International Journal of Statistics and Reliability Engineering

No Publication Cost

Vol 4, No 2 :

openaccess

Inferential Study of Self Relocated Design when Lifetime Followsthe Frechet Distribution

D. P. Raykundaliya

Abstract

Due to the extreme events happening in manufacturing industries and nature, recently, researchers have focused onstudy of extreme value distributions for better planning purpose. The Frechet (extreme value type II) distribution is one of the probability distributions used to model extreme events. It has many applications including in the events earthquakes, flood, queues in supermarkets and wind speeds [NadarajahandKotz(2000)].Recently,Shanubhogue and Raykundaliya (2015) has studied self-relocated experimental design introduced by Srivastva(1987)when lifetime of the system followsgeneralized exponential distribution and generalized inverted family of distribution. In this paper,an attempt has been made to study the self-relocated experimental design when the lifetime of the systems followsthe Frechet Distribution. We derive the maximum likelihood expressions and shows that ML estimators of parameters follow asymptotically normal. We also obtain Fisher Information matrix, estimate of hazard rate and reliability function when shape parameter is known and unknown. In our case,the ML expressions are not mathematically tractable, we suggest algorithm to obtain estimates of parameters and its standard error using Newton-Raphson method when shape parameter is known as well as unknown. Further, likelihood ratio test is discussed to test homogeneity of several scale parameters.

Full Text

PDF

References

A. Shanubhogue; D.P.Raykundaliya; Estimation of Parameters and Reliability Characteristics in Self Relocated Design under Generalized Inverted Family of Distribution, Special Issue on Reliability and Dependability Modeling Analysis for Complex Systems to the Journal Mathematics in Engineering, Science and Aerospace Vol.6 (2),157-176(2015).

A.Shanubhogue; D.P.Raykundaliya; Estimation of Parameters and Reliability Characteristics in Self Reliability Relocated Design. International Journal of Statistics and Reliability Engineering (IJSRE),Vol. 2 (1), 18-40(June 2015).

Balakrishnan; Aggarwala;Progressive Censoring: Theory, Methods, and Applications (Statistics for Industry and Technology), Birkhäuser(2012).

D.P.Raykundaliya; Inferential Problem about Homogeneity of Several Systems under Frechet Distribution, Journal Statistics Applications & Probability, Vol.5 (1), 1-8(2016).

J.N. Srivastava; Advances in the statistical theory of comparison of lifetimes of machines under the generalized Weibull distribution. Communication Statistics-Theory &Method, 18 (3), 1031-1045(1989).

J.N. Srivastava; Experimental designs for the assessment of reliability. In A.P.

Basu(Ed.), Reliability and Quality Control, Elsevier Science Publishers, Amsterdam, 369-394(1986).

J.N. Srivastava; More efficient and less time-consuming censoring designs for life testing. J.Statist.Plan. Inference 16, 389-413( ).

Ng. H.K.T. Parameter estimation for a modified Weibull distribution for progressive Type II censored samples. IEEE Trans. Reliab., 54, 374–380(2005).

S. Nadarajah; S. Kotz,;Extreme Value Distributions: Theory and Applications, Imperial College Press, London, UK. (2000).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

Journal Content