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Two modified estimators of reliability function with exponential failure model based on prior information and time-censored data

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  • ZA Al-Hemyari
  • JA Al-Dolami

Abstract

In this article, we have assumed that the observations are carried out for a period of time T , and when a unit failed, it was replaced with a new identical unit. We have considered the exponential distribution of failure, and we have proposed two estimators of reliability function ( R ( t ) ) by using time-censored data when a prior value (uncertain prior information) about the unknown parameter ( θ ) was previously available. The expressions for the bias, risk and relative efficiency were obtained. The investigation concerning the improvement of the proposed estimators of R ( t ) on the bases of the criterion of bias ratio, risk and relative efficiency under different cases showed that the proposed estimators were better than the classical estimators. The conclusions, concluding remarks and limitations were then reported.

Suggested Citation

  • ZA Al-Hemyari & JA Al-Dolami, 2014. "Two modified estimators of reliability function with exponential failure model based on prior information and time-censored data," Journal of Risk and Reliability, , vol. 228(6), pages 578-589, December.
    • Handle: RePEc:sae:risrel:v:228:y:2014:i:6:p:578-589
    DOI: 10.1177/1748006X14540634
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    References listed on IDEAS

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    1. Z.A. Al-Hemyari & I.H. Hussain, 2012. "Improved shrinkage testimators for the simple linear regression model," International Journal of Information and Decision Sciences, Inderscience Enterprises Ltd, vol. 4(1), pages 87-103.
    2. Katuomi Hirano, 1977. "Estimation procedures based on preliminary test, shrinkage technique and information criterion," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 21-34, December.
    3. Katuomi Hirano, 1977. "Corrections to “Estimation procedures based on preliminary test, shrinkage technique and information criterion”," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 317-317, December.
    4. Z.A. Al-Hemyari & I.H. Hussain & A.N. Al-Jobori, 2011. "A class of efficient and modified testimators for the mean of normal distribution using complete data," International Journal of Data Analysis Techniques and Strategies, Inderscience Enterprises Ltd, vol. 3(4), pages 406-425.
    5. Z.A. Al-Hemyari & Jabar A. Al-Dolami, 2012. "Optimised Shrinkage Testimator of reliability function in a failure-time model," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(6), pages 607-621.
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