Skip to main content

Advertisement

Springer Nature Link
Log in

Beyond precision: accelerated life testing for fuzzy life time data

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Reliability analysis comprises statistical analysis techniques that make inferences based on life time data. Swift progress has been observed in life time data analyses during the last few decades. Accelerated life testing models are regarded as the most popular techniques for engineering life time data analysis. Their main aim is to model life times under different stress levels that are more severe than the usual stress level. The existing techniques consider life times as precise measurements and do not contemplate the imprecision of observations. In fact, life time measurements are not precise quantities but more or less fuzzy. Therefore, in addition to standard statistical tools, fuzzy model approaches are also essential. The current study generalizes some parametric and nonparametric classical estimation procedures for accelerated life testing in order to accommodate both fuzziness and random variation. The proposed estimators cover both uncertainties, which make them more applicable and practicable for life time analysis. The results of fuzzy life times are considered under various stress conditions, and comparisons with precise life time analysis are further presented in examples.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Balakrishnan N, Kundu D, Ng HKT, Kannan N (2007) Point and interval estimation for a simple step-stress model with type II censoring. J Qual Technol 39(1):35–47

    Article  Google Scholar 

  • Barbato G, Germak A, Genta G, Barbato A (2013) Measurements for decision making. Measurements and basic statistics. Esculapio, Milano

    Book  Google Scholar 

  • Frühwirth-Schnatter S (1993) On fuzzy Bayesian inference. Fuzzy Sets Syst 60(1):41–58

    Article  MathSciNet  Google Scholar 

  • Gil MÁ, Hryniewicz O (2009) Statistics with imprecise data. In: Meyers RA (ed) Encyclopedia of complexity and systems science. Springer, New York, pp 8679–8690

    Google Scholar 

  • Gonzalez-Gonzalez DS, Alejo RJP, Cantú-Sifuentes M, Torres-Treviño LM, Méndez GM (2014) A non-linear fuzzy regression for estimating reliability in a degradation process. Appl Soft Comput 16:137–147

    Article  Google Scholar 

  • Huang H-Z, Zuo MJ, Sun Z-Q (2006) Bayesian reliability analysis for fuzzy lifetime data. Fuzzy Sets Syst 157(12):1674–1686

    Article  MathSciNet  Google Scholar 

  • Hung W-L, Liu Y-C (2004) Estimation of Weibull parameters using a fuzzy least-squares method. Int J Uncertain Fuzziness Knowl Based Syst 12(5):701–711

    Article  MathSciNet  Google Scholar 

  • Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice-Hall, New Jersey

    MATH  Google Scholar 

  • Lee E, Wang J (2013) Statistical methods for survival data analysis. Wiley, New Jersey

    MATH  Google Scholar 

  • Liu L, Li X-Y, Zhang W, Jiang T-M (2015) Fuzzy reliability prediction of rotating machinery product with accelerated testing data. J Vibroeng 17(8):4193–4210

    Google Scholar 

  • Nelson W (2009) Accelerated testing: statistical models, test plans, and data analysis. Wiley, New Jersey

    Google Scholar 

  • Pak A, Parham G, Saraj M (2013) Reliability estimation in Rayleigh distribution based on fuzzy lifetime data. Int J Syst Assur Eng Manag 5(4):487–494

    Article  Google Scholar 

  • Shafiq M, Atif M (2015) On the survival models for step-stress experiments based on fuzzy life time data. Qual Quant 51(1):79–91

    Article  Google Scholar 

  • Shafiq M, Viertl R (2015a) Empirical reliability functions based on fuzzy life time data. J Intell Fuzzy Syst 28(2):707–711

    MathSciNet  Google Scholar 

  • Shafiq M, Viertl R (2015b) Generalized Kaplan Meier estimator for fuzzy survival times. Sil Stat Rev 13(19):7–14

    Google Scholar 

  • Shafiq M, Khalil A, Atif M, Zaman Q (2016) Empirical acceleration functions and fuzzy information. Int J Uncertain Quant 6(3):215–228

    Article  MathSciNet  Google Scholar 

  • Shaked M, Zimmer WJ, Ball CA (1979) A nonparametric approach to accelerated life testing. J Am Stat Assoc 74(367):694–699

    Article  MathSciNet  Google Scholar 

  • Shapiro AF (2013) Modeling future lifetime as a fuzzy random variable. Insur: Math Econ 53(3):864–870

    MathSciNet  MATH  Google Scholar 

  • Viertl R (1988) Statistical methods in accelerated life testing. Vandenhoeck & Ruprecht, Göttingen

    MATH  Google Scholar 

  • Viertl R (2004) Accelerated life testing, fuzzy information and generalized probability. In: Balakrishnan N, Nikulin M, Mesbah M, Limnios N (eds) Parametric and semiparametric models with applications to reliability, survival analysis, and quality of life, statistics for industry and technology. Birkhäuser, Boston, pp 99–105

    Google Scholar 

  • Viertl R (2011) Statistical methods for fuzzy data. Wiley, Chichester

    Book  Google Scholar 

  • Viertl R, Gurker W (1995) Reliability estimation based on fuzzy life time data. In: Onisawa T, Kacprzyk J (eds) Reliability and safety analyses under fuzziness. Springer, Berlin, pp 153–168

    Chapter  Google Scholar 

  • Viertl R, Hareter D (2006) Beschreibung und analyse unscharfer information: statistische methoden für unscharfe daten. Springer, Wien

    MATH  Google Scholar 

  • Wu H-C (2004) Fuzzy Bayesian estimation on lifetime data. Comput Stat 19(4):613–633

    Article  MathSciNet  Google Scholar 

  • Xu H, Li X, Liu L (2015) Statistical analysis of accelerated life testing under Weibull distribution based on fuzzy theory. In: 2015 annual reliability and maintainability symposium (RAMS), IEEE, Palm Harbor, FL, pp 1–5

  • Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan

    Muhammad Shafiq

  2. Department of Statistics, University of Peshawar, Peshawar, Pakistan

    Muhammad Atif

  3. Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria

    Reinhard Viertl

Authors
  1. Muhammad Shafiq
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Muhammad Atif
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Reinhard Viertl
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Muhammad Shafiq.

Ethics declarations

Conflict of interest

In this paper, the authors have no conflict of interest.

Human and animal rights

Furthermore, this study does not have any involvement with human-related data and only used computer-simulated data.

Additional information

Communicated by A. Genovese and G. Bruno.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shafiq, M., Atif, M. & Viertl, R. Beyond precision: accelerated life testing for fuzzy life time data. Soft Comput 22, 7355–7365 (2018). https://doi.org/10.1007/s00500-018-3067-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-018-3067-3

Keywords