Calculation Method of Internetware Reliability Distribution

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1 Sed Orders for Rerts to 44 The Oe Cyberetcs & Systemcs Joural, 14, 8, Calculato Method of Iteretware Relably Dstrbuto Oe Access Jg Zhag 1,, *, Hag Le 1, Xua Ha 1 ad Yusheg Wag 1 1 School of Comuter Sece ad Egeerg, Uversy of Electroc ad Sece Techology of Cha, Chegdu, Schua, , PR Cha; School of Comuter, Pazhhau Uversy, Pazhhua, Schua, 617, PR Cha Abstract: To la Iteretware relably advace ca effectvely save cost ad guaratee the relably of Iteretware system The coverso method of Marov cha of Iteretware based o archecture ad the relably calculato method are studed; the relably fucto based o structure s roosed; the characterstcs of the mrovemet of Iteretware relably s aalyzed; the cost fucto of Iteretware relably s studed; the ucertaty of dyamc dstrbuto a certa rage ad the dstrbuto accuracy are mroved; the re-dstrbuto s ut forward; the effectve laed dstrbuto of Iteretware relably s realzed by usg otmzato calculato algorhm The exermets rove that the roosed method ca effectvely dstrbute Iteretware relably wh hgh system relably, low cost ad short dstrbuto calculato tme Keywords: Algorhm, archecture, cost, dstrbuto, Iteretware, relably, method 1 INTRODUCTION Iteretware, a mortat software alcato mode the teret evromet, uts software etes the form of software comoet to Iteret ode a way of beg oe ad dscretoary Every software ety ca ublsh some way the oe evromet, ad tercoects, tercommucates, cooerates ad forms coalo wh other software etes through cross-etwor oe way or aother to form teret alcato software system wh some alcato fuctos Adatvy, cooeratvy, reactvy, evoluto ad olymorhsms are the ma characterstcs of Iteretware [1, ] Accordg to the formato rocess of Iteretware, s relably s flueced by the la, desg, mlemetato ad oerato of the software, ad so o At reset the study of software relably maly tests the related oerato data of the exstg software system to calculate system relably O the Iteret, s dffcult to meet the demad for reacto ad adatato of Iteretware ad to mrove evoluto because of the comlex testg evromet, large amout of data ad delay So, to study relably la of the software the desg stage wll effectvely suort the relably aalyss of Iteretware system, ad revet the system from erfectg the desg ad develomet of the software because s relably ca ot meet the demad after the system s made Ths ca greatly reduce develomet cost ad shorte the cycle To dstrbute ad la the relably advace s beef for the effectve costructo of Iteretware system There are mature models ad methods of Iteretware relably study [3] Documet [4] has studed the test method X/14 of Iteretware relably; documets [5, 6] have roosed the calculato method of Iteretware relably based o Marov cha, ad realzed the relably calculato based o the state; documet [7] has studed the aroxmate redcto method of Iteretware relably based o structure; documet [8] has ut forward a aroxmate method of Iteretware relably ad test tme dstrbuto; documet [9] has roosed the dstrbuto method of test resources the develomet stage by usg software growth model; documet [1] has roosed the strategy model of relably dstrbuto, ad made dyamc la by usg Lagraga method, but has ot tae the demad for uer ad lower lm of relably realy to cosderato; documet [11] has made relably dstrbuto by usg ferece of Bayesa etwor ad codoal robably, ad calculated relably dstrbuto through codoal falure robably, but FTA, s dffcult to dede robably, the mortace of structure ad so o, ad ths s flueced by may factors; documet [1] has ut forward a dyamc aroxmato algorhm to dstrbute relably, ad measured the degree of aroxmato by usg the rato of the cost chage to the relably chage, whch has some lmatos ad the sgle determat I a word, because of dfferet relably calculato methods such as aroxmato method, or the method based o test data ad arameter otmzato, the result ad the effect of dstrbuto are dfferet Iteretware relably calculato has two ma methods, oe based o ath, ad the other based o state The method based o ath has o hgh accuracy It just maes the estmato of system relably, ad s ot suable for the fe ath system So has s lmatos The method based o state s suable for the fe ath system I the oe evromet, s loose coulg amog comoets, the comoets have comaratvely hgh deedece, ad the trasfer amog comoets s accordace wh 14 Betham Oe

2 Calculato Method of Iteretware Relably Dstrbuto The Oe Cyberetcs & Systemcs Joural, 14, Volume 8 45 Marov characterstcs, so s better to be used the oe evromet But the tradoal relably calculato method based o state has the followg shortcomgs: 1 the exaso of state sace I the oe evromet, there may be thousads of comoets a system The tradoal aalyss method wll lead to rad exaso of state sace ad crease calculato comlexy ad eve mae calculato mossble Beg usuable for software wh comlex rogram structure I the oe evromet, the system structure of software s more ad more dversfed The tradoal aalyss method has some lmatos both alcato scoe ad usage coveece It s oly suable for classc structures, ad ca ot deal wh comlex structure systems such as arallel ad call [4] So, based o UML, case dagram ad sequece dagram ca be used to aalyze ad smlfy structure [13, 14] The chage to state dagram whch s accordace wh Marov characterstcs At last the system relably ca be calculated the software desg stage ad the relably dstrbuto ca be acheved Ths aer has the followg arts: art s Iteretware relably calculato method, art 3 s Iteretware relably la, art 4 s exermet ad art 5 are coclusos ad future wor INTERNETWARE SYSTEM RELIABILITY 1 Relably Calculato Iteretware s comosed of deedet software etes, that s, comoets Comoets are combed to form Iteretware system wh certa archecture Iteretware acheves some sefc fuctos through comoets executg call (that s, comoet trasfer Comoet trasfer o certa archecture reflects ad embodes Iteretware fucto ad relably So, uder certa archecture, system relably s related ot oly to traso robably but also to comoet relably Defo 1 Calculato model of Iteretware relably Iteretware comoet set s R = { r 1, r,, r m}, + m N ; traso robably of comoets ad j s P = { j }, ad, j [1,,, m] ; ST s a sefc archecture, whch s emboded by comoet traso Iteretware relably model s RE : f ( ST, P, R [,1] Trasfer cotrol amog system comoets ca be descrbed by Marov cha Whe executed, each comoet s corresodg to a Marov cha state System relably calculato [4, 5] s as follows: + 1 ( I Q,1 RE = ( 1 r (1 ( I Q I Formula (1, I s characterstc matrx; ( I Q,1 meas deletg le colum 1 of matrx ( I Q ; q j = r j ; r meas relably of No comoet Traso robably embodes comoet coecto (trasfer drecto ad coecto measure (trasfer rato, ad also determes relably calculato result Software system structure ca be obtaed through system fucto desg or automatc toology dscovery Traso robably ca be obtaed through system fucto desg or later test Usually traso robably umbers are: 1 determed by referrg to oerato statstcs of the exstg smlar system software; determed by related exerts exerece the dustry ad feld; 3 obtaed by test case ad software oeratoal rofle The Formato of Marov Cha of Iteretware To obta traso robably, the early stage of software desg, UML sequece dagram s trasformed to Marov cha, each comoet s corresodg to a executo state, ad ths forms Marov cha state dagram, the trasfer relato (or system structure formato ad traso robably ca be obtaed, thus relably ca be calculated To trasform UML sequece dagram to Marov cha to form state dagram of Iteretware comoets ad coecto, the same boudares ad odes should be combed, ad traso robably should meet the requremet of Marov cha to form ormatve comoet trasfer dagram ad fally obta Marov cha ate dagram before trasformato < V, E > V = { v1, v,, vm} E = { e ej = ( s, s j, j },, j [1,,, m] V, E mea the vertex set of comoets ad the boudary set of comoet coecto; j meas traso robably; the state dagram after trasformato s < V, E > I UML sequece dagram, the defo of traso robably of comoet comoet trasfer j s as follows: j = s = 1 s t eract(, c t eract(, c l j l= 1,,, N c c S S: the umber of scees; s : executo robably of scee s ; N: the umber of comoets; t eract ( c, c j : the teracto umber of comoets ad j scee s The calculato of covertg UML sequece dagram to Marov cha s as follows: 1 Ialzato Set al valuev, E, V, E are emty If v, v V,, j [1,,, m], the j, j v V e jf, f, j [1,,, m], f v j = v f, the delete ay ode of v j, v f Suose deletg v j, the { e }, { v },, [1,,, j 1, f,, m] 3 If e, e jt If If e jt E, the e jt E, the E, v j, v V, v j = v, jt = + jt ; e jt E, e jt = ( v j, vt, jt (

3 46 The Oe Cyberetcs & Systemcs Joural, 14, Volume 8 Zhag et al E 4 v V, start from v ad form set of all boudares 5 I 6 I E, E, ej = ( v, v j, j qj = jr ;, udate to j = / j 7 calculate relably accordg to formula (1 3 Relably Calculato Fucto Suose the Iteretware system s comosed of comoets, start comoet s s 1, relably s r 1, ad ed comoet s s t As Fg (1, suose trasfer state matrx P The trasfer from s 1 to s t may go drectly, or go from brach odes, thus there would be K stes to acheve the goal There are the followg suatos: 1 drectly: s 1 s t go through trasfer odes: s 1 s + s t, or s 1 s1 1 s 1 1 Fg (1 ate dagram 1 S The system relably s: R = R1 t + R1, t + + R1, t s [ 1,, ] s t 1 + 1, t = R + ( r1 r = R t R 1 s s, j s t, or R = R + ( r r (3 1 If there s retur s, as Fg (, the obta: 1 R1, t r1 ( r r = r1 ( I Q r = Q = r =, whch s 1 1 P Fg ( ate dagram retur s P [ 1,, ] R R1 t + R1, t + + R1, t 1 1 { q j 1 = = R + ( r ( I Q r, whch I s u matrx, matrx Q = }, q 1 1 j= r, that s: j R = R + ( r ( I Q r (4 1 So relably ca be calculated by usg formula (4 If there are the suatos as Fgs (1 ad (, see Fg (3 s 1 1 Fg (3 ate dagram uder comrehesve suatos r1 ( I Q r s R = r, obta: R = r1 + r1 r /(1 r (5 For coveece, abbrevated to A1 t = r1, B1 = r1, C 1 t = r, D = r, the obta: R = A + B C /(1 D (6 1 D s the rel- C 1 t s the relably from s 1 to s t, ad ably from s to s P So, the degree of comoets flueg system relably, that s, the sesvy, s: / r = r1 /(1 r R (7 Accordg to formula (7, the mortace of comoets relably Iteretware system relably ca be evaluated Because 1, = 1, the: R t = + / r = r1 (1 /(1 r Chage formula (5 to obta: r = (R r 1 /( 1 r 1 r 1 + R (8 Obta re-dstrbuto relably of Iteretware comoet: r = ( R r1 /((1 r1 + ( R r1 (1 (9 I order to calculate easly, suose r1=1, that s, the start comoet s relable whch ca oerate successfully ad guaratee the trasfer of comoet executo state, thus formula (9 becomes: r = ( R /((1 + ( R (1 (1 = 1 = 1/(1/(1 = 1/ ( = 1/( I P = 1

4 Calculato Method of Iteretware Relably Dstrbuto The Oe Cyberetcs & Systemcs Joural, 14, Volume = 1/( I P (11 = 1 = 1 /((1 /(1 = 1 1 ( / ( = 1( 1 / ( = = = = = /( I P ( I P (1 11 S1 1 1 S Fg (4 System state dagram 31 As Fg (4, comoets S1, S ad form a Iteretware system Suose comoet relables are resectvely r1=997559, r=999939,r3=999989, ad traso robables P 11 =8, 1 =, 1 =4, =4, 3 =, 31 =4, 33 =4, 3t = Traso robably matrx s: Q=[8*r1 *r1 ; 4*r 4*r *r; 4*r3 4*r3] Accordg to documets [4, 5] ad formula (1, system relably exresso s: R=*(-r1*r/(5*((4*r1/5 + (*r/5 + (*r3/5 - (6*r1*r/5 - (8*r1*r3/5 - (4*r*r3/5 + (14*r1*r*r3/ 15-1 (13 Put each comoet relably value to the formula (13, obta system relably RE1 = Accordg to Fg (4 ad formula (6, 1,r 1 =,B 1 =1, suose C = C 1-t s the relably from s 1 to s t, that s, s1 s s 3 s t ; suose D = D 1-1 s the relably from state 1 to state 1, that s, s 1 s 1, s1 s s 1, s1 s s3 s 1, thus obta: C 1-t = r1**r**r3*/((1-r3*4*(1-r*4; D 1-1 =r1*8+r1**r*4/(1- r*4+r1**r**r3*4/((1-r*4*(1-r3*4; Accordg to formula (6, obta system relably RE= C /(1- D, that s: R=-(r1*r*r3/(15*((*r/5-1*((*r3/5-1*((4*r1/ 5 - (*r1*r/(5*((*r/5-1 + (*r1*r*r3/(15*((* r/5-1*((*r3/ (14 Put each comoet relably value to the formula (14, obta RE= Comare the calculato results, absolute error s e-6, ad relatve error s e-5 Usg Mote Carlo samlg method, the mea value of the formula (13 s , ad the varace s S e-8 The mea value of the formula (14 s , ad the varace s aroxmately zero So, the relably fucto s effectve 3 INTERNETWARE COMPONENT RELIABILITY DISTRIBUTION 31 Relably Cost Fucto Software relably s drectly related to develomet cost whch s flueced by may factors such as software comlexy, develomet tool, develomet exerece ad develoers Relably cost fucto has the followg sgfcat characterstcs: 1 The value of the fucto s osve; The fucto s o-decreasg; 3 The hgher the relably, the hgher the relably cost The reset relably cost fuctos are maly owerful umber model, olyomal model, Lagraga model, logarhm model, ad dex model Accordg to classc Mettas cost fucto, ad because Iteretware should coect ad call o cross-etwor to acheve teracto amog comoets, set a teracto rato arameter Cost fucto s as follows: C( R e R R,m (1 R, max R = (15 I whch s the comlexy of comoet, R s the relably of comoet, R, m s the mmum relably all comoets, ad R, max s the maxmum relably all comoets Comlexy referece c ca be tested by usg cyclomatc comlexy, but ths wll ot be dscussed ths aer I al stage, because of develoers degree of famlary wh software ad the rearato, earler stage cost s very hgh, Use LOG fucto f ( r = LOG( C( r (16 3 Relably Dstrbuto Relably dstrbuto demads that system relably be the hghest ad that cost be the lowest [15, 16] Accordg to comoet relably ad cost calculato formula, obta the followg system relably dstrbuto la model: M f ( r s t R( r >= R, 1 r > (17 > The above model ca be calculated by usg otmzato algorhm [17, 18] to obta comoet relably dstrbuto I order to mrove effecy, use formulas (1 - (1 to calculate ad obta comoet re-dstrbuto value ad use as referece value to obta calculato result faster ad more accurately

5 48 The Oe Cyberetcs & Systemcs Joural, 14, Volume 8 Zhag et al Table 1 Relably Dstrbuto No Pre-dstrbuto Value: (r1,r,r3 Module Dstrbuto Relably System Relably Cost Oerato Tme (Secod 1 (5 5 5 (1 1 1 ( ( e e ( ( e ILLUSTRATION Accordg to Fg (4, obta relably dstrbuto model: M log( e 1 R 1R s t R( r >= R, 1 r > 5 (18 > I whch calculate R(r by usg formula (14, ad set R =9 to mea the lowest value requred by system relably Use geetc algorhm, set some arameters: oulato:, the bggest eratve umber: 5, crossover robably :97, mutatoal rate: 1, ad mobly: Use formulas (1-(1 to obta resectvely relably re-dstrbuto values of comoets s: [r1, r, r3]=[ , , ] Use Matlab smulato software, relably dstrbuto ad corresodg system relably, ad cost are Table 1 I Table 1, for the scheme desged ths aer (that s, scheme 3, the cost s decreased by 68%, ad 117%, comared wh scheme 1 ad scheme ; the system relably s the hghest; the oerato tme s the shortest, whch has bee shorteed by 74% ad 537% So acheves the dstrbuto urose ad effect The mortace of relably s aalyzed by usg formula (7 ( R / r1, R / r, R / r3 = (36731,13188,417 The fluece o system relably are resectvely 6897%, 3137%, 7893% So system relably s maly flueced by comoet 1 ad comoet 5 CONCLUSIONS AND FUTURE WORK Iteretware relably la dstrbuto volves may factors Dog relably la dstrbuto desg stage s beef to system develomet ad costructo, decreases later modfcato cost ad guaratees Iteretware system relably The method to chage Iteretware to Marov state cha accordg to archecture desg stage has bee studed; the relably comutato ad the relably fucto geerato method have bee aalyzed Combed wh Iteretware characterstcs, the cost fucto of mrovg relably has bee studed Accordg to re-dstrbuto, usg geetc algorhm to mae dyamc la, relably has bee dstrbuted effectvely wh low cost, short dstrbuto tme ad mroved system relably Later automatc extracto method of Iteretware archecture ad automatc acquso method of traso robably wll be studed to mrove the geerato effecy of relably fucto The accuracy of relably cost fucto wll be studed to mrove the accuracy ad comrehesve effect of Iteretware relably dstrbuto CONFLICT OF INTEREST The authors cofrm that ths artcle cotet has o coflct of terest ACKNOWLEDGEMENTS Ths wor s sosored by the Foudato Project ( of atural sece of Haa rovce, ad the Foudato Project(14ZA341 of Schua Educato Deartmet Authors gratefully tha the aoymous revewers for ther valuable commets o ths mauscrt ABOUT THE AUTHORS Frst Author ZHANG Jg s curretly a doctor caddate School of Comuter Sece ad Egeerg, UESTC ad a rofessor at the Comuter School, Pazhhua Uversy Hs research terests clude software relably ad comuter etwor relably Secod Author LEI Hag, receved the PhD degree from UESTC 1997 He s curretly a rofessor wh UESTC Hs research terests clude software relably testg ad evaluato, hardware-software co-desg of embedded systems Thrd Author HAN Xua s curretly a doctor caddate School of Comuter Sece ad Egeerg, UESTC Hs research terests clude software egeerg, software relably aalyss techques ad software test case geerato

6 Calculato Method of Iteretware Relably Dstrbuto The Oe Cyberetcs & Systemcs Joural, 14, Volume 8 49 Fourth Author WANG Yu-sheg s a PhD Caddate School of Comuter Sece ad Egeerg of UESTC ad the rograms maager Cha Electroc Techology Avocs Co, LTD Hs research terests clude software egeerg ad avocs software relably REFERENCES [1] H Me, G Huag, ad T, Iteretware: A software aradgm for Iteret comutg, IEEE Softw, vol 45, o 6, 6-31, 1 [] W T Tsa, Z J, ad X Y Ba, Iretware Comutg:Issues ad Persectve, It J Softw Iform, vol 3, o 4, , 9 [3] K Tyag, A Sharma, Relably of comoet based systems - A crcal survey, WSEAS Tras Comut, vol, o 11, 45-54, 1 [4] C J Hsu ad C Y Huag, A adatve relably aalyss usg ath testg for comlex comoet-based software systems, IEEE Tras Relab, vol 6, o 1, , 11 [5] R C Cheug, A User-Oreted software relably model, IEEE Tras Softw Eg, vol 6, o, , 198 [6] J Lo, C Y Huag, I Y Che, S Y Kuo, ad M R Lyu, Relably assessmet ad sesvy aalyss of software relably growth modelg based o software module structure, Comut Softw Al, vol 76, o 1, 3-13, 5 [7] S S Gohale, K S Trved, Relably Predcto ad Sesvy Aalyss Based o Software Archecture, Proceedgs of the 13th Iteratoal Symosum o Software Relably Egeerg(ISSRE, Nov 1-15,,Aaols, MD, USA, [8] R Petratuoo, S Russo, K S Trved, Software Relably ad Testg Tme Allocato: A Archecture-Based Aroach, IEEE Tras Softw Eg, vol 36, o 3, , 1 [9] MR Lyu, SRagaraja, AP A va Moorsel, Otmal allocato of test resources for software relably growth modelg software develomet, IEEE Tras Relab, vol 51, o, , [1] J H Lo, S Y Kuo, M R Lyu, ad CY Huag, Otmal Resource Allocato ad Relably Aalyss for Comoet-Based Software Alcatos, Proceedgs of the 6 th Aual Iteratoal Comuter Software ad Alcatos Coferece (COMP- SAC, 6-9 August,, Oxford, Eglad, 7-1 [11] W X Qa, X W Y ad L Y Xe, System Relably Allocato Based o Bayesa Networ, Al Math Iform S, vol6, o 3, , 1 [1] H Gua, T M Wag, ad W R Che Exlorg Archecture- Based Software Relably Allocato Usg a Dyamc Programmg Algorhm, Proceedgs of the Secod Symosum Iteratoal Comuter Sece ad Comutatoal Techology (ISCSCT 9, Huagsha, PR Cha, 6-8, Dec 9, [13] J Ya, J Wag, H W Che, Dervg Software Marov Cha Usage Model from UML Models, J Softw, vol 16, o 8, , 5 [14] L Y Y, udy o software relably aalyss model automatcally trasform based o UML, MS Thess, Chogqg Uversy, Arl 1 [15] K K Aggarwal, J S Guta, O mmzg the cost of relable systems, IEEE Tras Relab, vol 4, o 3, 5-9, 1975 [16] A O C Elegbede, C Chu, K H Adjallah, ad F Yalaou, Relably allocato through cost mmzato, IEEE Tras Relabl, vol 5, o 1, , 3 [17] H Rathod, M Parmar, udy of geetc aroach estmatg relably of comoet based software, Ida J Res, vol 1, o 11, 17-19, 1 [18] S H Aljahdal, M E El-Telbay, Geetc algorhms for otmzg esemble of models software relably redcto, ICGST- AIML J, vol 8, o 1, 5-13, 8 Receved: Setember, 14 Revsed: November 3, 14 Acceted: December, 14 Zhag et al; Lcesee Betham Oe Ths s a oe access artcle lcesed uder the terms of the Creatve Commos Attrbuto No-Commeral Lcese (htt://creatvecommosorg/- lceses/by-c/3/ whch erms urestrcted, o-commeral use, dstrbuto ad reroducto ay medum, rovded the wor s roerly ced