Synthetic Weighted Method of Failure Samples Allocation in Maintainability Test

Transcription

1 26 3 rd Internatona onference on Sart Materas and Nanotechnoogy n Engneerng (SMNE 26) ISBN: Synthetc Weghted Method of aure Sapes Aocaton n Mantanabty Test Jayu Mao, Xshan Zhang, Pengcheng Yan 2, Guangyao an 2 Ordnance Engneerng oege, Shazhuang, hna 2 Ordnance Technoogca Research Insttute, Shazhuang, hna ABSTRAT: In the antanabty deonstraton and evauaton test, the faure sapes aocaton consders snge nfuence factor, the aocaton resut s not too reasonabe, t affected the accuracy of the antanabty deonstraton and evauaton resut. In order to sove the probe, the synthetc weghted ethod of faure sapes aocaton was proposed whch consdered the faure sapes aocaton nfuence factors synthetcay. rsty, on the bass of anayzng the nfuence factors, t defned the nfuence factor set of faure sapes aocaton, and ceared the synthetc weghted aocaton agorth; then, t deterned the nfuence coeffcent and the vaue of the nfuence factors; fnay, a antanabty deonstraton and evauaton test had been done on certan syste. The test resut showed, the ethod proposed n ths artce consdered ore nfuence. INTRODUTION Mantanabty verfcaton test s an anayss and evauaton work, and t s conducted by the specfed test unts or by the orderng party n preproducton n order to deterne whether the equpent eets the antanabty desgn requreents. The aocaton of faure sapes s a key technque of antanabty verfcaton test. It s not reastc to necton a the faure ode under the condton of sa sape antanabty verfcaton experent. When the test sape sze s deterned, t s an urgent probe to deterne the aocaton of faure sapes sze to the equpent syste of each unt. The aocaton of faure sapes s based on the copexty and reabty of the equpent []. It beongs to the scope of the appcaton of statstca sapng. The exstng doestc and foregn reevant ethod standard of faure sapes aocaton osty refer the stratfed sapng and spe rando sapng ethod based on the faure rate. The faure sapes aocaton ethod based on the faure rate factor consdered a snge factor, whch gnored the nfuence of other factors n the aocaton of faure sapes. Usng the cassca ethod to deterne the sape set can ead the representatve of the set unreasonabe, eventuay, naccurate antanabty verfcaton test evauaton resuts were created. To sove above probes, ths thess proposes a synthetc weghted ethod of faure sapes aocaton whch based on the coprehensve 34 anayss of nfuencng factors of faure sapes aocaton. rsty, on the bass of anayzng the nfuence factors, t defned the nfuences factor set of faure sapes aocaton, and ceared the synthetc weghted aocaton agorth; then, t deterned the nfuence coeffcent and the vaue of the nfuence factors; fnay, a antanabty deonstraton and evauaton test had been done on certan syste. 2 SYNTHETI WEIGHTED METHOD O AIURE SAMPES AOATION 2. Infuence factor set of faure sapes aocaton If the faure rate was consdered as the snge nfuence factor n the aocaton of faure sapes, t w nevtaby ead preproducton to dstrbute excessve antanabty resources n soe product odues whch have a hgh faure rate and ow dffcuty of testng, t w gnore those product odues whch have ow faure rate, hgh dffcuty of testng and strong destructveness, Eventuay, The concuson of antanabty verfcaton test w ose credbty. The reabty, antanabty, securty and the dfference of the usng requreent of the equpent have been taken nto coprehensve consderaton when the aocaton of faure sapes n antanabty verfcaton test was proposed [2].

2 The nfuence factor set of faure sapes aocaton has been defned to drect the aocaton of faure sapes n antanabty verfcaton test whch any ncuded the foowng severa factors: aure rate; The faure rate s an portant nfuence factor n the aocaton of faure sapes, unt wth a hgh faure rate shoud be aocated ore faure sapes, the nfuence coeffcent can be expressed by. aure pact; The faure pact refers to the degree of nfuence whch soe syste unts faure caused to the other coponent unts, unts whch have serous faure pact shoud aocate ore faure sapes, the nfuence coeffcent can be expressed by. Mantenance costs; More faure sapes shoud be aocated to these coponent unts whch cost ess antenance costs, the nfuence coeffcent can be expressed by. 2.2 Aocaton agorth of faure sapes based on synthetc weghted Synthetc weghted ethod of faure sapes aocaton need to anayze the characters of coponent unts, then deterne the nfuence coeffcent of a the nfuence factors and the weghted coeffcent of the unts based on engneerng anayss data or expert syste, fnay cacuate the assgned vaue of each coponent unt based on atheatca ode. As shown n forua (). n nξ ξ () ω + ω + + ω In the forua, n represents a the faure sapes to be aocated; n represents the sapes aocated to coponent unt ; ξ represents the reatve weght of coponent unt ; represents the tota nfuence coeffcent of oponent unt ; ω represents the weght of each nfuencng factors whch s deterned by ther degree of portance. The su of the weght of factors equas to. It can draw ths concuson fro forua () that both and ω of each coponent unts shoud be cacuated n order to aocate faure sapes. These paraeters w be deterned n the foowng papers. 3 DETERMINATION O THE INUENE OEIIENT 3. Deternaton of the nfuence coeffcent of faure rate ) Infuence coeffcent of faure rate. can be expressed by the faure rate of coponent unt,as shown n the forua (2). (2) 2) Estaton of faure rate based on the dstrbuton ode of Gaa. or the syste whose servce fe foow exponenta dstrbuton, dstrbuton of Gaa was seected as the pror dstrbutons of faure rate. As shown n forua (3). a b a b π ( ) e a, b > (3) Γ( a) In the forua, a t a t e dt Γ ( ), a and b are the hyper-paraeters of dstrbuton Gaa whch can be obtaned by pror nforaton. Hyper-paraeter dstrbuton a, b can be obtaned by the dfferent fracte of dstrbuton Gaa [3]. The agntude of faure rate K, nu vaue of faure rate correspondng confdence coeffcent and the axu vaue of faure rate U correspondng confdence coeffcent 2 can be obtaned fro equpent test run data and expert experence of reabty. Then the quante of dstrbuton Gaa was cacuated by the foowng forua. a b a b e d a t t e dt (4) U a b a b e d 2 a t t e dt The ean of dstrbuton Gaa represents the pont estates of faure rate whch was used for faure sapes aocaton n antanabty. As shown n forua (5). a (5) b 3.2 Deternaton of nfuence coeffcent of faure pact ) aure pact coeffcent. can be represented by, and s the su of faure ode severe degree. As shown n forua (6). 35

3 (6) 2) The anayss of the severe degree of faure ode was based on trapezoda fuzzy nuber. uzzy anguage was adopted to ake sure the faure ode severe degree because of subectvty and uncertanty. Every faure ode severe degree eve was defned a trapezoda fuzzy nuber on the bass of the herarchy of severe degree [4]. It s shown n Tabe. Tabe. assfcaton crtera of severe degree and trapezoda fuzzy nuber. Severe degree of faure ode aure pact Trapezoda uzzy Nuber eve I (Bady daaged) eve II (Severey daaged) eve III (Moderatey daaged) eve IV (Mdy daaged) asuates or bad syste daage were caused. Serous nury, great econoc osses or severe syste daage were caused. Moderate nury, oderate econoc osses or syste daage were caused. No nury, d econoc osses or d syste daage were caused. (.85,.95,, ) (.6,.75,.8,.9) (.35,.45,.55,.65) (,.5,.25,.4) Trapezoda ebershp functon correspondng wth the severe degree of faure ode was shown n fg.. Basc expressons can be expressed as f ( f, f2, f3, f 4). Trapezoda fuzzy nuber can be obtaned wth the foowng forua (7). f + f2 + f3 + f4 f (7) Deternaton of the nfuence coeffcent of antenance costs Mantenance costs were ade up of the costs of antenance resource aocaton and the costs of antenance procedure. osts of antenance resource aocaton were expressed by.osts of antenance procedure were expressed by 2 [5]. Mantenance costs can be obtaned wth the foowng forua (8) + 2 (8) The nfuence coeffcent of antenance costs can be obtaned fro forua (9). gure. Trapezoda ebershp functon DETERMINATION O THE WEIGHT O INUENING ATORS (9) The weght of nfuencng factors was obtaned by the ethod of anaytc herarchy process. 4. Estabshent of evauaton atrx Each nfuencng factor was copared wth the others based on expert syste. The eve of each factor was evauated based on portance [6]. Nne portance degrees and ther assgnent were sted n Tabe 2. The udgent atrx was shown as forua (). represents the degree of sgnfcance when factor copared wth factor. It s obvous that >,

4 , () 2 M 3 23 M Tabe 2. Degree of sgnfcance and evauaton n factors coparng. Nuber Degree of sgnfcance Evauaton, are equay portant 2 s sghty portant than 3 3 s obvousy portant than 5 4 s Strongy portant than 7 5 s Extreey portant than 9 6 s sghty unportant than /3 7 s obvousy unportant than 8 s Strongy unportant than 9 s Extreey unportant than /5 /7 /9 ω ( ω, ω, K, ω ) T onsstency test The ratonaty of udgent atrx was checked by the consstency test. onsstency rato (R) was ntroduced to check the consstency of the udgent atrx, the udgent atrx s consstent f R <., otherwse t s necessary to adust the udgent atrx unt t eets the consstency condtons [7]. R can be cacuated by forua (4). I ax n R (4) RI RI ( n ) In the forua, the axu egenvaue of the udgent atrx was expressed as ax ; the average of rando consstency ndcators was expressed as RI, ts vaue vares wth the order of udgeent atrx. The average of 4~9 order rando consstency ndcators was represented n Tabe 3. Tabe 3. The average of rando consstency ndcators. Order RI APPIATION 4.2 acuaton of the weght vector Reatve weghts of every factor were cacuated by the ethod of Reguarzaton suaton n the foowng. ) Every couns of coparng atrx were norazed:,,,2, K, () b k k 2) Every rows of norazed atrx were added: W,,2, K, (2) 5. Aocaton of faure sapes based on synthetc weghted ethod As shown n fg 2, the test syste s coposed of functona odue A, B,, D and E. In the foowng artce, faure sapes of the test syste were aocated by the ethod of synthetc weghted ethod. aure sape sze n 5, faure rate of each coponent unt can be cacuated based on Eq.(4) and Eq.(5), then substtute the nto Eq.(2), the nfuence coeffcent of faure rate can be cacuated; The resuts of the anayss of the severe degree of faure ode can be concuded based on expert syste, then substtute the nto Eq.(6), the 3) Matrx W ( W, W2, K, W ) T was norazed: faure pact coeffcent W can be cacuated; the ω,,2,, K (3) nfuence coeffcent of antenance costs can be W cacuated based on Eq.(8) and Eq.(9).The paraeter of each nfuence coeffcent was shown n Tabe 4 4) Reatve weghts of every factor were shown n and Tabe 5. Tabe 4. The vaue of nfuence coeffcent. Modue aure rate( ) Su of faure ode severe degree() Mantenance costs() A B D E Tota

5 Tabe 5. The weght of nfuence coeffcent. Weght ω.45 ω.3 ω.25 ω Modue A B D E Tota. It can be cacuated fro the paraeters n the tabes that ξ A.32, ξ B.7, ξ.2397, ξ D.3222, ξ E.889, then substtute the nto Eq.(), t can draw ths concuson that na 7, nb 6, n 2, nd 7, ne. onsderng the non-nteger of the aocaton vaued the saest nteger greater than the vaue of aocaton, the tota sapes reached to oparson of dfferent aocatons The sae faure sapes fro the test syste w be aocated wth the ethod of aocaton of faure sapes based on faure rate whch s entoned n thess [8], forua s shown as foows. n n p Q T p (5) QT The eanng of the etters n the forua, data and the resut of two dfferent aocatons were shown n Tabe 6. It can be known by coparng the two ethods of aocaton that: ) onsderng the non-nteger of the aocaton vaued the saest nteger greater than the aocaton, the tota sapes reached to 52. Modue aure rate( ) Nuber of unts(q) Tabe 6. oparson of aocaton. oeffcent of work Resut based on ethod te(t) of faure rate Resut based on ethod of synthetc weghted A B D E 5 7 Tota ) When faure sapes were aocated based on faure rate, ore faure sapes were aocated to odue than odue D because of the hgher faure rate; Because the synthetc weghted ethod of faure sapes aocaton consdered ore nfuences factors, the sapes aocated to odue and odue D was decreased, the decreased sapes were aocated to odue A, odue B and odue E whch got the ower faure rate but worse faure pact and hgher antenance costs. test of a certan syste. When coparng wth the ethod whch accordng to the proportona dstrbuton of stratfed sapng based on faure rate, the aocaton based on synthetc weghted ethod was proved ore reasonabe, The resut of antanabty test based on synthetc weghted ethod of faure sapes got ore coser to the true eve of antanabty desgn of the syste, The synthetc weghted ethod of faure sapes aocaton has great vaue n engneerng appcaton. 6 SUMMARY In ths thess, the nfuencng factors n the aocaton of faure sapes were anayzed. Synthetc weghted ethod of faure sapes aocaton was proposed for the aocaton probes of faure sapes n antanabty test. The ethod was proved consderng the nfuencng factors ore coprehensve n the antanabty REERENES [] SHI Jun-you, KANG Ru. Study on the Pan of Testabty Deonstraton Based on the Genera Adequacy rteron. Acta Aeronautca et Astronautca Snca. Vo. 26 (25) No.6, p [2] Tane, Qu Jng, u Guanun. Aocaton Pan of aure Sapes Based on aure Rate n Testabty. Acta Aeronautca et Astronautca Snca. Vo. 3 (29) No. 9, p

6 [3] MI-HDBK-265 Testabty handbook for systes and equpent. USA, 995. [4] GJB/Z Gude to faure ode, effects and crtcaty anayss. Standards press of chna. 26, p. 4-6 [5] Departent of Defense.MI-STD-47A Mantanabty verfcaton/ deonstraton/ evauaton.u.s.governent Prntng Offce, 973. [6] Yu Sq, Jng Bo, Huang Yfeng. Study on aocaton schee of faure sape n testabty vadaton tests based on contrbuton. hna Measureent & Test. Vo. 4(25) No.2, p [7] Zhao Janyang, Xaon, e Qn. Reatve crtcaty rato based on faure sapes aocaton. Journa of Detecton & contro. Vo 33(2) No. 2, p [8] v huan, Zhou Dong. Desgn, Anayss and Verfcaton of Mantanabty. Natona Defend Industy Press. 22, p