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Progressive Type‐II censoring and coherent systems

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  • Erhard Cramer
  • Jorge Navarro

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. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 512–530, 2015

Suggested Citation

  • Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:6:p:512-530
    DOI: 10.1002/nav.21661
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    References listed on IDEAS

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    1. Debasis Bhattacharya & Francisco J. Samaniego, 2010. "Estimating component characteristics from system failure‐time data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 380-389, June.
    2. Jorge Navarro & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2012. "Parametric inference for component distributions from lifetimes of systems with dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 487-496, October.
    3. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    4. Fischer, T. & Balakrishnan, N. & Cramer, E., 2008. "Mixture representation for order statistics from INID progressive censoring and its applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1999-2015, October.
    5. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, January.
    6. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    7. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    8. Hon Ng & Jorge Navarro & Narayanaswamy Balakrishnan, 2012. "Parametric inference from system lifetime data under a proportional hazard rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 367-388, April.
    9. Navarro, Jorge & Pellerey, Franco & Di Crescenzo, Antonio, 2015. "Orderings of coherent systems with randomized dependent components," European Journal of Operational Research, Elsevier, vol. 240(1), pages 127-139.
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