The Weibull failure model is considered in this paper. Some testimators are proposed of the scale parameter (β) and of the reliability function (R(t)) using life-testing data when a prior value about the unknown parameter (β) is available. The expressions for the bias, mean squared error and relative efficiency are obtained and compared with existing estimators.
WeibullW.‘A statistical distribution function of wide applicability’J. Appl. Mech.18 (1951): 293–297
2.
WeibullW.‘Discussion: A statistical distribution function of wide applicability’J. Appl. Mech.19 (1952): 233–234
3.
BainL. JEngelhardtMStatistical analysis of reliability and life testing models (New York: Marcel Dekker1991)
4.
GnedenkoB. VBalyayevKu. K.SolovyevA.D.Mathematical methods of reliability theory (New York: Academic Press1968)
5.
SinhaS. KReliability and life testing (New York: Wiley1986)
6.
RinneH.The Weibull distribution a handbook (New York: Taylor & Francis Group2009)
7.
ThompsonJ. R‘Some shrinkage techniques for estimating the mean’J. Am. Statist. Assoc.63 (1962): 113–123
8.
LiebleinJ.ZelenM‘Statistical investigation of the fatigue life of deep groove ball bearings’J. Res. Natl Bureaus Stand.57 (1956): 273–315
9.
KaoJ. H. K.‘A graphical presentation of mixed Weibull parameters in life-testing electron tubes’Technometrics4 (1959): 309–407
10.
BerrettoniJ. A‘Practical applications of the Weibull distribution’Ind. Qual. Control21 (1964): 71–79
11.
HarrisE.ShakarkiG‘Use of the population distribution to improve estimation of individual mean in epidemiological studies’J. Chronic Disease32 (1979): 233–243
12.
DallaportasP.WrightD. E‘Numerical prediction for the two-parameter Weibull distribution’The Statistician40 (1991): 365–372
13.
MarshallR. J‘Mapping disease and mortality using empirical Bays estimator’J. Appl. Statistics40 (1991): 283–294
14.
MittnikS.RachevS. T‘Modeling asset returns with alternative stable distribution’Economic Rev.12 (1993): 261–330
15.
SinghJ.BhatkulikarS. G‘Shrunken estimation in Weibull distribution’Sankhya B39 (1978): 382–393
16.
PandeyM.‘Shrunken estimators of the Weibull shape parameters in censored samples’IEEE Trans. Reliability32 (1983): 200–203
17.
PandeyB. NMalikH. JSrivastavaR‘Shrinkage testimators for the shape parameter of Weibull distribution under type II censoring’Commun. Statistics Theory and Method18 (1989): 1175–1191
18.
HisadaK.ArizinoI‘Reliability tests for Weibull distribution with varying shape parameter based on complete data’IEEE Trans. Reliability51 (3) (2002): 331–336
19.
SinghH. PSaxenaSAllenJSinghSSmarandacheFEstimation of Weibull shape parameter by shrinkage towards an interval under failure censored sampling (2002): 1–20 available from: http://arxiv.org/ftp/math/papers/0202/0202274.pdf.
20.
RaiA. N‘Shrinkage testimator of shape parameter of Weibull distribution under asymmetric loss function’. Twelfth International Conference onStatistics, combinatorics, mathematics and applications, 2005, available from www.stat.auburn.edu/scma2005/SCMA2005Schedule.pdf.
21.
ParkashG.SinghD. CSinhaS. K‘On shrinkage estimation for the scale parameter of Weibull distribution’Data Sci. J.7 (2008): 125136
22.
ParkashG.SinghD. C‘A Bayesian shrinkage approach in Weibull type-II censored data using prior point information’REVESTAT- Statist. J.2 (2009): 171–187
23.
Al-HemyariZ. A‘Shrinkage estimation techniques in the Weibull lifetime distribution’IAENG Intl J. App. Math. (2009) (in Press)