Reliability analysis of time - dependent stress - strength system when the number of cycles follows binomial distribution

Transcription

1 raoal Joural of Sascs ad Ssms SSN Volum, Numbr 7, sarch da Publcaos h:// labl aalss of m - dd srss - srgh ssm wh h umbr of ccls follows bomal dsrbuo T.Sumah Umamahswar, N.Swah, M.Trumala Dv ad P. Ashok * Darm of Mahmacs, Kakaa Uvrs, Waragal, Tlagaa Sa, da. Absrac cass of Mchacal, Hdralc, c ssms; Srucural modllg s hard o al bcaus of hr dsrbud aur of h dvcs. som cass chags ma b du o ag ad cumulav damag or du o h formao gad b a cha. Tm dd modls ar usful for hs cass. hs ar rlabl aalss of m dd srss srgh ssm s carrd ou b cosdrg radom umbr of ccls. labl formula of umbr ccls s drvd wh umbr of ccls follows bomal dsrbuo. ad srss ad srgh followg oal dsrbuo. Kwords: Bomal dsrbuo, Eoal dsrbuo, drmsc, radom- fd, radom- dd ad labl. NOTATON f: Th robabl ds fuco of radom varabl X. g:th robabl ds fuco of radom varabl Y. G: cumulav dsrbuo of : labl a m wh umbr of ccls

2 576 T.Sumah Umamahswar, N.Swah, M.Trumala Dv ad P. Ashok : labl afr ccls : Ma of a adom varabl : Ma of a radom varabl NTODUCTON Tm dd srss srgh ssm s dfd b Kaur, K.C. ad Lambrso L. []. srss-srgh modls como fals f h srss o cds srgh. Th ucra abou h srss ad srgh varabls s classfd o hr cagors. Drmsc, adom fd, adom dd, hs ar, d, ad rd cass ar cosdrd h comos ar assumd o b dcal ad h umbr of ccls for a m rod s assumd o b radom. Erssos for ssm rlabl hav b aad wh umbrs of ccls follow bomal dsrbuo ad srss ad srgh boh follow oal dsrbuo. ELABLTY EVALUATON Numbr of ccls occurrg a gv m rval s follows bomal dsrbuo s π = PX = =, =,,,... Cas : adom- fd srss ad adom- dd srgh L f b h robabl ds fuco of radom fd srss X ad g b h robabl ds fuco of radom dd srgh Y. = f g, =,,,.. = π = = f g =o

3 labl aalss of m - dd srss - srgh ssm 577 = f g = = f + g = f + G, whr G = g = f + G, whr G = g. Cas : adom- dd srss ad adom- fd srgh L g b h robabl ds fuco of radom fd srgh Y ad f b h robabl ds fuco of radom dd srss X. = =o g f = g f = = g + f = g + F, whr F = f = g + F, whr F = f.

4 578 T.Sumah Umamahswar, N.Swah, M.Trumala Dv ad P. Ashok f Srss ad Srgh Follow Eoal Dsrbuo Cas : adom - fd srss ad adom- dd srgh From uao = f o + G, whr G = g G = μ μ = μ = λ λ + μ Whr

5 labl aalss of m - dd srss - srgh ssm 579 Euao bcoms... Whr Th uao bcoms

6 58 T.Sumah Umamahswar, N.Swah, M.Trumala Dv ad P. Ashok Coug hs rocss u o ms, w g = + µ = λ+µ o Cas : adom- dd srss ad adom- fd srgh From uao = g + F, whr F = f F = λ λ = λ = μ μ + λ = μ μ λ

7 labl aalss of m - dd srss - srgh ssm Euao bcoms... Whr

8 58 T.Sumah Umamahswar, N.Swah, M.Trumala Dv ad P. Ashok... Th uao bcoms Coug hs rocss u o ms mor, w g = λ µ+λ = µ+λ o

9 labl aalss of m - dd srss - srgh ssm 58 CONCLUSON Gral rlabl formula for ccls s drvd wh umbr of ccls follows bomal dsrbuo for h followg wo cass. radom- fd srss ad radom- dd Srgh. radom- dd Srss ad radom- fd Srgh. B Comuaos s obsrvd ha rlabl s crasd wh λ crass ad µ dcrass EFEENCES [] Kaur, K.C. ad Lambrso, L.. 977: labl Egrg Dsg, Joh Wl ad Sos, c. [] M.N.Goala, P. Vkaswarlu98: labl aalss of m dd cascad ssm wh drmsc ccl ms, Mcrolcro lb., Vol., No. 4, : [] Schaz,., Shooma, M. Ad Shaw, L.974: Alcaos of Tm- Dd Srss- Srgh Modls of No- Elcrcal ad Elcrcal Ssms, Procdgs of labl ad Maaabl Smosum, Jauar, [4] Gogo. J, Borah. M, ad Srwasav G. L. A rfrc Modl Wh Numbr of Srsss A Posso Procss, APQ Trasacos, 4, 9-5,. [5] Dolo. C, Borah. M. Cascad Ssm wh Mur of Dsrbuos, raoal Joural of Sascs ad Ssms, 7, -4,. [6] Sha, S.K. 986: labl ad Lf Tsg, Wl Easr Lmd, Nw Dlh. [7] Lawlss, J.F. 98: Sascal Modls ad Mhods for Lfm daa. Wl, Nw York. [8] Shaw, L., Shooma, M. ad Scharz,. 97: Tm dd srsssrgh modls for o-lcrcal ad lcrcal ssms, Procdg labl ad Maaabl Smosum,

10 584 T.Sumah Umamahswar, N.Swah, M.Trumala Dv ad P. Ashok