Inrnaional Journal on Rcn Innovaion rnd in Comuing Communicaion ISSN: -869 Volum: Iu: 6 Eimaion of Man im bwn Failur in wo Uni Paralll Rairabl Sym Sma Sahu V.K. Paha Kamal Mha hih Namdo 4 ian Profor D. Of Mahmaic & I Gov. P.G. Collg Dhamari C.G. ian Profor & Had D. Of Mahmaic & I Gov. P.G. Collg Dhamari C.G. ocia Profor D. Of Comur Scinc Nirma Univriy hmdabad Gujara 4 Dircor Com-ch Collg Dhamari C.G. brac--man im bwn failur i a mhod for imaing h rliabiliy aramr of any rairabl ym. MBF i alo hlful in rforming dciion analyi in aralll ri ym ubym. h MBF i h rcirocal of h failur ra whn ach comonn which fail i rlacd immdialy wih anohr having h idnical failur ra. hr ar iuaion whn h aumion of a conan failur ra i no raliic in many of h iuaion on aum inad ha h failur ra funcion incra or dcra moohly wih im i.. hr ar no diconinuiy or urning oin. In hi ar w hav rid o ima MBF aing ral failur ra in ca of wo uni aralll rairabl ym udy i conincy wih ihr h iniial or h la ag of h failur ra curv. Kyword: Man im bwn failur rliabiliy failur ra curv rairabl ym. Subjc Claificaion: 4 *****. Inroducion In many ral lif iuaion mor han on faild comonn can b raird oghr. a rul of hi h lif of any ym can b incrad conidrably hrfor hr i a chanc in imrovmn in man im bwn failur. Rliabiliy maur for a wo uni aralll ym wih aralll rair faciliy wa dicud by Rau [] aing h aumion ha h failur rair im of h comonn ar indndnly idnically diribud. Svral auhor bfor hi uch a Vnaarihnan al[] Klin Mochbrgr al[] Oai al [4] Dharmadhiari al[6] hav conidrd by aralll ri ym wih aralll faciliy in which h comonn failur im rair im ar no ncarily indndn. Rcnly Paha al[8] hav don comaraiv analyi of rliabiliy aramr aing wo diffrn y of diribuion. In hi ar w hav conidrd a mulivaria xonnial diribuion of Marhall Olin [] for h failur rair im dicud variou rliabiliy maur. If w ma h xonnial aumion abou h diribuion of failur im om vry uful rul can b drivd concrning MBF - h man im bwn failur for ri aralll ym. For doing hi w hall hav o fir obain a rlaion xring h rliabiliy of a comonn in rm of i rvic im =. Maing u of h fac ha R F f x dx w obain ha R x dx for h rliabiliy funcion of h xonnial modl. hu if a comonn ha a failur ra hr α of. r hou hour h robabiliy ha i will urviv a la hour. of oraion aing = i. 67 IJRICC Ocobr 4 vailabl @ h://www.ijricc.org
Inrnaional Journal on Rcn Innovaion rnd in Comuing Communicaion ISSN: -869 Volum: Iu: 6 Now uo ha a ym coni of n comonn conncd in ri ha h comonn hav h rciv failur ra a α α α n. hn h rliabiliy funcion of h ri ym can b xrd a n i i R i n i h xrion for MBF can b wrin a... n Whr μ i i h MBF of i comonn. For aralll ym rul ar howvr inring. If a ym coni of n comonn in aralll configuraion having h rciv failur ra α α. α n h ym hn h xrion for Man im bwn failur i givn by [... ] n Whr α i h idnical failur ra.. iraur Rviw MBF ha bn ud a a ool for maing dciion around yar now. Variou mhod rocdur of imaing MBF hav bn dvlod during h yar. h dm for b co roducr g highr highr mor rarch on finding mhod of imaing MBF hav com o ligh a i i conidrd mo ffciv ool in hi fild. h main hru ha bn in imroving h rliabiliy of ym afr h imrovmn in h mhod of imaing h MBF.. Problm Dfiniion Conidr a wo comonn ym wih aralll rair faciliy in which comonn failur rair im follow xonnial diribuion. Whnvr a comonn fail i i immdialy raird. If h rair faciliy i no immdialy availabl i wai for rair. Comonn ar raird on fir com fir rv FCFS bai. X dno h numbr of faild comonn a im. W dfin IJRICC Ocobr 4 vailabl @ h://www.ijricc.org 6
Inrnaional Journal on Rcn Innovaion rnd in Comuing Communicaion ISSN: -869 Volum: Iu: 6 7 IJRICC Ocobr 4 vailabl @ h://www.ijricc.org S i i X P i } { Whr S i h a ac. hroughou h char w dno ha X =. dno h failur im of comonn R R dno hir rair im. W aum ha h comonn ar idnical in naur. W conidr h following mulivaria xonnial diribuion of R R wih h urvival funcion: max F whr > ; > ; From h a raniion diagram givn abov w form h following diffrnial quaion for.. aing lalac ranform on boh h id noing ha i ={ i } h alac ranform of i. W g h following ym of quaion. lying Cramr rul for olving h quaion w g If dno h roo of h quaion in h dnominaor of h abov xrion hn 8 Obviouly <. bov xrion for can alo b wrin a Now Invr alac ranform on abov wo xrion yild h following rul for : Hnc h ym rliabiliy i givn by: 8
Inrnaional Journal on Rcn Innovaion rnd in Comuing Communicaion ISSN: -869 Volum: Iu: 6 8 IJRICC Ocobr 4 vailabl @ h://www.ijricc.org { R hn d d R MBF Whn hr i no rair faciliy hn } {max [ } {max d P d P MBF d d hu gain in avrag lif of h ym du o rair faciliy i givn by 4. vailabiliy Man Down im nalyi In hi cion w obain h availabiliy maur uch a ady-a availabiliy oin wi availabiliy h man down im of h ym. bfor w conidr h following diffrnial quaion: aing alac ranform on boh h id of abov quaion uing Cramr rul w g: } { } { b h roo of h quaion h xrion for can b wrin a Rolving ino arial fracion h abov quaion olving i aing h invr alac-ranform of h xrion o obaind w g h following xrion for. } {
Inrnaional Journal on Rcn Innovaion rnd in Comuing Communicaion ISSN: -869 Volum: Iu: 6 9 IJRICC Ocobr 4 vailabl @ h://www.ijricc.org ] } { } { [ ] ] [ ] [ [ ] [ W now g h oin wi availabiliy of h ym by +. hu nd h ady-a availabiliy of h ym i obaind by im nd h ym man down im MD i givn by MBF. Rul Concluion h rom variabl R ar indndn if only if =. In our ca h abov xrion clarly dic ha imly rair ror mainnanc of h ym i on of h main ulling facor for any Indury. I affc h organizaion in many way in rm of annual roducion cuomr aifacion comany imag. Variaion of failur ra vru im i dicd by h Bahub diagram givn blow. h uful lif im of h figur indica ha a roduc can b of high MBF bu can hav low rvic lif. Fla ar of h curv indica uful lif riod of h roduc. 6. Rfrnc [] Marhall.W. Olin I.967. mulivaria xonial diribuion. J. mr. Sa. oc. 6-4. [] Rau J.G. 97. Oimizaion robabiliy in Sym Enginring. Van Nor Rinhold Nw Yor. ] [
Inrnaional Journal on Rcn Innovaion rnd in Comuing Communicaion ISSN: -869 Volum: Iu: 6 [] Vnaarihnan K. S.97 Probabiliy analyi of rairabl rdundan ym. hi for Ph.D. in Mahmaic I.I.. Chnnai India. [4] Oai S. 98. wo uni aralll rdundan ym wih bivaria xonnial lif im. Microlcron Rliab. -. [] Klin J.P. Mochbrgr M..986. h indndnc aumion for a ri or aralll ym whn comonn lifim ar xonnial. IEEE ran Rlaib R- no. -. [6] Dharmadhiari.D. Sarmah P. 988. Saiical analyi of a wo-uni dndn rairabl ym. Commun. Sai.-hory Mh 7 8-4. [7] Pijnnburg M. Ravichran N. Rgrchof G.99. Sochaic analyi of a dndn aralll ym. Euroan J. O. r. 68 9-4. [8] Paha V.K. Mha K. Sahu Sma Namdo hih4. Comaraiv udy of rliabiliy aramr of a ym undr diffrn y of diribuion funcion. JMCSR Vol.74 47-4. IJRICC Ocobr 4 vailabl @ h://www.ijricc.org 6