Skip to main content
SpringerLink
Log in

Robust Statistical Inference for One-Shot Devices Based on Density Power Divergences: An Overview

  • Chapter
  • First Online:
Methodology and Applications of Statistics

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

In this chapter, we provide a detailed review of divergence-based robust inferential methods for one-shot device testing under different lifetime distributions. Proposed estimators and Wald-type tests are shown to possess a more robust behavior than the classical maximum likelihood estimator (MLE) and Wald test. Some simulation results and real data examples are also presented to illustrate the methods detailed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Aerts, S., Haesbroeck, G.: Robust asymptotic tests for the equality of multivariate coefficients of variation. Test 26(1), 163–187 (2017)

    Article  MathSciNet  Google Scholar 

  • Balakrishnan, N., Castilla, E., Martín, N., Pardo, L.: Robust estimators for one-shot device testing data under gamma lifetime model with an application to a tumor toxicological data. Metrika 82(8), 991–1019 (2019a)

    Google Scholar 

  • Balakrishnan, N., Castilla, E., Martín, N., Pardo, L.: Robust estimators and test statistics for one-shot device testing under the exponential distribution. IEEE Trans. Inf. Theory 65(5), 3080–3096 (2019b)

    Google Scholar 

  • Balakrishnan, N., Castilla, E., Martín, N., Pardo, L.: Robust inference for one-shot device testing data under exponential lifetime model with multiple stresses. Qual. Reliab. Eng. Int. 36(6), 1916–1930 (2020a).

    Google Scholar 

  • Balakrishnan, N., Castilla, E., Martín, N., Pardo, L.: Robust inference for one-shot device testing data under Weibull lifetime model. IEEE Trans. Reliab. (2020b). https://doi.org/10.1109/TR.2019.2954385

  • Balakrishnan, N., Castilla, E., Martín, N., Pardo, L.: Divergence-based robust inference under proportional hazards model for one-shot device life-test IEEE transactions on Reliability (2021). https://doi.org/10.1109/TR.2021.3062289

  • Balakrishnan, N., Castilla, E., Martín, N., Pardo, L.: Power divergence approach for one-shot device testing under competing risk (2020d). arXiv:2004.13372

  • Balakrishnan, N., Ling, M.H.: EM algorithm for one-shot device testing under the exponential distribution. Comput. Stat. & Data Anal. 56(3), 502–509 (2012a)

    Google Scholar 

  • Balakrishnan, N., Ling, M.H.: Multiple-stress model for one-shot device testing data under exponential distribution. IEEE Trans. Reliab. 61(3), 809–821 (2012b)

    Google Scholar 

  • Balakrishnan, N., Ling, M.H.: Expectation maximization algorithm for one shot device accelerated life testing with Weibull lifetimes, and variable parameters over stress. IEEE Trans. Reliab. 62(2), 537–551 (2013)

    Article  Google Scholar 

  • Balakrishnan, N., Ling, M.H.: Gamma lifetimes and one-shot device testing analysis. Reliab. Eng. & Syst. Safety 126, 54–64 (2014)

    Article  Google Scholar 

  • Balakrishnan, N., So, H.Y., Ling, M.H.: A Bayesian approach for one-shot device testing with exponential lifetimes under competing risks. IEEE Trans. Reliab. 65(1), 469–485 (2015a)

    Google Scholar 

  • Balakrishnan, N., So, H.Y., Ling, M.H.: EM algorithm for one-shot device testing with competing risks under Weibull distribution. IEEE Trans. Reliab. 65(2), 973–991 (2015b)

    Google Scholar 

  • Basu, A., Harris, I.R., Hjort, N.L., Jones, M.: Robust and efficient estimation by minimising a density power divergence. Biometrika 85(3), 549–559 (1998)

    Article  MathSciNet  Google Scholar 

  • Basu, A., Mandal, A., Martin, N., Pardo, L.: Generalized Wald-type tests based on minimum density power divergence estimators. Statistics 50(1), 1–26 (2016)

    Article  MathSciNet  Google Scholar 

  • Basu, A., Ghosh, A., Martin, N., Pardo, L.: Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator. Metrika 81(5), 493–522 (2018)

    Article  MathSciNet  Google Scholar 

  • Crowder, M.: “Competing risks,” Encyclopedia of Actuarial Science, vol. 1. Wiley, Huboken (2006)

    Google Scholar 

  • Fan, T.-H., Balakrishnan, N., Chang, C.-C.: The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing. J. Stat. Comput. Simul. 79(9), 1143–1154 (2009)

    Article  MathSciNet  Google Scholar 

  • Ghosh, A., Basu, A.: Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression. Electr. J. Stati. 7, 2420–2456 (2013)

    MathSciNet  MATH  Google Scholar 

  • Ghosh, A., Basu, A.: Robust bounded influence tests for independent non-homogeneous observations. Stat. Sinica 28(3), 1133–1155 (2018)

    MathSciNet  MATH  Google Scholar 

  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions. Wiley, New York (1986)

    Google Scholar 

  • Husak, G.J., Michaelsen, J., Funk, C.: Use of the gamma distribution to represent monthly rainfall in Africa for drought monitoring applications. Int. J. Climatol.: J. R. Meteorol. Soc. 27(7), 935–944 (2007)

    Article  Google Scholar 

  • Kodell, R., Nelson, C.: An illness-death model for the study of the carcinogenic process using survival/sacrifice data. Biometrics 267–277 (1980)

    Google Scholar 

  • Kullback, S., Leibler, R.: On information and sufficiency. Ann. Math. Stat 22, 79–86 (1951)

    Article  MathSciNet  Google Scholar 

  • Kwon, K., Frangopol, D.M.: Bridge fatigue reliability assessment using probability density functions of equivalent stress range based on field monitoring data. Int. J. Fatigue 32(8), 1221–1232 (2010)

    Article  Google Scholar 

  • Ling, M.H., So, H.Y., Balakrishnan, N.: Likelihood inference under proportional hazards model for one-shot device testing. IEEE Trans. Reliab. 65(1), 446–458 (2015)

    Article  Google Scholar 

  • Meeker, W.Q., Escobar, L.A., Lu, C.J.: Accelerated degradation tests: modeling and analysis. Technometrics 40(2), 89–99 (1998)

    Article  Google Scholar 

  • Meeter, C.A., Meeker, W.Q.: Optimum accelerated life tests wth a nonconstant scale parameter. Technometrics 36(1), 71–83 (1994)

    MATH  Google Scholar 

  • Newby, M.: Monitoring and maintenance of spares and one shot devices. Reliab. Eng. & Syst. Safety 93(4), 588–594 (2008)

    Article  Google Scholar 

  • Ng, H.K.T., Chan, P., Balakrishnan, N.: Estimation of parameters from progressively censored data using EM algorithm. Comput. Stat. & Data Anal. 39(4), 371–386 (2002)

    Article  MathSciNet  Google Scholar 

  • Nogueira, E., Vázquez, M., Núñez, N.: Evaluation of AlGaInP LEDs reliability based on accelerated tests. Microelectr. Reliab. 49(9–11), 1240–1243 (2009)

    Article  Google Scholar 

  • Olwell, D., Sorell, A.: Warranty calculations for missiles with only current-status data, using Bayesian methods. In: Annual Reliability and Maintainability Symposium. 2001 Proceedings. International Symposium on Product Quality and Integrity (Cat. No. 01CH37179), pp. 133–138, IEEE (2001)

    Google Scholar 

  • Rigdon, S.E., Englert, B.R., Lawson, I.A., Borror, C.M., Montgomery, D.C., Pan, R.: Experiments for reliability achievement. Qual. Eng. 25(1), 54–72 (2012)

    Article  Google Scholar 

  • Ronchetti, E., Rousseeuw, P.: The influence curve for tests. In: Research Report No 21, Fachgruppe für Statistik ETH Zürich (1979)

    Google Scholar 

  • Seaborn, J.B.: The confluent hypergeometric function. In: Hypergeometric Functions and Their Applications, pp. 41–51, Springer (1991)

    Google Scholar 

  • So, H.Y.: Some Inferential Results for One-Shot Device Testing Data Analysis. Ph.D. thesis, McMaster University, Hamilton, Ontario, Canada (2016)

    Google Scholar 

  • Tseng, S.-T., Balakrishnan, N., Tsai, C.-C.: Optimal step-stress accelerated degradation test plan for gamma degradation processes. IEEE Trans. Reliab. 58(4), 611–618 (2009)

    Article  Google Scholar 

  • Vázquez, M., Núñez, N., Nogueira, E., Borreguero, A.: Degradation of AlInGaP red LEDs under drive current and temperature accelerated life tests. Microelectr. Reliab. 50(9–11), 1559–1562 (2010)

    Article  Google Scholar 

  • Warwick, J., Jones, M.: Choosing a robustness tuning parameter. J. Stat. Comput. Simul. 75(7), 581–588 (2005)

    Article  MathSciNet  Google Scholar 

  • Zelen, M.: Factorial experiments in life testing. Technometrics 1(3), 269–288 (1959)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank the referees for carefully reading our manuscript and for giving such valuable comments which substantially improved the paper. This research has been partially supported by Grant PGC2018-095194-B-100 from Miniserio de Ciencia Innovaci Universidades (Spanish goverment).

Author information

Authors and Affiliations

  1. McMaster University, Hamilton, ON, Canada

    N. Balakrishnan

  2. Complutense University of Madrid, Madrid, Spain

    E. Castilla & L. Pardo

Authors
  1. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Castilla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Pardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Balakrishnan .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of California, Riverside, CA, USA

    Barry C. Arnold

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

    Narayanaswamy Balakrishnan

  3. NOVA School of Science and Technology, NOVA University of Lisbon, Caparica, Portugal

    Carlos A. Coelho

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Balakrishnan, N., Castilla, E., Pardo, L. (2021). Robust Statistical Inference for One-Shot Devices Based on Density Power Divergences: An Overview. In: Arnold, B.C., Balakrishnan, N., Coelho, C.A. (eds) Methodology and Applications of Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-83670-2_1

Download citation

Publish with us

Policies and ethics

Search

Navigation