On reliability analysis of consecutive k -out-of- n systems with arbitrarily dependent components

Ebrahim Salehi

Applications of Mathematics (2016)

  • Volume: 61, Issue: 5, page 565-584
  • ISSN: 0862-7940

Abstract

top
In this paper, we consider the linear and circular consecutive k -out-of- n systems consisting of arbitrarily dependent components. Under the condition that at least n - r + 1 components ( r ≤ n ) of the system are working at time t , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive k -out-of- n systems. In the following, we investigate the inactivity time of the component with lifetime T r : n at the system level for the consecutive k -out-of- n systems under the condition that the system is not working at time t > 0 , and obtain some stochastic properties of this conditional random variable.

How to cite

top

Salehi, Ebrahim. "On reliability analysis of consecutive $k$-out-of-$n$ systems with arbitrarily dependent components." Applications of Mathematics 61.5 (2016): 565-584. <http://eudml.org/doc/286789>.

@article{Salehi2016,
abstract = {In this paper, we consider the linear and circular consecutive $k$-out-of-$n$ systems consisting of arbitrarily dependent components. Under the condition that at least $n-r+1$ components ($r\le n$) of the system are working at time $t$, we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive $k$-out-of-$n$ systems. In the following, we investigate the inactivity time of the component with lifetime $T_\{r:n\}$ at the system level for the consecutive $k$-out-of-$n$ systems under the condition that the system is not working at time $t>0$, and obtain some stochastic properties of this conditional random variable.},
author = {Salehi, Ebrahim},
journal = {Applications of Mathematics},
keywords = {residual lifetime; inactivity time; stochastic order; dependence; reliability; residual lifetime; inactivity time; stochastic order; dependence; reliability},
language = {eng},
number = {5},
pages = {565-584},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On reliability analysis of consecutive $k$-out-of-$n$ systems with arbitrarily dependent components},
url = {http://eudml.org/doc/286789},
volume = {61},
year = {2016},
}

TY - JOUR
AU - Salehi, Ebrahim
TI - On reliability analysis of consecutive $k$-out-of-$n$ systems with arbitrarily dependent components
JO - Applications of Mathematics
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 5
SP - 565
EP - 584
AB - In this paper, we consider the linear and circular consecutive $k$-out-of-$n$ systems consisting of arbitrarily dependent components. Under the condition that at least $n-r+1$ components ($r\le n$) of the system are working at time $t$, we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive $k$-out-of-$n$ systems. In the following, we investigate the inactivity time of the component with lifetime $T_{r:n}$ at the system level for the consecutive $k$-out-of-$n$ systems under the condition that the system is not working at time $t>0$, and obtain some stochastic properties of this conditional random variable.
LA - eng
KW - residual lifetime; inactivity time; stochastic order; dependence; reliability; residual lifetime; inactivity time; stochastic order; dependence; reliability
UR - http://eudml.org/doc/286789
ER -

References

top
  1. Aki, S., Hirano, K., 10.1007/BF00049298, Ann. Inst. Stat. Math. 48 (1996), 185-199. (1996) Zbl0857.62094MR1392525DOI10.1007/BF00049298
  2. Asadi, M., 10.1016/j.jspi.2004.08.021, J. Stat. Plann. Inference 136 (2006), 1197-1206. (2006) Zbl1088.62120MR2253758DOI10.1016/j.jspi.2004.08.021
  3. Asadi, M., Bayramoglu, I., 10.1109/TR.2006.874934, IEEE Trans. Reliab. 55 (2006), 314-318. (2006) MR2412846DOI10.1109/TR.2006.874934
  4. Bairamov, I., Ahsanullah, M., Akhundov, I., A residual life function of a system having parallel or series structures, J. Stat. Theory Appl. 1 (2002), 119-131. (2002) MR1952705
  5. Bairamov, I., Gurler, S., Ucer, B., 10.1080/03610918.2013.763979, Commun. Stat., Simulation Comput. 44 (2015), 1-13. (2015) Zbl1325.62187MR3238547DOI10.1080/03610918.2013.763979
  6. Boland, P. J., Samaniego, F. J., 10.1109/TR.2004.824830, IEEE Trans. Reliab. 53 (2004), 7-10. (2004) MR2182122DOI10.1109/TR.2004.824830
  7. Chang, G. J., Cui, L., Hwang, F. K., Reliabilities of consecutive- k systems, Network Theory and Applications 4 Kluwer Academic Publishers, Dordrecht (2000). (2000) Zbl0988.90010MR1813954
  8. Chen, R. W., Hwang, F. K., 10.1109/TR.1985.5222180, IEEE Trans. Reliab. 34 (1985), 338-341. (1985) Zbl0588.62181DOI10.1109/TR.1985.5222180
  9. Eryılmaz, S., 10.1109/TR.2006.890902, IEEE Trans. Reliab. 56 (2007), 35-39. (2007) MR2749971DOI10.1109/TR.2006.890902
  10. Eryılmaz, S., 10.1016/j.ress.2008.03.027, Reliab. Eng. Syst. Saf. 94 (2009), 350-356. (2009) MR2749971DOI10.1016/j.ress.2008.03.027
  11. Eryılmaz, S., 10.1109/TR.2010.2040775, IEEE Trans. Reliab. 59 (2010), 178-182. (2010) MR2987530DOI10.1109/TR.2010.2040775
  12. Eryılmaz, S., 10.1016/j.jspi.2010.07.014, J. Stat. Plann. Inference 141 (2011), 725-733. (2011) Zbl1214.62103MR2732943DOI10.1016/j.jspi.2010.07.014
  13. Jia, X., Cui, L., Yan, J., 10.1080/03610921003778134, Comm. Stat., Theory Methods 39 (2010), 2455-2472. (2010) Zbl1201.62109MR2755631DOI10.1080/03610921003778134
  14. Khaledi, B.-E., Shaked, M., 10.1016/j.jspi.2006.01.012, J. Stat. Plann. Inference 137 (2007), 1173-1184. (2007) Zbl1111.60012MR2301471DOI10.1016/j.jspi.2006.01.012
  15. Kochar, S., Xu, M., 10.1017/S0269964809990167, Probab. Eng. Inf. Sci. 24 (2010), 109-127. (2010) Zbl1190.90060MR2575845DOI10.1017/S0269964809990167
  16. Koutras, M. V., Triantafyllou, I. S., Eryılmaz, S., 10.1007/s11009-014-9433-4, Methodol. Comput. Appl. Probab. 22 (2014), DOI 10.1007/s11009-014-9433-4. (2014) MR3564854DOI10.1007/s11009-014-9433-4
  17. Kuo, W., Zuo, M. J., Optimal Reliability Modeling: Principles and Applications, John Wiley & Sons (2003). (2003) 
  18. Li, X., Zhang, Z., 10.1002/asmb.715, Appl. Stoch. Models Bus. Ind. 24 (2008), 541-549. (2008) MR2473025DOI10.1002/asmb.715
  19. Li, X., Zhao, P., 10.1080/03610910801943784, Commun. Stat., Simulation Comput. 37 (2008), 1005-1019. (2008) Zbl1162.60307MR2744074DOI10.1080/03610910801943784
  20. Navarro, J., Balakrishnan, N., Samaniego, F. J., 10.1017/S0021900200005003, J. Appl. Probab. 45 (2008), 1097-1112. (2008) Zbl1155.60305MR2484164DOI10.1017/S0021900200005003
  21. Navarro, J., Eryılmaz, S., 10.1239/jap/1175267165, J. Appl. Probab. 44 (2007), 82-98. (2007) Zbl1135.62084MR2312989DOI10.1239/jap/1175267165
  22. Navarro, J., Rubio, R., 10.1002/nav.20463, Nav. Res. Logist. 58 (2011), 478-489. (2011) Zbl1218.90068MR2857517DOI10.1002/nav.20463
  23. Navarro, J., Ruiz, J. M., Sandoval, C. J., 10.1080/03610920600966316, Commun. Stat., Theory Methods 36 (2007), 175-191. (2007) Zbl1121.60015MR2391869DOI10.1080/03610920600966316
  24. Navarro, J., Spizzichino, F., 10.1002/asmb.819, Appl. Stoch. Models Bus. Ind. 26 (2010), 775-791. (2010) Zbl1226.90031MR2752386DOI10.1002/asmb.819
  25. Rezapour, M., Salehi, E. T., Alamatsaz, M. H., 10.1080/03610926.2011.606484, Commun. Stat., Theory Methods 42 (2013), 2185-2199. (2013) Zbl1282.60025MR3053319DOI10.1080/03610926.2011.606484
  26. Sadegh, M. K., 10.1080/03610920701713278, Commun. Stat., Theory Methods 37 (2008), 1134-1145. (2008) Zbl1138.62065MR2408294DOI10.1080/03610920701713278
  27. Sadegh, M. K., 10.1016/j.jspi.2011.04.013, J. Stat. Plann. Inference 141 (2011), 3267-3275. (2011) Zbl1216.62158MR2796030DOI10.1016/j.jspi.2011.04.013
  28. Salehi, E. T., Asadi, M., 10.1007/s00184-010-0335-3, Metrika 75 (2012), 439-454. (2012) Zbl1300.62103MR2922155DOI10.1007/s00184-010-0335-3
  29. Salehi, E., Asadi, M., Badia, F. G., Assessing the reliability and the stochastic properties of the components of consecutive k -out-of- n systems, (to appear) in J. Appl. Stat. Sci. (2016). 
  30. Salehi, E. T., Asadi, M., Eryılmaz, S., 10.1016/j.jspi.2011.03.014, J. Stat. Plann. Inference 141 (2011), 2920-2932. (2011) Zbl1213.62163MR2787755DOI10.1016/j.jspi.2011.03.014
  31. Salehi, E. T., Asadi, M., Eryılmaz, S., 10.1007/s11749-011-0237-3, Test 21 (2012), 93-115. (2012) Zbl1262.90055MR2912973DOI10.1007/s11749-011-0237-3
  32. Sfakianakis, M. E., Papastavridis, S. G., 10.1109/24.257837, IEEE Trans. Reliab. 42 (1993), 491-496. (1993) Zbl0800.90480DOI10.1109/24.257837
  33. Shaked, M., Shanthikumar, J. G., Stochastic Orders and Their Applications, Probability and Mathematical Statistics Academic Press, Boston (1994). (1994) Zbl0806.62009MR1278322
  34. Shanthikumar, J. G., 10.1109/TR.1985.5222236, IEEE Trans. Reliab. 34 (1985), 480-483. (1985) Zbl0588.62180DOI10.1109/TR.1985.5222236
  35. Tavangar, M., Asadi, M., 10.1007/s00184-009-0241-8, Metrika 72 (2010), 59-73. (2010) Zbl1189.62161MR2658206DOI10.1007/s00184-009-0241-8
  36. Tavangar, M., Asadi, M., The inactivity time of exchangeable components of k -out-of- n structures, Sankhy, Ser. B 77 (2015), 141-164. (2015) Zbl1312.60013MR3337568
  37. Zhang, Z., 10.1016/j.jspi.2009.07.029, J. Stat. Plann. Inference 140 (2010), 454-460. (2010) Zbl1229.62137MR2558377DOI10.1016/j.jspi.2009.07.029
  38. Zhao, P., Li, X., Balakrishnan, N., 10.1239/jap/1231340237, J. Appl. Probab. 45 (2008), 1113-1125. (2008) Zbl1155.60309MR2484165DOI10.1239/jap/1231340237

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.