Record-based inference and associated cost analysis for the Weibull distribution

• Autorzy: Doostparast M.
• Języki publikacji: EN

Abstrakty

EN

In statistical process control, record schemes are used to reduce the total time on test for the inspection inquiry. In these schemes, units are examined sequentially and successive minimum values are recorded. On the basis of record data, Samaniego and Whitaker (1986) obtained the maximum likelihood (ML) estimate of the mean for an exponential distribution. Since the two parameter Weibull model, as an extension of the exponential distribution, has a wide range of application, Hoinkes and Padgett (1994) derived the record-based ML estimators for the parameters of interest in this model. This paper shows that the ML estimates of the Weibull parameters do not always exist for the basis of records. Thus, a new scheme is proposed, in which the ML estimates of the parameters always exist. An analytic cost-based comparison between the usual and the New scheme is also carried out. Finally, some concluding remarks and open problems are formulated.

Słowa kluczowe

EN

cost analysis; likelihood function; record data; total time on test; Weibull model; lifetime model

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2015
• Tom: Vol. 44, no. 1
• Strony: 163--177
• Opis fizyczny: Bibliogr. 6 poz., rys., tab.

Twórcy

autor

Doostparast M.

• Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 91775-1159, Mashhad, Iran

Bibliografia

• 1. DOOSTPARAST, M. (2009) A note on estimation based on record data. Metrika 69, 69-80. DOOSTPARAST, M. and BALAKRISHNAN, N. (2010) Optimal sample size for record data and associated cost analysis for exponential distribution. Journal of Statistical Computation and Simulation 80(12), 1389-1401.
• 2. GLICK, N. (1978) Breaking record and breaking boards. American Mathemathical Monthly 85, 2-26. GULATI, S. and PADGETT, W. J. (1994) Smooth nonparametric estimation of the distribution and density functions from record-breaking data. Communications in Statistics - Theory and Methods 23(5), 1259-1274.
• 3. HOINKES, L. A. and PADGETT, W. J. (1994) Maximum likelihood estimation from record-breaking data for the Weibull distribution. Quality and Reliability Engineering International 10, 5-13.
• 4. LAWLESS, J. F. (2003) Statistical Models and Methods for Lifetime Data, second edition. John Wiley & Sons, New York. NELSON, W. (1985) Weibull analysis of reliability data with few or no failures. Journal of Quality Technology 17(3), 140-146.
• 5. PIKE, M. (1966) A suggested method of analysis of a certain class of experiments in carcinogenesis. Biometrics 22, 142-161. SAMANIEGO, F. J. and WHITAKER, L. R. (1986) On estimating population characteristics from record breaking observations I. Parametric results. Naval Research Logistics Quarterly 33, 531-543.
• 6. SOLIMAN, A. A., ABD ELLAHB, A. H. and SULTAN, K. S. (2006) Comparison of estimates using rekord statistics from Weibull model: Bayesian and non-Bayesian approaches. Computational Statistics and Data Analysis 51, 2065-2077.