numbers of censored units at the Censoring times, are used to derive estimates of the reliability function at the Censoring times. Then two parametric estimators, the maximum likelihood and the minimum-distance, are used to estimate the unknown Euclidean parameters of a parametric model. We use D-optimality criterion to determine an optimal sequential step-stress plan under progressive Type-I Censoring. Simulation studies are also conducted to assess the finite performance of our estimators.

  • Minimum-distance parametric estimation under progressive type-I Censoring
    IEEE Transactions on Reliability, 2010
    Co-Authors: N. Balakrishnan, Laurent Bordes, Xuejing Zhao
    Abstract:

    The objective of this paper is to provide a new estimation method for parametric models under progressive Type-I Censoring. First, we propose a Kaplan-Meier nonparametric estimator of the reliability function taken at the Censoring times. It is based on the observable number of failures, and the number of censored units occurring from the progressive Censoring Scheme at the Censoring times. This estimator is then shown to asymptotically follow a normal distribution. Next, we propose a minimum-distance method to estimate the unknown Euclidean parameter of a given parametric model. This method leads to consistent, asymptotically normal estimators. The maximum likelihood estimation method based on group-censored samples is discussed next, and the efficiencies of these two methods are compared numerically. Then, based on the established results, we derive a method to obtain the optimal Type-I progressive Censoring Scheme, Finally we illustrate all these results through a Monte Carlo simulation study, and an illustrative example. © 2006 IEEE.

Ritwik Bhattacharya - One of the best experts on this subject based on the ideXlab platform.

  • Statistical inference and Bayesian optimal life-testing plans under Type-II unified hybrid Censoring Scheme
    arXiv: Statistics Theory, 2020
    Co-Authors: Tanmay Sen, Ritwik Bhattacharya, Biswabrata Pradhan, Yogesh Mani Tripathi
    Abstract:

    This article describes the inferential procedures and Bayesian optimal life-testing issues under Type-II unified hybrid Censoring Scheme. First, the explicit expressions of expected number of failures, expected duration of testing and Fisher information matrix for the unknown parameters of the underlying lifetime model are derived. Then, using these quantities, the Bayesian optimal life-testing plans are computed in subsequent section. A cost constraint D-optimal optimization problem has been formulated and the corresponding solution algorithm is provided to obtain optimal plans. Computational procedures are illustrated through numerical examples.

  • Multi-criteria-based optimal life-testing plans under hybrid Censoring Scheme
    TEST, 2019
    Co-Authors: Ritwik Bhattacharya, Graceila González Farías, Baidya Nath Saha, Narayanaswamy Balakrishnan
    Abstract:

    In designing an optimal life-testing experiment under Censoring setup, the design parameters are usually chosen by optimizing a suitable criterion function. The criterion function is chosen by using either a variance-based or a cost-based model, and sometimes a combination of both these factors. However, it is an optimization problem with a single objective function. In this article, a multi-criteria-based optimization problem is considered in the context of hybrid censored life-testing experiment. Both the variance and the cost factors are optimized simultaneously. The exact distribution of the maximum likelihood estimate of the lifetime model parameter is used to construct the optimality criteria. All the proposed methods are illustrated through numerical examples. One dataset is finally analyzed for real-life applications.

  • bayesian design of life testing plans under hybrid Censoring Scheme
    Quality and Reliability Engineering International, 2018
    Co-Authors: Ritwik Bhattacharya, Biswabrata Pradhan
    Abstract:

    This article describes Bayes design of hybrid-censored life testing plans. A design criterion based on posterior variance of quantile of suitable order is proposed. The Weibull lifetime model with gamma prior distribution on model parameters is considered for illustration. Instead of using Markov chain Monte Carlo technique to compute the posterior quantities of interest, a large sample approximation is considered, which is easy to apply. Some life testing plans are presented. The effect of different prior information on the posterior quantity of interest is studied.

  • Design of Control Chart in Presence of Hybrid Censoring Scheme
    IEEE Access, 2018
    Co-Authors: Muhammad Aslam, Ritwik Bhattacharya, Mansour Sattam Aldosari
    Abstract:

    In this paper, a new reliability testing control chart has been developed using the hybrid Censoring Scheme for the Weibull distribution. The in-control and out-of-control probabilities are estimated for the desired quality characteristic using the reliability acceptance sampling plan. The performance of the proposed chart has been evaluated by estimating the average run lengths for the shifted process under the simulation. A numerical example has been given for the practical implementation of the proposed chart. It has been observed that the proposed chart is a valuable addition in the process monitoring for the life testing of the products.

  • On optimum life-testing plans under Type-II progressive Censoring Scheme using variable neighborhood search algorithm
    TEST, 2015
    Co-Authors: Ritwik Bhattacharya, Biswabrata Pradhan, Anup Dewanji
    Abstract:

    In determination of optimum Type-II progressive Censoring Scheme, the experimenter needs to carry out an exhaustive search within the set of all admissible Censoring Schemes. The existing recommendations are only applicable for small sample sizes. The implementation of exhaustive search techniques for large sample sizes is not feasible in practice. In this article, a meta-heuristic algorithm based on variable neighborhood search approach is proposed for large sample sizes. It is found that the algorithm gives exactly the same solution for small sample sizes as the solution obtained in an exhaustive search; however, for large sample sizes, it gives near-optimum solution. We have proposed a cost function-based optimum criterion, which is scale invariant for location-scale and log-location-scale families of distribution. A sensitivity analysis is also considered to study the effect of misspecification of parameter values or cost coefficients on the optimum solution.