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Estimating component characteristics from system failure‐time data

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  • Debasis Bhattacharya
  • Francisco J. Samaniego

Abstract

Suppose that failure times are available from a random sample of N systems of a given, fixed design with components which have i.i.d. lifetimes distributed according to a common distribution F. The inverse problem of estimating F from data on observed system lifetimes is considered. Using the known relationship between the system and component lifetime distributions via signature and domination theory, the nonparametric maximum likelihood estimator $ \hat{ \bar{F}} $N(t) of the component survival function $ \bar{F} $(t) is identified and shown to be accessible numerically in any application of interest. The asymptotic distribution of $ \hat{ \bar{F}} $N(t) is also identified, facilitating the construction of approximate confidence intervals for $ \bar{F} $(t) for N sufficiently large. Simulation results for samples of size N = 50 and N = 100 for a collection of five parametric lifetime models demonstrate the utility of the recommended estimator. Possible extensions beyond the i.i.d. framework are discussed in the concluding section. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:4:p:380-389
    DOI: 10.1002/nav.20407
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    1. 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, December.
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    2. Jorge Navarro & Marco Burkschat, 2011. "Coherent systems based on sequential order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 123-135, March.
    3. Jorge Navarro & Rafael Rubio, 2011. "A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 478-489, August.
    4. 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.
    5. 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.
    6. Jian Zhang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2015. "Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 550-563, October.
    7. Zhu, Xiaojun & Balakrishnan, N., 2023. "Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    8. Yandan Yang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2019. "Expectation–maximization algorithm for system-based lifetime data with unknown system structure," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 69-98, March.
    9. Jingjing Qu & Hon Keung Tony Ng & Chul Moon, 2024. "Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data," Computational Statistics, Springer, vol. 39(6), pages 3007-3029, September.
    10. Mohammad Nourmohammadi & Mohammad Jafari Jozani & Brad C. Johnson, 2020. "Parametric Inference Using Nomination Sampling with an Application to Mercury Contamination in Fish," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 115-146, February.
    11. Jia, Xujie & Shen, Jingyuan & Xu, Fanqi & Ma, Ruihong & Song, Xueying, 2019. "Modular decomposition signature for systems with sequential failure effect," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 435-444.

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