References [1] Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977). Maximum-likelihood from incomplete data via the em algorithm,, J. Royal Statist. Soc. Ser. B. 39 : 1-38. [2] Feller, W. (1965). An introduction to probability theory and its applications. Vol 1, John Wiley&Sons, New York . [3] Gonzales, L.A.P., Vaduva, I. (2010). Simulation of some mixed lifetime distributions. The 13-rd Conference of Romanian Society of Probability and Statistics, Technical University of Civil Engineering, Bucharest, April, 16-17 . [4] Jose Flores D

### Carmen Elena Lupu, Sergiu Lupu and Adina Petcu

### N. B. Khoolenjani and O. Chatrabgoun

. and Whisenand, C. W. (1973). Best linear estimator of the parameter of the Rayleigh distribution-Part I: Small sample theory for censored order statistics. IEEE Transactions on Reliability, 22, 27-34. Gebhardt, J., Gil M.A. and Kruse R., (1998). Fuzzy set-theoretic methods in statistics, in: R. Slowinski(Ed.), Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer Academic Publishers, Boston, pp.311-347. Huang, H., Zuo, M. and Sun, Z., (2006). Bayesian reliability analysis for fuzzy lifetime data. Fuzzy Sets and Systems, 157

### S.O. Pyskunov, Yu.V. Maksimyk and V.V. Valer

1 Introduction Structural elements of responsible objects function often under long-term static or cyclic force loading. The process of creep or fatigue, accompanied by the gradual accumulation of scattered damage, the formation and growth of macroscopic defects (fracture zones) are occurs under such a loading conditions. This problem, similarly as well as other aspects of reliability analysis [ 1 , 2 , 5 ], is very important for a reliable determination of long-term strength and lifetime. A description of above mentioned processes, which took the name

### Adil Rashid, Tariq Rashid Jan, Akhtar Hussain Bhat and Z. Ahmad

References [1] Adamidis, K., and Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Journal of Statistics & Probability Letters, 39, 35-42. [2] Adil, R., Zahoor, A., and Jan, T.R. (2016). A new count data model with application in genetics and ecology. Electronic Journal of Applied Statistical Analysis, 9(1), 213-226 [3] Adil, R., Zahoor, A., and Jan, T.R. (2017). Complementary compound Lindley power series distribution with application. Journal of Reliability and Statistical Studies, 10

### Irina Băncescu

References [1] Aarset M.V., How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36, (1987). [2] Akgul F., Frangopol DM, Computational platform for predicting lifetime system reliability pro_tes for di_erent structure types in a network, Jour- nal of Computing in Civil Engineering, 18(2) (2004), 92-104. [3] Andrews D.F., Herzberg A.M., Data: a collection of problems from many fields for the student and research worker, Springer Science Business Me- dia (2012). [4] Arnold B

### Jorge A. Achcar, Emílio A. Coelho-Barros and Josmar Mazucheli

## ABSTRACT

We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a life- time data set.

### Prafulla Kumar Swain, Gurprit Grover and Komal Goel

## Abstract

The cure fraction models are generally used to model lifetime data with long term survivors. In a cohort of cancer patients, it has been observed that due to the development of new drugs some patients are cured permanently, and some are not cured. The patients who are cured permanently are called cured or long term survivors while patients who experience the recurrence of the disease are termed as susceptibles or uncured. Thus, the population is divided into two groups: a group of cured individuals and a group of susceptible individuals. The proportion of cured individuals after the treatment is typically known as the cure fraction. In this paper, we have introduced a three parameter Gompertz (viz. scale, shape and acceleration) or generalized Gompertz distribution in the presence of cure fraction, censored data and covariates for estimating the proportion of cure fraction through Bayesian Approach. Inferences are obtained using the standard Markov Chain Monte Carlo technique in openBUGS software.

### Kristal K. Trejo, Julio B. Clempner and Alexander S. Poznyak

-29. Clempner, J.B. and Poznyak, A.S. (2011). Convergence method, properties and computational complexity for Lyapunov games, International Journal of Applied Mathematics and Computer Science 21(2): 349-361, DOI: 10.2478/v10006-011-0026-x. Clempner, J.B. and Poznyak, A.S. (2014). Simple computing of the customer lifetime value: A fixed local-optimal policy approach, Journal of Systems Science and Systems Engineering 23(4): 439-459. De Fraja, G. and Delbono, F. (1990 ). Game theoretic models of mixed oligopoly, Journal of Economic Surveys 4

### Kai-Uwe Dettmann and Dirk Söffker

References Banjevic, D. (2009). Remaining useful life in theory and practice, Metrika 69(2-3): 337-349. Bebbington, M., Lai, C.-D. and Zitikis, R. (2007). A flexible weibull extension, Reliability Engineering & System Safety 92(6): 719-726. Castillo, E. and FernéaAndez-Canteli, A. (2006). A parametric lifetime model for the prediction of high-cycle fatigue based on stress level and amplitude, Fatigue & Fracture of Engineering Materials & Structures 29(12): 1031

### Ján Katrenič and Gabriel Semanišin

approximation algorithm for the load-balanced semi-matching problem in weighted bipartite graphs“ , Inform. Process.Lett. 109 (2009) 608-610. doi:10.1016/j.ipl.2009.02.010 [13] D. Luo, X. Zhu, X. Wu, and G. Chen, Maximizing lifetime for the shortest path aggregation tree in wireless sensor networks, in: INFOCOM 2011, K. Gopalan and A.D. Striegel (Ed(s)), (IEEE, 2011) 1566-1574. doi:10.1109/INFCOM.2011.5934947 [14] R. Machado and S. Tekinay, A survey of game-theoretic approaches in wireless sensor networks, Computer Networks 52 (2008) 3047