American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2019, 7(3), 101-104
DOI: 10.12691/ajams-7-3-3
Open AccessArticle

Life Expectancy of a System with Successive Stages of Deterioration

Meenaxi1, , Dalip Singh1 and Narender Singh2

1Department of Mathematics, M.D. University, Rohtak-124001

2Govt College, Birohar, Jhajjar-124106

Pub. Date: April 18, 2019

Cite this paper:
Meenaxi, Dalip Singh and Narender Singh. Life Expectancy of a System with Successive Stages of Deterioration. American Journal of Applied Mathematics and Statistics. 2019; 7(3):101-104. doi: 10.12691/ajams-7-3-3


In this paper we present Life Expectancy and Availability of a patient suffering from Kidney disease, where the deteriorating rates follow the Weibull distribution. In our paper, we present modelling and estimate the life expectancy/mean time to absorbtion and availability of the system having four successive stages of deteriorating system. Explicit expressions for the availability, mean sojourn time and life expectancy/mean time to absorbtion are obtained consequently. Graphs of availability and mean time to absorbtion are also plotted to dispose the nature with respect to time for distinct values of deteriorating rates.

life expectancy mean time to absorbtion availability

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[1]  Kay, R., A Markov model for analysing cancer markers and diseases states in survival studies. Biometrics, 42, 855-865, 1986.
[2]  Andersen, P.K., Multistate models in survival analysis: a study of nephropathy and mortality in diabetes. Statist. Med., 7, 661-670, 1988.
[3]  Longini, I.M., Clark, W.S., Byers, R.H., Ward, J.W., Darrow, W.W., Lemp, G.F. and Hethocote, H.W., Statistical analysis of the stages of HIV infection using a Markov model. Statist. Med., 8, 831-843, 1989.
[4]  Klotz, J. H. And Sharples, L.D., Estimation for a Markov heart transplant model. Statistician, 43, 431-438, 1994.
[5]  Duffy, S.W. and Chen, H.H., Estimation of mean sojourn time in breast cancer screening using a Markov chain model entry to and exit from preclinical detectable phase. Statist. Med. 14, 1531-1543, 1995.
[6]  L. Chiang, Introduction to Stochastic Processes in Biostatistics (1st edition, John Willy & Sons, Inc., 1968).
[7]  Haggag, M.Y., Cost analysis of k-out-of-n repairable system with dependent failure and stand by support using kolmogorov’s forward equations method. J. Maths. And Stat. 5(4), 401-407, 2009.
[8]  El-Said, K.M., and M.S. El-Sherbeny, Profit analysis of a two unit cold standby system with preventive maintenance and random change in units. J. Maths and Stat., 1 (1) 71-77, 2005.
[9]  Wang, K., Hseih, C., and Liou, C. H., Cost benefit analysis of series systems with cold standby components and a repairable service station. Quality technology and quantitative management. Vol. 3(1), pp 77-92, 2006.