Reduction in mean residual life in the presence of a constant competing risk

Applied Stochastic Models in Business and Industry

Volumn 24, Issue 1, 2008, Pages 51-63

  Bebbington, Mark ^a   Lai, Chin Diew ^a   Zitikis, Ricardas ^b  

^a MASSEY UNIVERSITY   (New Zealand)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Bathtub distribution; Competing risks; Hazard rate; Mean residual life; Reliability

Indexed keywords

HUMAN RESOURCE MANAGEMENT; RELIABILITY ANALYSIS; STOCHASTIC MODELS; WORK FUNCTION;

BATHTUB DISTRIBUTION; COMPETING RISKS; HAZARD RATES; MEAN RESIDUAL LIFE; RELIABILITY ENGINEERING;

RISK ANALYSIS;

EID: 40449119869     PISSN: 15241904     EISSN: 15264025     Source Type: Journal    
DOI: 10.1002/asmb.693     Document Type: Article

References (28)

1. Bebbington M, Lai CD, Zitikis R. Estimating the turning points of failure rate and mean residual life functions. Communications in Dependability and Quality Management 2005; 8:11-15.
2. Bebbington M, Lai CD, Zitikis R. Useful periods for lifetime distributions with bathtub shaped hazard rate functions. IEEE Transactions on Reliability 2006; 55:245-251.
3. Nelson WB. Applied Life Data Analysis. Wiley: New York, 2003.
4. Griffith WS. Shock models. In Encyclopedia of Statistical Sciences, Kotz S et al. (eds), vol. 8. Wiley: New York, 1988; 442-446.
5. Block HW, Savits TH. Laplace transforms for classes of life distributions. Annals of Probability 1980; 8:465-474.
6. Klefsjö B. A useful ageing property based on the Laplace transform. Journal of Applied Probability 1983; 20:615-626.
7. Alzaid A, Kim JS, Proschan F. Laplace ordering and its applications. Journal of Applied Probability 1991; 28:116-130.
8. Belzunce F, Ortega E, Ruiz JM. On non-monotonic ageing properties from the Laplace transform, with actuarial applications. Insurance: Mathematics and Economics 2007; 40:1-14.
9. Denuit M. Laplace transform ordering of actuarial quantities. Insurance: Mathematics and Economics 2001; 29:83-102.
10. Li X. Some properties of ageing notions based on the moment-generating- function order. Journal of Applied Probability 2004; 41:927-934.
11. Lomax KS. Business failures: another example of the analysis of failure data. Journal of the American Statistical Association 1954; 49:847-852.
12. Kodlin D. A new response time distribution. Biometrics 1967; 23:227-239.
13. Carbone PP, Kellerhouse LE, Gehan EA. Plasmacytic myeloma-a study of the relationship of survival to various clinical manifestations and anomalous protein type in 112 patients. American Journal of Medicine 1967; 42:937-948.
14. Lai CD, Xie M. Stochastic Ageing and Dependence for Reliability. Springer: New York, 2006.
15. Kleiber C, Kotz S. Statistical Size Distributions in Economics and Actuarial Sciences. Wiley: Hoboken, NJ, 2003.
16. Govil KK, Aggarwal KK. Mean residual life function for normal, gamma and lognormal densities. Reliability Engineering 1983; 5:47-51.
17. Bebbington M, Lai CD, Zitikis R. Modeling human mortality using mixtures of bathtub shaped failure distributions. Journal of Theoretical Biology 2007; 245:528-538.
18. Block HW, Jong YK, Savits TH. Bathtub functions and burn in. Probability in the Engineering and Informational Sciences 1999; 13:97-507.
19. Bebbington M, Lai CD, Zitikis R. Optimum burn-in time for a bathtub shaped failure distribution. Methodology and Computing in Applied Probability 2007; 9:1-20.
20. Gupta RC, Akman OH. Mean residual life function for certain types of non-monotonic ageing. Communications in Statistics-Stochastic Models 1995; 11:219-225.
21. Hjorth U. A reliability distribution with increasing, decreasing, constant and bathtub-shaped failure rates. Technometrics 1980; 22:99-107.
22. Mi J. Bathtub failure rate and upside-down bathtub residual life. IEEE Transactions on Reliability 1995; 44: 388-391.
23. Guess F, Nam KH, Park DH. Failure rate and mean residual life with trend changes. Asia-Pacific Journal of Operational Research 1998; 15:239-244.
24. Xie M, Lai CD. Reliability analysis using additive Weibull model with bathtub-shaped failure rate function. Reliability Engineering and System Safety 1995; 52:87-93.
25. Lai CD, Zhang LY, Xie M. Mean residual life and other properties of Weibull related bathtub shape failure rate distributions. International Journal of Reliability, Quality and Safety Engineering 2004; 11:113-132.
26. Bebbington M, Lai CD, Zitikis R. A flexible Weibull extension. Reliability Engineering and System Safety 2007; 92:719-726.
27. Carpenter WF. On the solution of the real quartic. Mathematics Magazine 1966; 39:28-30.
28. Bronshtein IN, Semendyayev KA, Musiol G, Muehlig H. Handbook of Mathematics (4th edn). Springer: Berlin, 2004.