Weibull Distribution Illustration In Excel 35967

Weibull Distribution Characteristic Life= 1000 MTTF (hrs)= 9260.52826671 η (in hrs)= Shape parameter= β= 0.3 WEIBULL PLOTS Reliability% at MTTF Time multiplication factor= 50 = 14.2302106016 Time (t)pdf f(t) Failure fn F(t)=Reliability R(t) Reliability % Hazard Fn 0 0 0 0 1 100 0 1 50 0.00163 0.3344160688 0.6655839312 66.558 0.0024425432 2 100 0.00091 0.3941890066 0.6058109934 60.581 0.0015035617 3 150 0.00064 0.4322160296 0.5677839704 56.778 0.0011320285 4 200 0.0005 0.4604575766 0.5395424234 53.954 0.0009255508 5 250 0.00041 0.4830214814 0.5169785186 51.698 0.0007917047 6 300 0.00035 0.5018456459 0.4981543541 49.815 0.0006968453 7 350 0.0003 0.5180080271 0.4819919729 48.199 0.0006255667 8 400 0.00027 0.5321735068 0.4678264932 46.783 0.0005697433 9 450 0.00024 0.5447825701 0.4552174299 45.522 0.0005246534 10 500 0.00022 0.5561428029 0.4438571971 44.386 0.0004873514 11 550 0.0002 0.5664778524 0.4335221476 43.352 0.0004558977 12 600 0.00018 0.5759556374 0.4240443626 42.404 0.0004289586 13 650 0.00017 0.5847055702 0.4152944298 41.529 0.000405585 14 700 0.00016 0.5928295731 0.4071704269 40.717 0.0003850815 15 750 0.00015 0.6004093995 0.3995906005 39.959 0.0003669259 16 800 0.00014 0.6075116595 0.3924883405 39.249 0.0003507182 17 850 0.00013 0.6141913648 0.3858086352 38.581 0.000336146 18 900 0.00012 0.6204944893 0.3795055107 37.951 0.0003229621 19 950 0.00012 0.6264598568 0.3735401432 37.354 0.0003109673 20 1000 0.00011 0.6321205588 0.3678794412 36.788 0.0003 21 1050 0.00011 0.6375050354 0.3624949646 36.249 0.0002899271 22 1100 0.0001 0.6426379121 0.3573620879 35.736 0.0002806379 23 1150 9.59E-05 0.6475406564 0.3524593436 35.246 0.00027204 24 1200 9.18E-05 0.6522320975 0.3477679025 34.777 0.000264055 25 1250 8.81E-05 0.6567288434 0.3432711566 34.327 0.0002566163 26 1300 8.46E-05 0.6610456185 0.3389543815 33.895 0.0002496669 27 1350 8.14E-05 0.6651955393 0.3348044607 33.48 0.0002431575 28 1400 7.84E-05 0.6691903404 0.3308096596 33.081 0.0002370455 29 1450 7.56E-05 0.6730405634 0.3269594366 32.696 0.0002312936 30 1500 7.3E-05 0.6767557131 0.3232442869 32.324 0.0002258694 31 1550 7.06E-05 0.6803443901 0.3196556099 31.966 0.0002207441 32 1600 6.83E-05 0.6838144018 0.3161855982 31.619 0.0002158924 33 1650 6.61E-05 0.6871728574 0.3128271426 31.283 0.0002112917 34 1700 6.41E-05 0.6904262489 0.3095737511 30.957 0.0002069222 35 1750 6.21E-05 0.6935805209 0.3064194791 30.642 0.0002027658 36 1800 6E-05 0.6966411299 0.3033588701 30.336 0.0001988065 37 1850 5.86E-05 0.6996130971 0.3003869029 30.039 0.0001950298

Weibull 0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0

0 50 0 0 50 00 50 0 0 50 00 1 3 4 6 7 9 1 0 12 1

Hazard Fun 0.003 0.0025 0.002 0.0015 0.001 0.0005 0

0 50 0 0 50 00 50 0 0 50 00 1 3 4 6 7 9 1 0 12 1

1 Charateristic life is the time whe 2 when beta=1, MTTF=eta. Bec

38 39 40 41 42 43 44 45 46 47 48 49 50

1900 1950 2000 2050 2100 2150 2200 2250 2300 2350 2400 2450 2500

5.69E-05 0.7025010532 5.54E-05 0.7053092779 5.39E-05 0.7080417345 5.25E-05 0.7107021007 5.12E-05 0.7132937948 5E-05 0.7158200001 4.87E-05 0.7182836857 4.75E-05 0.7206876252 4.64E-05 0.7230344138 4.53E-05 0.7253264828 4.43E-05 0.7275661137 4.33E-05 0.7297554496 4.24E-05 0.7318965068

0.2974989468 0.2946907221 0.2919582655 0.2892978993 0.2867062052 0.2841799999 0.2817163143 0.2793123748 0.2769655862 0.2746735172 0.2724338863 0.2702445504 0.2681034932

29.75 29.469 29.196 28.93 28.671 28.418 28.172 27.931 27.697 27.467 27.243 27.024 26.81

0.0001914228 0.0001879737 0.0001846717 0.0001815071 0.000178471 0.0001755555 0.0001727529 0.0001700566 0.0001674603 0.0001649581 0.0001625449 0.0001602157 0.0001579659

Weibull Reliability

Weibull pdf 1.2 1 0.8 0.6 0.4 0.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 30 4 5 60 7 5 90 1 0 5 12 0 1 3 5 1 5 0 1 6 5 1 8 0 19 5 2 1 0 22 5 2 4 0

0 0 00 0 0 00 00 0 0 0 0 00 0 0 00 00 00 00 00 00 00 0 0 00 1 2 3 4 5 6 7 8 9 1 0 11 1 2 1 3 14 1 5 16 17

Weibull Unreliability

Hazard Function 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 30 4 5 60 7 5 90 1 0 5 12 0 1 3 5 1 5 0 1 6 5 1 8 0 19 5 2 1 0 22 5 2 4 0

0 00 0 0 0 0 0 0 00 00 00 0 0 0 0 00 00 00 00 00 00 00 00 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 13 14 15 16 1 7

Charateristic life is the time when only 36.7% of the population remains or when 63.3% of the population has gone defective (The beta does not ma

when beta=1, MTTF=eta. Because when beta=1, it is exponential

Weibull Reliability

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 1 0 0 11 0 1 2 0 1 3 0 14 0 1 5 0 16 0 17 0 1 8 0 19 0 20 0 2 1 0 22 0 2 3 0 2 4 0 25 0

Weibull Unreliability

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 1 0 0 1 1 0 1 2 0 13 0 14 0 15 0 16 0 1 7 0 1 8 0 1 9 0 2 0 0 21 0 22 0 23 0 24 0 25 0

gone defective (The beta does not matter here)