Skip to main content
SpringerLink
Log in

Analysis of Instantaneous and Early Failures in Weibull Distribution

  • Original Article
  • Published:
Metrika Aims and scope Submit manuscript

Abstract

There are many situations in life testing experiment where an item fail instantaneously and hence the observed lifetime is reported as zero. The items that fail prematurely are called early failures. We propose a modified Weibull distribution as a suitable model to represent such situations by mixture of a singular distribution at zero and a two parameter Weibull distribution. We obtain the maximum likelihood estimates of the parameters and their asymptotic distributions. The methods are illustrated on drying of woods under different experiments and schedules reported by Vanmann (Research report, 1991:2).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aitchison J (1955) On the distribution of a positive random variable having a discrete probability mass at the origin. J Am Stat Assoc 50:901–908

    Article  MATH  MathSciNet  Google Scholar 

  • Andrei DP, Alexander VM (1998) Handbook of integral equations. CRC Press, New York

    Google Scholar 

  • Kale BK (1999) A first course on parametric inference. Narosa Publishers, New Delhi

    MATH  Google Scholar 

  • Kale BK (2001) Industrial mathematics and statistics – Chapter 20. Narosa Publishers, New Delhi

    Google Scholar 

  • Kale BK, Muralidharan K (2000) Optimal estimating equations in mixture distributions accommodating instantaneous or early failures. J Indian Statist Assoc 38:317–329

    MathSciNet  Google Scholar 

  • Kleyle RM, Dahiya RL (1975) Estimation of parameters of mixed failure time distribution from censored data. Comm. Stat Theory Methods 4(9):873–882

    MATH  MathSciNet  Google Scholar 

  • Jayade VP, Prasad MS (1990) Estimation of parameters of mixed failure time distribution. Comm Stat Theory Methods 19(12):4667–4677

    MATH  MathSciNet  Google Scholar 

  • Liang KY (1983) On information and ancilarity in the presence of a nuisance Parameter. Biometrika 70:607–612

    Article  MATH  MathSciNet  Google Scholar 

  • Meeker WQ, Escobar LA (1998) Statistical Methods for reliability data. Wiley, New York

    MATH  Google Scholar 

  • Muralidharan K (1999) Tests for the mixing proportion in the mixture of a degene-rate and exponential distribution. J Indian Stat Assoc 37(2)

  • Muralidharan K (2000) The UMVUE and Bayes estimate of reliability of mixed failure time distribution. Comm Stat Simul comput 29(2):603–619

    MATH  MathSciNet  Google Scholar 

  • Muralidharan K, Kale BK (2002) Modified gamma distribution with singularity at zero. Comm Stat Simul Comput 31(1):143–158

    Article  MATH  MathSciNet  Google Scholar 

  • Muralidharan K, Shanubhogue A, Jani PN (2001) Conditional tests for the shape parameter in the mixture of a degenerate and a weibull distribution. J Appl Stati Sci 10(4):299–313

    MATH  MathSciNet  Google Scholar 

  • Sinha SK, Kale BK (1980) Reliability and life testing. Wiley, New York

    Google Scholar 

  • Vannman K (1991) Comparing samples from nonstandard mixtures of distributions with applications to quality comparison of wood. Research report 1991:2 submitted to division of quality technology, Lulea University, Lulea, Sweden

  • Vannman K (1995) On the distribution of the estimated mean from the nonstandard mixtures of distribution. Comm Statist Theory Methods 24(6):1569–1584

    MathSciNet  Google Scholar 

  • White JS (1969) The moments of Log–Weibull order statistics. Technometrics 11:373–386

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Bhavnagar University, Bhavnagar, 364 002, India

    K. Muralidharan & P. Lathika

  2. Department of Statistics, The M. S. University of Baroda, Vadodara, 390 002, India

    K. Muralidharan

Authors
  1. K. Muralidharan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Lathika
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Muralidharan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muralidharan, K., Lathika, P. Analysis of Instantaneous and Early Failures in Weibull Distribution. Metrika 64, 305–316 (2006). https://doi.org/10.1007/s00184-006-0050-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-006-0050-2

Keywords

Search

Navigation