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proiect la disciplina FST fiabilitatea sistemelor
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Pentru realizarea acestui proiect s-au ordonat crescator in functie de numarul de kilometri evenimentele care au avut loc. Acest lucru ajuta la determinarea marimii intervalului t asa cum este prezentat mai jos.
Nr crt.KmDefectiuneMasina
127000BateriaFord Fiesta
255000Cutia de vitezeOpel Insignia
395000AmbreiajulSkoda Superb
4100000Pompa combustibilOpel Astra Clasic
5110000TurbosuflantaVW Passat
6120000Caseta de directieHonda Civic
7160000Sistemul de franareRenault Clio
8180000AmbreiajulVW Touran
9190000Pompa de racireSkoda Octavia Tour
10220000InjectoareleFiat Sedici
Cu ajutorul relatiei de mai jos se determina intervalul t.==4457,74t min- timpul la care a fost observat primul eveniment (in km)
t max- parcursul cel mai mare (in km)
N= numar de interogari
Se adopta t=45000 [km]
Pentru determinarea intervalelor de timp si numarul de defectiuni se realizeaza urmatorul tabel:
Interval0-4500045000-9000090000-135000135000-180000180000-225000
ti22.50067.500112500157500202500
Ni12331
N136910
F(ti)0,10,30,60,91
F(ti)[%]10306090100
Se determina frecventa cumulata a defectarilor cu relatia:
=
unde: Ni- numarul de defecte pe fiecare interval
Se traseaza frecventa cumulata a defectarilor pe diagrama Weibull apoi se estimeaza cu
ajutorul diagramei, parametrii constanti ai legii Weibull astfel:
-se evidentiaza mijlocul fiecarui interval si frecventa cumulata a defectarilor
-daca punctele se afla pe o dreapta, cu aproximatie, atunci este zero;
-se intersecteaza dreapta formata de puncte cu dreapta randamentului
de pe abscisa corespunzatoare punctului de intersectie, afland astfel parametrul de scara,
-parametrul de forma se determina prin trasarea unei paralele prin punctul de
coordonate la dreapta valorilor experimentale.
Valorile obtinute:
108000Parametruvietii caracteristice
1,6parametru de forma
0parametru de pozitie
Pentru determinarea valorilor pentru fiabilitate, densitatea de probabilitate, intensitatea
de defectare si nefiabilitate se folosesec relatiile:
F(t)= 1-R(t)
Valorile obtinute se gasesc in tabelul urmator:
t(km)ExponentR(t)R(t)F(t)f(t)Z(t)
001000
3000-0,0036592660,9963474210,0036525791,94448E-061,95161E-06
6000-0,0110928210,9889684780,0110315222,92545E-062,95809E-06
9000-0,0212220830,9790015210,0209984793,69359E-063,77281E-06
12000-0,0336271450,9669319630,0330680374,33535E-064,48362E-06
15000-0,0480558220,9530805820,0469194184,88545E-065,12595E-06
18000-0,0643333270,937692390,062307615,36221E-065,71852E-06
21000-0,0823286270,9209692540,0790307465,77692E-066,27266E-06
24000-0,1019384410,9030851430,0969148576,13727E-066,7959E-06
27000-0,1230784510,8841942940,1158057066,4489E-067,29354E-06
30000-0,1456780120,8644359960,1355640046,71623E-067,76949E-06
33000-0,1696767370,8439375860,1560624146,94286E-068,22675E-06
36000-0,1950221780,822816410,177183597,13189E-068,66765E-06
39000-0,2216681880,8011811620,1988188387,28601E-069,09408E-06
42000-0,2495737270,7791328360,2208671647,40766E-069,50757E-06
45000-0,2787019590,7567654160,2432345847,49909E-069,9094E-06
48000-0,3090195670,7341664040,2658335967,56239E-061,03007E-05
51000-0,340496210,7114172230,2885827777,59953E-061,06822E-05
54000-0,3731040950,688593550,311406457,61236E-061,10549E-05
57000-0,4068176330,6657655930,3342344077,60267E-061,14194E-05
60000-0,4416131540,6429983290,3570016717,57217E-061,17764E-05
63000-0,4774686690,6203517210,3796482797,5225E-061,21262E-05
66000-0,5143636820,5978809160,4021190847,45523E-061,24694E-05
69000-0,552279020,5756364280,4243635727,37187E-061,28065E-05
72000-0,5911966910,5536643230,4463356777,27388E-061,31377E-05
75000-0,6310997690,5320063950,4679936057,16265E-061,34635E-05
78000-0,671972290,5107003350,4892996657,03952E-061,3784E-05
81000-0,7137991560,4897799080,5102200926,90577E-061,40997E-05
84000-0,7565660650,4692751240,5307248766,76262E-061,44108E-05
87000-0,8002594370,4492124070,5507875936,61125E-061,47174E-05
90000-0,8448663540,4296147710,5703852296,45275E-061,50198E-05
93000-0,8903745090,4105019870,5894980136,28818E-061,53183E-05
96000-0,9367721540,3918907590,6081092416,11854E-061,56129E-05
99000-0,9840480640,3737948860,6262051145,94476E-061,59038E-05
102000-1,0321914920,3562254390,6437745615,76773E-061,61912E-05
105000-1,0811921370,3391909230,6608090775,58828E-061,64753E-05
108000-1,1310401160,3226974390,6773025615,40717E-061,67561E-05
111000-1,1817259330,3067488540,6932511465,22513E-061,70339E-05
114000-1,2332404530,291346950,708653055,04282E-061,73086E-05
117000-1,2855748830,2764915880,7235084124,86086E-061,75805E-05
120000-1,3387207460,262180850,737819154,67983E-061,78496E-05
123000-1,3926698650,2484111940,7515888064,50022E-061,8116E-05
126000-1,4474143440,2351775910,7648224094,32253E-061,83799E-05
129000-1,5029465520,2224736630,7775263374,14718E-061,86412E-05
132000-1,5592591090,2102918170,7897081833,97454E-061,89001E-05
135000-1,6163448720,1986233680,8013766323,80496E-061,91567E-05
138000-1,6741969190,1874586640,8125413363,63876E-061,9411E-05
141000-1,7328085420,1767871980,8232128023,47618E-061,96631E-05
144000-1,7921732360,166597720,833402283,31747E-061,9913E-05
147000-1,8522846840,1568783390,8431216613,16281E-062,01609E-05
150000-1,9131367510,1476166230,8523833773,01238E-062,04068E-05
153000-1,9747234760,1387996880,8612003122,86631E-062,06507E-05
156000-2,0370390630,1304142880,8695857122,72471E-062,08927E-05
159000-2,1000778720,1224468930,8775531072,58765E-062,11329E-05
162000-2,1638344120,1148837640,8851162362,4552E-062,13712E-05
165000-2,2283033370,1077110240,8922889762,3274E-062,16078E-05
168000-2,2934794380,1009147240,8990852762,20425E-062,18427E-05
171000-2,3593576340,0944808950,9055191052,08575E-062,20759E-05
174000-2,4259329720,088395610,911604391,97188E-062,23074E-05
177000-2,493200620,0826450280,9173549721,8626E-062,25374E-05
180000-2,5611558590,0772154390,9227845611,75787E-062,27658E-05
183000-2,6297940810,0720933060,9279066941,65762E-062,29927E-05
186000-2,6991107860,0672652990,9327347011,56178E-062,32182E-05
189000-2,7691015750,0627183270,9372816731,47025E-062,34421E-05
192000-2,8397621470,0584395640,9415604361,38295E-062,36647E-05
195000-2,9110882960,0544164760,9455835241,29978E-062,38859E-05
198000-2,9830759060,050636840,949363161,22063E-062,41057E-05
201000-3,0557209510,047088760,952911241,14539E-062,43241E-05
204000-3,1290194870,0437606840,9562393161,07395E-062,45413E-05
207000-3,2029676530,0406414150,9593585851,00617E-062,47572E-05
210000-3,2775616660,0377201190,9622798819,41943E-072,49719E-05
213000-3,352797820,0349863320,9650136688,81143E-072,51853E-05
216000-3,4286724820,0324299640,9675700368,23642E-072,53976E-05
219000-3,5051820880,0300413030,9699586977,69317E-072,56086E-05
220000-3,5308257830,0292807260,9707192747,51892E-072,56787E-05
Diagrame:
Diagrama defectiunilor :
1