1695:
1166:
1821:
the failure of the whole system, so (assuming that failure probabilities are small, which is usually the case) probability of the failure of the whole system within a given interval can be approximated as a sum of failure probabilities of the components. With parallel components the situation is a bit more complicated: the whole system will fail if and only if after one of the components fails, the other component fails while the first component is being repaired; this is where MDT comes into play: the faster the first component is repaired, the less is the "vulnerability window" for the other component to fail.
1690:{\displaystyle {\begin{aligned}{\text{mtbf}}(c_{1}\parallel c_{2})&={\frac {1}{{\frac {1}{{\text{mtbf}}(c_{1})}}\times {\text{PF}}(c_{2},{\text{mdt}}(c_{1}))+{\frac {1}{{\text{mtbf}}(c_{2})}}\times {\text{PF}}(c_{1},{\text{mdt}}(c_{2}))}}\\&={\frac {1}{{\frac {1}{{\text{mtbf}}(c_{1})}}\times {\frac {{\text{mdt}}(c_{1})}{{\text{mtbf}}(c_{2})}}+{\frac {1}{{\text{mtbf}}(c_{2})}}\times {\frac {{\text{mdt}}(c_{2})}{{\text{mtbf}}(c_{1})}}}}\\&={\frac {{\text{mtbf}}(c_{1})\times {\text{mtbf}}(c_{2})}{{\text{mdt}}(c_{1})+{\text{mdt}}(c_{2})}}\;,\end{aligned}}}
778:= MTBF. This inaccuracy can lead to bad design decisions. Furthermore, probabilistic failure prediction based on MTBF implies the total absence of systematic failures (i.e., a constant failure rate with only intrinsic, random failures), which is not easy to verify. Assuming no systematic errors, the probability the system survives during a duration, T, is calculated as exp^(-T/MTBF). Hence the probability a system fails during a duration T, is given by 1 - exp^(-T/MTBF).
82:
1112:
813:(KPI) within TPM, guiding decisions on maintenance schedules, spare parts inventory, and ultimately, optimizing the lifespan and efficiency of machinery. This strategic use of MTBF within TPM frameworks enhances overall production efficiency, reduces costs associated with breakdowns, and contributes to the continuous improvement of manufacturing processes.
789:(MDT). MDT can be defined as mean time which the system is down after the failure. Usually, MDT is considered different from MTTR (Mean Time To Repair); in particular, MDT usually includes organizational and logistical factors (such as business days or waiting for components to arrive) while MTTR is usually understood as more narrow and more technical.
2029:
2633:
69:
Mean time between failures (MTBF) describes the expected time between two failures for a repairable system. For example, three identical systems starting to function properly at time 0 are working until all of them fail. The first system fails after 100 hours, the second after 120 hours and the third
60:
systems, failures are considered to be those out of design conditions which place the system out of service and into a state for repair. Failures which occur that can be left or maintained in an unrepaired condition, and do not place the system out of service, are not considered failures under this
2674:
In fact the MTBF counting only failures with at least some systems still operating that have not yet failed underestimates the MTBF by failing to include in the computations the partial lifetimes of the systems that have not yet failed. With such lifetimes, all we know is that the time to failure
1820:
Intuitively, both these formulae can be explained from the point of view of failure probabilities. First of all, let's note that the probability of a system failing within a certain timeframe is the inverse of its MTBF. Then, when considering series of components, failure of any component leads to
2196:
Through successive application of these four formulae, the MTBF and MDT of any network of repairable components can be computed, provided that the MTBF and MDT is known for each component. In a special but all-important case of several serial components, MTBF calculation can be easily generalised
886:
1160:
For the network containing parallel repairable components, to find out the MTBF of the whole system, in addition to component MTBFs, it is also necessary to know their respective MDTs. Then, assuming that MDTs are negligible compared to MTBFs (which usually stands in practice), the MTBF for the
808:
By integrating MTBF with TPM principles, manufacturers can achieve a more proactive maintenance approach. This synergy allows for the identification of patterns and potential failures before they occur, enabling preventive maintenance and reducing unplanned downtime. As a result, MTBF becomes a
781:
MTBF value prediction is an important element in the development of products. Reliability engineers and design engineers often use reliability software to calculate a product's MTBF according to various methods and standards (MIL-HDBK-217F, Telcordia SR332, Siemens SN 29500, FIDES, UTE 80-810
2191:
2474:
153:
220:
770:
The MTBF value can be used as a system reliability parameter or to compare different systems or designs. This value should only be understood conditionally as the “mean lifetime” (an average value), and not as a quantitative identity between working and failed units.
2333:
1830:
87:
For each observation, the "down time" is the instantaneous time it went down, which is after (i.e. greater than) the moment it went up, the "up time". The difference ("down time" minus "up time") is the amount of time it was operating between these two events.
2499:(MTBUR). Such nomenclature is used when it is desirable to differentiate among types of failures, such as critical and non-critical failures. For example, in an automobile, the failure of the FM radio does not prevent the primary operation of the vehicle.
2518:
61:
definition. In addition, units that are taken down for routine scheduled maintenance or inventory control are not considered within the definition of failure. The higher the MTBF, the longer a system is likely to work before failing.
1107:{\displaystyle {\text{mtbf}}(c_{1};c_{2})={\frac {1}{{\frac {1}{{\text{mtbf}}(c_{1})}}+{\frac {1}{{\text{mtbf}}(c_{2})}}}}={\frac {{\text{mtbf}}(c_{1})\times {\text{mtbf}}(c_{2})}{{\text{mtbf}}(c_{1})+{\text{mtbf}}(c_{2})}}\;,}
538:") when only random failures are occurring. In other words, it is assumed that the system has survived initial setup stresses and has not yet approached its expected end of life, both of which often increase the failure rate.
3313:
Systems reliability assessment – Proceedings of the Ispra Course held at the
Escuela Tecnica Superior de Ingenieros Navales, Madrid, Spain, September 19–23, 1988 in collaboration with Universidad Politecnica de
337:
2040:
879:
causes the network to fail. The MTBF of the resulting two-component network with repairable components can be computed according to the following formulae, assuming that the MTBF of both individual components is known:
3187:
We see that the difference between the MTBF considering only failures and the MTBF including censored observations is that the censoring times add to the numerator but not the denominator in computing the MTBF.
2769:
1171:
2344:
2523:
501:
97:
164:
805:. MTBF provides a quantitative measure of the time elapsed between failures of a system during normal operation, offering insights into the reliability and performance of manufacturing equipment.
661:
782:(RDF2000), etc.). The Mil-HDBK-217 reliability calculator manual in combination with RelCalc software (or other comparable tool) enables MTBF reliability rates to be predicted based on design.
3093:
2024:{\displaystyle {\text{mdt}}(c_{1};c_{2})={\frac {{\text{mtbf}}(c_{1})\times {\text{mdt}}(c_{2})+{\text{mtbf}}(c_{2})\times {\text{mdt}}(c_{1})}{{\text{mtbf}}(c_{1})+{\text{mtbf}}(c_{2})}}\;,}
2203:
2967:
732:
1737:
2506:(MTTF) instead of MTBF in cases where a system is replaced after a failure ("non-repairable system"), since MTBF denotes time between failures in a system which can be repaired.
3182:
3126:
2628:{\displaystyle {\begin{aligned}{\text{MTTF}}&\approx {\frac {B_{10}}{0.1n_{\text{onm}}}},\\{\text{MTTFd}}&\approx {\frac {B_{10d}}{0.1n_{\text{op}}}},\end{aligned}}}
871:. The terminology is here used by close analogy to electrical circuits, but has a slightly different meaning. We say that the two components are in series if the failure of
2832:
1155:
859:
3146:
3028:
2870:
603:
559:
439:
376:
1775:
530:
Any practically-relevant calculation of the MTBF assumes that the system is working within its "useful life period", which is characterized by a relatively constant
2897:
2803:
3000:
760:
3657:
1815:
1795:
623:
579:
525:
400:
248:
91:
By referring to the figure above, the MTBF of a component is the sum of the lengths of the operational periods divided by the number of observed failures:
70:
after 130 hours. The MTBF of the systems is the average of the three failure times, which is 116.667 hours. If the systems were non-repairable, then their
2186:{\displaystyle {\text{mdt}}(c_{1}\parallel c_{2})={\frac {{\text{mdt}}(c_{1})\times {\text{mdt}}(c_{2})}{{\text{mdt}}(c_{1})+{\text{mdt}}(c_{2})}}\;.}
256:
3504:
797:
MTBF serves as a crucial metric for managing machinery and equipment reliability. Its application is particularly significant in the context of
3364:
3296:
2512:
is an extension of MTTF, and is only concerned about failures which would result in a dangerous condition. It can be calculated as follows:
2689:
2469:{\displaystyle {\text{mdt}}(c_{1}\parallel \dots \parallel c_{n})=\left(\sum _{k=1}^{n}{\frac {1}{{\text{mdt}}(c_{k})}}\right)^{-1}\;,}
3716:
3488:
3459:"Reliability Characteristics for Two Subsystems in Series or Parallel or n Subsystems in m_out_of_n Arrangement (by Don L. Lin)"
148:{\displaystyle {\text{MTBF}}={\frac {\sum {({\text{start of downtime}}-{\text{start of uptime}})}}{\text{number of failures}}}.}
447:
215:{\displaystyle {\text{MDT}}={\frac {\sum {({\text{start of uptime}}-{\text{start of downtime}})}}{\text{number of failures}}}.}
3592:
774:
Since MTBF can be expressed as “average life (expectancy)”, many engineers assume that 50% of items will have failed by time
2479:
since the formula for the mdt of two components in parallel is identical to that of the mtbf for two components in series.
3801:
631:
3811:
3643:
862:
798:
379:
3650:
2328:{\displaystyle {\text{mtbf}}(c_{1};\dots ;c_{n})=\left(\sum _{k=1}^{n}{\frac {1}{{\text{mtbf}}(c_{k})}}\right)^{-1}\;,}
77:
In general, MTBF is the "up-time" between two failure states of a repairable system during operation as outlined here:
3240:
3037:
3806:
3458:
3216:
2645:
is the number of operations that a device will operate prior to 10% of a sample of those devices would fail and
3007:
2904:
676:
582:
682:
3234:
3198:
3775:
2680:
2676:
1702:
3151:
810:
785:
A concept which is closely related to MTBF, and is important in the computations involving MTBF, is the
3514:
3326:
3102:
672:
403:
3620:
3685:
3628:
3222:
41:
of a mechanical or electronic system during normal system operation. MTBF can be calculated as the
3695:
3690:
2810:
1120:
824:
671:
that any one particular system will be operational for a given duration can be inferred from the
56:
The definition of MTBF depends on the definition of what is considered a failure. For complex,
3666:
3484:
3360:
3292:
3131:
3013:
2839:
1161:
parallel system consisting from two parallel repairable components can be written as follows:
588:
544:
408:
345:
3535:
1742:
3570:
3284:
3601:
3402:
3377:
2875:
2805:
is the failure time for failures and the censoring time for units that have not yet failed,
2781:
45:(average) time between failures of a system. The term is used for repairable systems while
3210:
2976:
42:
1824:
Using similar logic, MDT for a system out of two serial components can be calculated as:
737:
875:
causes the failure of the network, and that they are in parallel if only the failure of
3561:
3228:
1800:
1780:
786:
608:
564:
510:
385:
233:
3612:
734:. In particular, the probability that a particular system will survive to its MTBF is
81:
3795:
3246:
802:
535:
3204:
2970:
531:
3427:
3288:
668:
332:{\displaystyle {\text{MTBF}}=\mathbb {E} \{T\}=\int _{0}^{\infty }tf_{T}(t)\,dt}
667:
Once the MTBF of a system is known, and assuming a constant failure rate, the
57:
3201: – Probability that a device or component will fail during a year of use
27:
Predicted elapsed time between inherent failures of a system during operation
3509:
3536:"B10d Assessment – Reliability Parameter for Electro-Mechanical Components"
3237: – Sub-discipline of systems engineering that emphasizes dependability
2659:
is the same calculation, but where 10% of the sample would fail to danger.
861:(for instance hard drives, servers, etc.) may be arranged in a network, in
3574:
2034:
and for a system out of two parallel components MDT can be calculated as:
801:(TPM), a comprehensive maintenance strategy aimed at maximizing equipment
3563:
Likelihood
Construction, Inference for Parametric Survival Distributions
3231: – The length of time that electrical power is applied to a device
38:
3635:
3744:
1739:
is the network in which the components are arranged in parallel, and
3207: – Frequency with which an engineered system or component fails
53:) denotes the expected time to failure for a non-repairable system.
17:
625:, it is given by the reciprocal of the failure rate of the system,
3770:
3739:
3734:
3730:
3725:
3721:
2509:
762:, or about 37% (i.e., it will fail earlier with probability 63%).
2764:{\displaystyle L=\prod _{i}\lambda (u_{i})^{\delta _{i}}S(u_{i})}
3780:
3765:
3760:
3711:
3680:
3639:
1157:
is the network in which the components are arranged in series.
250:
indicating the time until failure. Thus, it can be written as
3453:
3451:
3449:
3447:
2681:
likelihood for the experience on any given day is as follows
158:
In a similar manner, mean down time (MDT) can be defined as
3225: – Measure of the maintainability of repairable items
3219: – Average service life for non-repairable components
402:. Equivalently, the MTBF can be expressed in terms of the
3243: – Statistical parameter of random process evolution
496:{\displaystyle {\text{MTBF}}=\int _{0}^{\infty }R(t)\,dt}
3002:= the probability density function of the distribution).
2679:. In fact with a parametric model of the lifetime, the
3629:"What is Mean Time to Failure and How Do We Calculate?"
3279:
J. Lienig, H. Bruemmer (2017). "Reliability
Analysis".
2675:
exceeds the time they've been running. This is called
230:
The MTBF is the expected value of the random variable
3621:"Simple Guide to MTBF: What It Is and When To use It"
3283:. Springer International Publishing. pp. 45–73.
3154:
3134:
3105:
3040:
3016:
2979:
2907:
2878:
2842:
2813:
2784:
2692:
2521:
2347:
2206:
2043:
1833:
1803:
1783:
1745:
1705:
1169:
1123:
889:
827:
740:
685:
634:
611:
591:
567:
547:
513:
450:
411:
388:
348:
259:
236:
167:
100:
3753:
3704:
3673:
3213: – Term of reliability in the bowling industry
656:{\displaystyle {\text{MTBF}}={\frac {1}{\lambda }}}
3176:
3140:
3120:
3087:
3022:
2994:
2961:
2891:
2864:
2826:
2797:
2763:
2627:
2468:
2327:
2185:
2023:
1809:
1789:
1769:
1731:
1689:
1149:
1106:
853:
754:
726:
655:
617:
597:
573:
553:
519:
495:
433:
394:
370:
331:
242:
214:
147:
3327:"Defining Failure: What Is MTTR, MTTF, and MTBF?"
37:) is the predicted elapsed time between inherent
3088:{\displaystyle 1/{\hat {\lambda }}=\sum u_{i}/k}
3311:Colombo, A.G., and Sáiz de Bustamante, Amalio:
2666:is the number of operations/cycle in one year.
2973:, the instantaneous force of mortality (where
2338:which can be shown by induction, and likewise
3651:
3403:"MTBF: What it means and how to calculate it"
8:
3357:Reliability Engineering: Theory and Practice
3184:is the number of uncensored observations.
3148:, maximizing the likelihood given above and
2872:= the probability that the lifetime exceeds
279:
273:
3030:, is constant. In this case, the MBTF is
2834:= 1 for failures and 0 for censoring times,
2487:There are many variations of MTBF, such as
1777:is the probability of failure of component
3658:
3644:
3636:
3483:(eighth ed.). Butterworth-Heinemann.
3351:
3349:
3347:
2462:
2321:
2179:
2017:
1679:
1100:
605:. Since the MTBF is the expected value of
3281:Fundamentals of Electronic Systems Design
3249: – Curve for failure rates over time
3168:
3153:
3133:
3107:
3106:
3104:
3077:
3071:
3050:
3049:
3044:
3039:
3015:
2978:
2962:{\displaystyle \lambda (u_{i})=f(u)/S(u)}
2942:
2918:
2906:
2883:
2877:
2853:
2841:
2818:
2812:
2789:
2783:
2752:
2734:
2729:
2719:
2703:
2691:
2609:
2592:
2586:
2574:
2558:
2544:
2538:
2526:
2522:
2520:
2453:
2436:
2424:
2418:
2412:
2401:
2379:
2360:
2348:
2346:
2312:
2295:
2283:
2277:
2271:
2260:
2238:
2219:
2207:
2205:
2167:
2155:
2143:
2131:
2120:
2108:
2096:
2084:
2081:
2069:
2056:
2044:
2042:
2005:
1993:
1981:
1969:
1958:
1946:
1934:
1922:
1910:
1898:
1886:
1874:
1871:
1859:
1846:
1834:
1832:
1802:
1782:
1744:
1723:
1710:
1704:
1667:
1655:
1643:
1631:
1620:
1608:
1596:
1584:
1581:
1556:
1544:
1533:
1521:
1518:
1503:
1491:
1485:
1470:
1458:
1447:
1435:
1432:
1417:
1405:
1399:
1393:
1368:
1356:
1347:
1335:
1320:
1308:
1302:
1287:
1275:
1266:
1254:
1239:
1227:
1221:
1215:
1199:
1186:
1174:
1170:
1168:
1141:
1128:
1122:
1088:
1076:
1064:
1052:
1041:
1029:
1017:
1005:
1002:
984:
972:
966:
951:
939:
933:
927:
915:
902:
890:
888:
845:
832:
826:
744:
739:
712:
690:
684:
643:
635:
633:
610:
590:
566:
546:
512:
486:
468:
463:
451:
449:
416:
410:
387:
353:
347:
322:
307:
294:
289:
269:
268:
260:
258:
235:
194:
186:
182:
176:
168:
166:
127:
119:
115:
109:
101:
99:
3623:. Road to Reliability. 10 December 2021.
3274:
3272:
3270:
3268:
3266:
3264:
3474:
3472:
3260:
817:MTBF and MDT for networks of components
727:{\displaystyle R_{T}(t)=e^{-\lambda t}}
71:
3128:is the maximum likelihood estimate of
3593:"Reliability and Availability Basics"
3481:Reliability, Maintainability and Risk
2497:mean time between unscheduled removal
7:
3426:PhD, Bartosz Misiurek (2021-11-22).
1732:{\displaystyle c_{1}\parallel c_{2}}
793:Application of MTBF in manufacturing
3613:"Failure Rates, MTBF, and All That"
2899:, called the survival function, and
2493:mean time between critical failures
3177:{\displaystyle k=\sum \sigma _{i}}
527:have units of time (e.g., hours).
469:
295:
25:
3121:{\displaystyle {\hat {\lambda }}}
541:Assuming a constant failure rate
3607:. Vicor Reliability Engineering.
3428:"MTBF MTTR MTTF: TPM Indicators"
80:
3602:"Reliability and MTBF Overview"
3463:auroraconsultingengineering.com
3383:. Vicor Reliability Engineering
3378:"Reliability and MTBF Overview"
2489:mean time between system aborts
3112:
3055:
2989:
2983:
2956:
2950:
2939:
2933:
2924:
2911:
2859:
2846:
2758:
2745:
2726:
2712:
2442:
2429:
2385:
2353:
2301:
2288:
2244:
2212:
2173:
2160:
2149:
2136:
2126:
2113:
2102:
2089:
2075:
2049:
2011:
1998:
1987:
1974:
1964:
1951:
1940:
1927:
1916:
1903:
1892:
1879:
1865:
1839:
1797:during "vulnerability window"
1764:
1752:
1673:
1660:
1649:
1636:
1626:
1613:
1602:
1589:
1562:
1549:
1539:
1526:
1509:
1496:
1476:
1463:
1453:
1440:
1423:
1410:
1377:
1374:
1361:
1340:
1326:
1313:
1296:
1293:
1280:
1259:
1245:
1232:
1205:
1179:
1094:
1081:
1070:
1057:
1047:
1034:
1023:
1010:
990:
977:
957:
944:
921:
895:
702:
696:
483:
477:
428:
422:
365:
359:
319:
313:
199:
183:
132:
116:
1:
3505:"MTBF Allocations Analysis1"
799:total productive maintenance
380:probability density function
3479:Dr. David J. Smith (2011).
3289:10.1007/978-3-319-55840-0_4
3241:Residence time (statistics)
2827:{\displaystyle \delta _{i}}
1150:{\displaystyle c_{1};c_{2}}
854:{\displaystyle c_{1},c_{2}}
3828:
3217:Mean time to first failure
2670:MTBF considering censoring
31:Mean time between failures
3359:. Springer, Berlin 2013,
3331:Stephen Foskett, Pack Rat
2652:is number of operations.
2502:It is recommended to use
811:key performance indicator
534:(the middle part of the "
3705:Electricity distribution
3141:{\displaystyle \lambda }
3023:{\displaystyle \lambda }
3008:exponential distribution
2865:{\displaystyle S(u_{i})}
677:exponential distribution
598:{\displaystyle \lambda }
583:exponential distribution
554:{\displaystyle \lambda }
434:{\displaystyle R_{T}(t)}
371:{\displaystyle f_{T}(t)}
226:Mathematical description
74:would be 116.667 hours.
3631:. NEXGEN. 21 June 2023.
3407:total-manufacturing.com
3235:Reliability engineering
3199:Annualized failure rate
1770:{\displaystyle PF(c,t)}
3754:Electricity generation
3600:Speaks, Scott (2005).
3178:
3142:
3122:
3089:
3024:
2996:
2963:
2893:
2866:
2828:
2799:
2765:
2629:
2470:
2417:
2329:
2276:
2187:
2025:
1811:
1791:
1771:
1733:
1691:
1151:
1108:
855:
756:
728:
657:
619:
599:
575:
555:
521:
497:
435:
396:
372:
333:
244:
216:
149:
3355:Alessandro Birolini:
3179:
3143:
3123:
3090:
3025:
2997:
2964:
2894:
2892:{\displaystyle u_{i}}
2867:
2829:
2800:
2798:{\displaystyle u_{i}}
2766:
2630:
2471:
2397:
2330:
2256:
2188:
2026:
1812:
1792:
1772:
1734:
1692:
1152:
1109:
856:
757:
729:
658:
620:
600:
576:
556:
522:
498:
436:
397:
373:
334:
245:
217:
150:
3802:Engineering failures
3152:
3132:
3103:
3038:
3014:
2995:{\displaystyle f(u)}
2977:
2905:
2876:
2840:
2811:
2782:
2690:
2519:
2504:Mean time to failure
2345:
2204:
2041:
1831:
1801:
1781:
1743:
1703:
1167:
1121:
887:
825:
738:
683:
673:reliability function
632:
609:
589:
565:
545:
511:
448:
409:
404:reliability function
386:
346:
257:
234:
165:
98:
47:mean time to failure
3812:Reliability indices
3667:Reliability indices
3517:on November 6, 2002
3223:Mean time to repair
755:{\displaystyle 1/e}
473:
299:
3174:
3138:
3118:
3085:
3020:
2992:
2959:
2889:
2862:
2824:
2795:
2761:
2708:
2625:
2623:
2483:Variations of MTBF
2466:
2325:
2183:
2021:
1807:
1787:
1767:
1729:
1687:
1685:
1147:
1104:
851:
752:
724:
653:
615:
595:
571:
551:
517:
493:
459:
431:
392:
368:
329:
285:
240:
212:
205:number of failures
145:
138:number of failures
3807:Survival analysis
3789:
3788:
3365:978-3-642-39534-5
3298:978-3-319-55839-4
3115:
3058:
2699:
2616:
2612:
2577:
2565:
2561:
2529:
2446:
2427:
2351:
2305:
2286:
2210:
2177:
2158:
2134:
2111:
2087:
2047:
2015:
1996:
1972:
1949:
1925:
1901:
1877:
1837:
1810:{\displaystyle t}
1790:{\displaystyle c}
1677:
1658:
1634:
1611:
1587:
1569:
1566:
1547:
1524:
1513:
1494:
1480:
1461:
1438:
1427:
1408:
1381:
1359:
1338:
1330:
1311:
1278:
1257:
1249:
1230:
1177:
1098:
1079:
1055:
1032:
1008:
997:
994:
975:
961:
942:
893:
651:
638:
618:{\displaystyle T}
574:{\displaystyle T}
520:{\displaystyle T}
454:
395:{\displaystyle T}
263:
243:{\displaystyle T}
207:
206:
197:
196:start of downtime
189:
171:
140:
139:
130:
122:
121:start of downtime
104:
16:(Redirected from
3819:
3660:
3653:
3646:
3637:
3632:
3624:
3616:
3608:
3606:
3596:
3579:
3577:
3568:
3557:
3551:
3550:
3548:
3546:
3540:
3532:
3526:
3525:
3523:
3522:
3513:. Archived from
3501:
3495:
3494:
3476:
3467:
3466:
3455:
3442:
3441:
3439:
3438:
3423:
3417:
3416:
3414:
3413:
3399:
3393:
3392:
3390:
3388:
3382:
3374:
3368:
3353:
3342:
3341:
3339:
3338:
3323:
3317:
3309:
3303:
3302:
3276:
3183:
3181:
3180:
3175:
3173:
3172:
3147:
3145:
3144:
3139:
3127:
3125:
3124:
3119:
3117:
3116:
3108:
3094:
3092:
3091:
3086:
3081:
3076:
3075:
3060:
3059:
3051:
3048:
3029:
3027:
3026:
3021:
3001:
2999:
2998:
2993:
2968:
2966:
2965:
2960:
2946:
2923:
2922:
2898:
2896:
2895:
2890:
2888:
2887:
2871:
2869:
2868:
2863:
2858:
2857:
2833:
2831:
2830:
2825:
2823:
2822:
2804:
2802:
2801:
2796:
2794:
2793:
2770:
2768:
2767:
2762:
2757:
2756:
2741:
2740:
2739:
2738:
2724:
2723:
2707:
2634:
2632:
2631:
2626:
2624:
2617:
2615:
2614:
2613:
2610:
2600:
2599:
2587:
2578:
2575:
2566:
2564:
2563:
2562:
2559:
2549:
2548:
2539:
2530:
2527:
2475:
2473:
2472:
2467:
2461:
2460:
2452:
2448:
2447:
2445:
2441:
2440:
2428:
2425:
2419:
2416:
2411:
2384:
2383:
2365:
2364:
2352:
2349:
2334:
2332:
2331:
2326:
2320:
2319:
2311:
2307:
2306:
2304:
2300:
2299:
2287:
2284:
2278:
2275:
2270:
2243:
2242:
2224:
2223:
2211:
2208:
2192:
2190:
2189:
2184:
2178:
2176:
2172:
2171:
2159:
2156:
2148:
2147:
2135:
2132:
2129:
2125:
2124:
2112:
2109:
2101:
2100:
2088:
2085:
2082:
2074:
2073:
2061:
2060:
2048:
2045:
2030:
2028:
2027:
2022:
2016:
2014:
2010:
2009:
1997:
1994:
1986:
1985:
1973:
1970:
1967:
1963:
1962:
1950:
1947:
1939:
1938:
1926:
1923:
1915:
1914:
1902:
1899:
1891:
1890:
1878:
1875:
1872:
1864:
1863:
1851:
1850:
1838:
1835:
1816:
1814:
1813:
1808:
1796:
1794:
1793:
1788:
1776:
1774:
1773:
1768:
1738:
1736:
1735:
1730:
1728:
1727:
1715:
1714:
1696:
1694:
1693:
1688:
1686:
1678:
1676:
1672:
1671:
1659:
1656:
1648:
1647:
1635:
1632:
1629:
1625:
1624:
1612:
1609:
1601:
1600:
1588:
1585:
1582:
1574:
1570:
1568:
1567:
1565:
1561:
1560:
1548:
1545:
1542:
1538:
1537:
1525:
1522:
1519:
1514:
1512:
1508:
1507:
1495:
1492:
1486:
1481:
1479:
1475:
1474:
1462:
1459:
1456:
1452:
1451:
1439:
1436:
1433:
1428:
1426:
1422:
1421:
1409:
1406:
1400:
1394:
1386:
1382:
1380:
1373:
1372:
1360:
1357:
1352:
1351:
1339:
1336:
1331:
1329:
1325:
1324:
1312:
1309:
1303:
1292:
1291:
1279:
1276:
1271:
1270:
1258:
1255:
1250:
1248:
1244:
1243:
1231:
1228:
1222:
1216:
1204:
1203:
1191:
1190:
1178:
1175:
1156:
1154:
1153:
1148:
1146:
1145:
1133:
1132:
1113:
1111:
1110:
1105:
1099:
1097:
1093:
1092:
1080:
1077:
1069:
1068:
1056:
1053:
1050:
1046:
1045:
1033:
1030:
1022:
1021:
1009:
1006:
1003:
998:
996:
995:
993:
989:
988:
976:
973:
967:
962:
960:
956:
955:
943:
940:
934:
928:
920:
919:
907:
906:
894:
891:
860:
858:
857:
852:
850:
849:
837:
836:
761:
759:
758:
753:
748:
733:
731:
730:
725:
723:
722:
695:
694:
662:
660:
659:
654:
652:
644:
639:
636:
624:
622:
621:
616:
604:
602:
601:
596:
580:
578:
577:
572:
560:
558:
557:
552:
526:
524:
523:
518:
502:
500:
499:
494:
472:
467:
455:
452:
440:
438:
437:
432:
421:
420:
401:
399:
398:
393:
377:
375:
374:
369:
358:
357:
338:
336:
335:
330:
312:
311:
298:
293:
272:
264:
261:
249:
247:
246:
241:
221:
219:
218:
213:
208:
204:
203:
202:
198:
195:
190:
187:
177:
172:
169:
154:
152:
151:
146:
141:
137:
136:
135:
131:
128:
123:
120:
110:
105:
102:
84:
21:
3827:
3826:
3822:
3821:
3820:
3818:
3817:
3816:
3792:
3791:
3790:
3785:
3749:
3700:
3669:
3664:
3627:
3619:
3611:
3604:
3599:
3591:
3588:
3583:
3582:
3566:
3559:
3558:
3554:
3544:
3542:
3538:
3534:
3533:
3529:
3520:
3518:
3503:
3502:
3498:
3491:
3478:
3477:
3470:
3457:
3456:
3445:
3436:
3434:
3425:
3424:
3420:
3411:
3409:
3401:
3400:
3396:
3386:
3384:
3380:
3376:
3375:
3371:
3354:
3345:
3336:
3334:
3325:
3324:
3320:
3310:
3306:
3299:
3278:
3277:
3262:
3257:
3252:
3211:Frames per stop
3194:
3164:
3150:
3149:
3130:
3129:
3101:
3100:
3067:
3036:
3035:
3012:
3011:
3006:For a constant
2975:
2974:
2971:hazard function
2914:
2903:
2902:
2879:
2874:
2873:
2849:
2838:
2837:
2814:
2809:
2808:
2785:
2780:
2779:
2748:
2730:
2725:
2715:
2688:
2687:
2672:
2665:
2658:
2651:
2644:
2622:
2621:
2605:
2601:
2588:
2579:
2571:
2570:
2554:
2550:
2540:
2531:
2517:
2516:
2485:
2432:
2423:
2396:
2392:
2391:
2375:
2356:
2343:
2342:
2291:
2282:
2255:
2251:
2250:
2234:
2215:
2202:
2201:
2163:
2139:
2130:
2116:
2092:
2083:
2065:
2052:
2039:
2038:
2001:
1977:
1968:
1954:
1930:
1906:
1882:
1873:
1855:
1842:
1829:
1828:
1799:
1798:
1779:
1778:
1741:
1740:
1719:
1706:
1701:
1700:
1684:
1683:
1663:
1639:
1630:
1616:
1592:
1583:
1572:
1571:
1552:
1543:
1529:
1520:
1499:
1490:
1466:
1457:
1443:
1434:
1413:
1404:
1398:
1384:
1383:
1364:
1343:
1316:
1307:
1283:
1262:
1235:
1226:
1220:
1208:
1195:
1182:
1165:
1164:
1137:
1124:
1119:
1118:
1084:
1060:
1051:
1037:
1013:
1004:
980:
971:
947:
938:
932:
911:
898:
885:
884:
841:
828:
823:
822:
821:Two components
819:
795:
768:
736:
735:
708:
686:
681:
680:
630:
629:
607:
606:
587:
586:
585:with parameter
563:
562:
543:
542:
509:
508:
446:
445:
412:
407:
406:
384:
383:
349:
344:
343:
303:
255:
254:
232:
231:
228:
188:start of uptime
178:
163:
162:
129:start of uptime
111:
96:
95:
67:
43:arithmetic mean
28:
23:
22:
15:
12:
11:
5:
3825:
3823:
3815:
3814:
3809:
3804:
3794:
3793:
3787:
3786:
3784:
3783:
3778:
3773:
3768:
3763:
3757:
3755:
3751:
3750:
3748:
3747:
3742:
3737:
3728:
3719:
3714:
3708:
3706:
3702:
3701:
3699:
3698:
3693:
3688:
3683:
3677:
3675:
3671:
3670:
3665:
3663:
3662:
3655:
3648:
3640:
3634:
3633:
3625:
3617:
3609:
3597:
3587:
3586:External links
3584:
3581:
3580:
3552:
3541:. TUVRheinland
3527:
3496:
3490:978-0080969022
3489:
3468:
3443:
3432:Lean Community
3418:
3394:
3369:
3343:
3318:
3304:
3297:
3259:
3258:
3256:
3253:
3251:
3250:
3244:
3238:
3232:
3229:Power-on hours
3226:
3220:
3214:
3208:
3202:
3195:
3193:
3190:
3171:
3167:
3163:
3160:
3157:
3137:
3114:
3111:
3097:
3096:
3084:
3080:
3074:
3070:
3066:
3063:
3057:
3054:
3047:
3043:
3019:
3010:, the hazard,
3004:
3003:
2991:
2988:
2985:
2982:
2969:is called the
2958:
2955:
2952:
2949:
2945:
2941:
2938:
2935:
2932:
2929:
2926:
2921:
2917:
2913:
2910:
2900:
2886:
2882:
2861:
2856:
2852:
2848:
2845:
2835:
2821:
2817:
2806:
2792:
2788:
2773:
2772:
2760:
2755:
2751:
2747:
2744:
2737:
2733:
2728:
2722:
2718:
2714:
2711:
2706:
2702:
2698:
2695:
2671:
2668:
2663:
2656:
2649:
2642:
2636:
2635:
2620:
2608:
2604:
2598:
2595:
2591:
2585:
2582:
2580:
2573:
2572:
2569:
2557:
2553:
2547:
2543:
2537:
2534:
2532:
2525:
2524:
2484:
2481:
2477:
2476:
2465:
2459:
2456:
2451:
2444:
2439:
2435:
2431:
2422:
2415:
2410:
2407:
2404:
2400:
2395:
2390:
2387:
2382:
2378:
2374:
2371:
2368:
2363:
2359:
2355:
2336:
2335:
2324:
2318:
2315:
2310:
2303:
2298:
2294:
2290:
2281:
2274:
2269:
2266:
2263:
2259:
2254:
2249:
2246:
2241:
2237:
2233:
2230:
2227:
2222:
2218:
2214:
2194:
2193:
2182:
2175:
2170:
2166:
2162:
2154:
2151:
2146:
2142:
2138:
2128:
2123:
2119:
2115:
2107:
2104:
2099:
2095:
2091:
2080:
2077:
2072:
2068:
2064:
2059:
2055:
2051:
2032:
2031:
2020:
2013:
2008:
2004:
2000:
1992:
1989:
1984:
1980:
1976:
1966:
1961:
1957:
1953:
1945:
1942:
1937:
1933:
1929:
1921:
1918:
1913:
1909:
1905:
1897:
1894:
1889:
1885:
1881:
1870:
1867:
1862:
1858:
1854:
1849:
1845:
1841:
1806:
1786:
1766:
1763:
1760:
1757:
1754:
1751:
1748:
1726:
1722:
1718:
1713:
1709:
1682:
1675:
1670:
1666:
1662:
1654:
1651:
1646:
1642:
1638:
1628:
1623:
1619:
1615:
1607:
1604:
1599:
1595:
1591:
1580:
1577:
1575:
1573:
1564:
1559:
1555:
1551:
1541:
1536:
1532:
1528:
1517:
1511:
1506:
1502:
1498:
1489:
1484:
1478:
1473:
1469:
1465:
1455:
1450:
1446:
1442:
1431:
1425:
1420:
1416:
1412:
1403:
1397:
1392:
1389:
1387:
1385:
1379:
1376:
1371:
1367:
1363:
1355:
1350:
1346:
1342:
1334:
1328:
1323:
1319:
1315:
1306:
1301:
1298:
1295:
1290:
1286:
1282:
1274:
1269:
1265:
1261:
1253:
1247:
1242:
1238:
1234:
1225:
1219:
1214:
1211:
1209:
1207:
1202:
1198:
1194:
1189:
1185:
1181:
1173:
1172:
1144:
1140:
1136:
1131:
1127:
1115:
1114:
1103:
1096:
1091:
1087:
1083:
1075:
1072:
1067:
1063:
1059:
1049:
1044:
1040:
1036:
1028:
1025:
1020:
1016:
1012:
1001:
992:
987:
983:
979:
970:
965:
959:
954:
950:
946:
937:
931:
926:
923:
918:
914:
910:
905:
901:
897:
848:
844:
840:
835:
831:
818:
815:
794:
791:
787:mean down time
767:
764:
751:
747:
743:
721:
718:
715:
711:
707:
704:
701:
698:
693:
689:
665:
664:
650:
647:
642:
614:
594:
570:
550:
516:
505:
504:
492:
489:
485:
482:
479:
476:
471:
466:
462:
458:
430:
427:
424:
419:
415:
391:
367:
364:
361:
356:
352:
340:
339:
328:
325:
321:
318:
315:
310:
306:
302:
297:
292:
288:
284:
281:
278:
275:
271:
267:
239:
227:
224:
223:
222:
211:
201:
193:
185:
181:
175:
156:
155:
144:
134:
126:
118:
114:
108:
66:
63:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3824:
3813:
3810:
3808:
3805:
3803:
3800:
3799:
3797:
3782:
3779:
3777:
3774:
3772:
3769:
3767:
3764:
3762:
3759:
3758:
3756:
3752:
3746:
3743:
3741:
3738:
3736:
3732:
3729:
3727:
3723:
3720:
3718:
3715:
3713:
3710:
3709:
3707:
3703:
3697:
3694:
3692:
3689:
3687:
3684:
3682:
3679:
3678:
3676:
3672:
3668:
3661:
3656:
3654:
3649:
3647:
3642:
3641:
3638:
3630:
3626:
3622:
3618:
3614:
3610:
3603:
3598:
3595:. EventHelix.
3594:
3590:
3589:
3585:
3576:
3572:
3565:
3564:
3556:
3553:
3537:
3531:
3528:
3516:
3512:
3511:
3506:
3500:
3497:
3492:
3486:
3482:
3475:
3473:
3469:
3464:
3460:
3454:
3452:
3450:
3448:
3444:
3433:
3429:
3422:
3419:
3408:
3404:
3398:
3395:
3379:
3373:
3370:
3366:
3362:
3358:
3352:
3350:
3348:
3344:
3333:. 6 July 2011
3332:
3328:
3322:
3319:
3315:
3308:
3305:
3300:
3294:
3290:
3286:
3282:
3275:
3273:
3271:
3269:
3267:
3265:
3261:
3254:
3248:
3247:Bathtub curve
3245:
3242:
3239:
3236:
3233:
3230:
3227:
3224:
3221:
3218:
3215:
3212:
3209:
3206:
3203:
3200:
3197:
3196:
3191:
3189:
3185:
3169:
3165:
3161:
3158:
3155:
3135:
3109:
3082:
3078:
3072:
3068:
3064:
3061:
3052:
3045:
3041:
3033:
3032:
3031:
3017:
3009:
2986:
2980:
2972:
2953:
2947:
2943:
2936:
2930:
2927:
2919:
2915:
2908:
2901:
2884:
2880:
2854:
2850:
2843:
2836:
2819:
2815:
2807:
2790:
2786:
2778:
2777:
2776:
2753:
2749:
2742:
2735:
2731:
2720:
2716:
2709:
2704:
2700:
2696:
2693:
2686:
2685:
2684:
2682:
2678:
2669:
2667:
2662:
2655:
2648:
2641:
2618:
2606:
2602:
2596:
2593:
2589:
2583:
2581:
2567:
2555:
2551:
2545:
2541:
2535:
2533:
2515:
2514:
2513:
2511:
2507:
2505:
2500:
2498:
2494:
2490:
2482:
2480:
2463:
2457:
2454:
2449:
2437:
2433:
2420:
2413:
2408:
2405:
2402:
2398:
2393:
2388:
2380:
2376:
2372:
2369:
2366:
2361:
2357:
2341:
2340:
2339:
2322:
2316:
2313:
2308:
2296:
2292:
2279:
2272:
2267:
2264:
2261:
2257:
2252:
2247:
2239:
2235:
2231:
2228:
2225:
2220:
2216:
2200:
2199:
2198:
2180:
2168:
2164:
2152:
2144:
2140:
2121:
2117:
2105:
2097:
2093:
2078:
2070:
2066:
2062:
2057:
2053:
2037:
2036:
2035:
2018:
2006:
2002:
1990:
1982:
1978:
1959:
1955:
1943:
1935:
1931:
1919:
1911:
1907:
1895:
1887:
1883:
1868:
1860:
1856:
1852:
1847:
1843:
1827:
1826:
1825:
1822:
1818:
1804:
1784:
1761:
1758:
1755:
1749:
1746:
1724:
1720:
1716:
1711:
1707:
1697:
1680:
1668:
1664:
1652:
1644:
1640:
1621:
1617:
1605:
1597:
1593:
1578:
1576:
1557:
1553:
1534:
1530:
1515:
1504:
1500:
1487:
1482:
1471:
1467:
1448:
1444:
1429:
1418:
1414:
1401:
1395:
1390:
1388:
1369:
1365:
1353:
1348:
1344:
1332:
1321:
1317:
1304:
1299:
1288:
1284:
1272:
1267:
1263:
1251:
1240:
1236:
1223:
1217:
1212:
1210:
1200:
1196:
1192:
1187:
1183:
1162:
1158:
1142:
1138:
1134:
1129:
1125:
1101:
1089:
1085:
1073:
1065:
1061:
1042:
1038:
1026:
1018:
1014:
999:
985:
981:
968:
963:
952:
948:
935:
929:
924:
916:
912:
908:
903:
899:
883:
882:
881:
878:
874:
870:
869:
865:
846:
842:
838:
833:
829:
816:
814:
812:
806:
804:
803:effectiveness
800:
792:
790:
788:
783:
779:
777:
772:
765:
763:
749:
745:
741:
719:
716:
713:
709:
705:
699:
691:
687:
678:
674:
670:
648:
645:
640:
628:
627:
626:
612:
592:
584:
568:
561:implies that
548:
539:
537:
536:bathtub curve
533:
528:
514:
507:The MTBF and
490:
487:
480:
474:
464:
460:
456:
444:
443:
442:
425:
417:
413:
405:
389:
381:
362:
354:
350:
326:
323:
316:
308:
304:
300:
290:
286:
282:
276:
265:
253:
252:
251:
237:
225:
209:
191:
179:
173:
161:
160:
159:
142:
124:
112:
106:
94:
93:
92:
89:
85:
83:
78:
75:
73:
64:
62:
59:
54:
52:
48:
44:
40:
36:
32:
19:
3615:. MathPages.
3562:
3555:
3543:. Retrieved
3530:
3519:. Retrieved
3515:the original
3508:
3499:
3480:
3462:
3435:. Retrieved
3431:
3421:
3410:. Retrieved
3406:
3397:
3385:. Retrieved
3372:
3356:
3335:. Retrieved
3330:
3321:
3312:
3307:
3280:
3205:Failure rate
3186:
3098:
3005:
2774:
2673:
2660:
2653:
2646:
2639:
2637:
2508:
2503:
2501:
2496:
2492:
2488:
2486:
2478:
2337:
2195:
2033:
1823:
1819:
1698:
1163:
1159:
1116:
876:
872:
867:
863:
820:
807:
796:
784:
780:
775:
773:
769:
666:
540:
532:failure rate
529:
506:
341:
229:
157:
90:
86:
79:
76:
68:
55:
50:
46:
34:
30:
29:
2495:(MTBCF) or
766:Application
669:probability
3796:Categories
3521:2016-12-23
3437:2024-02-07
3412:2024-02-07
3337:2016-01-18
3255:References
58:repairable
3575:Q98961801
3560:Lu Tian,
3510:Angelfire
3166:σ
3162:∑
3136:λ
3113:^
3110:λ
3065:∑
3056:^
3053:λ
3018:λ
2909:λ
2816:δ
2732:δ
2710:λ
2701:∏
2677:censoring
2584:≈
2536:≈
2491:(MTBSA),
2455:−
2399:∑
2373:∥
2370:⋯
2367:∥
2314:−
2258:∑
2229:…
2106:×
2063:∥
1944:×
1896:×
1717:∥
1606:×
1516:×
1430:×
1333:×
1252:×
1193:∥
1027:×
717:λ
714:−
649:λ
593:λ
549:λ
470:∞
461:∫
296:∞
287:∫
192:−
180:∑
125:−
113:∑
3571:Wikidata
3192:See also
868:parallel
65:Overview
39:failures
3674:Generic
3034:MTBF =
2775:where
675:of the
581:has an
378:is the
3745:CTAIDI
3573:
3545:7 July
3487:
3387:1 June
3363:
3316:, 1988
3314:Madrid
3295:
3099:where
2638:where
2197:into
1699:where
1117:where
873:either
866:or in
864:series
342:where
3771:LOLEV
3740:MAIFI
3735:SAIFI
3731:CAIFI
3726:SAIDI
3722:CAIDI
3605:(PDF)
3567:(PDF)
3539:(PDF)
3381:(PDF)
2576:MTTFd
2510:MTTFd
3781:LOLH
3776:LOLF
3766:LOLE
3761:LOLP
3717:ASAI
3712:ASUI
3696:EFOR
3686:MTTR
3681:MTBF
3547:2015
3485:ISBN
3389:2017
3361:ISBN
3293:ISBN
2528:MTTF
2285:mtbf
2209:mtbf
1995:mtbf
1971:mtbf
1924:mtbf
1876:mtbf
1610:mtbf
1586:mtbf
1546:mtbf
1493:mtbf
1460:mtbf
1407:mtbf
1310:mtbf
1229:mtbf
1176:mtbf
1078:mtbf
1054:mtbf
1031:mtbf
1007:mtbf
974:mtbf
941:mtbf
892:mtbf
877:both
637:MTBF
453:MTBF
262:MTBF
103:MTBF
72:MTTF
51:MTTF
35:MTBF
18:MTTF
3691:FOR
3285:doi
2657:10d
2603:0.1
2560:onm
2552:0.1
2426:mdt
2350:mdt
2157:mdt
2133:mdt
2110:mdt
2086:mdt
2046:mdt
1948:mdt
1900:mdt
1836:mdt
1657:mdt
1633:mdt
1523:mdt
1437:mdt
1358:mdt
1277:mdt
441:as
382:of
170:MDT
3798::
3569:,
3507:.
3471:^
3461:.
3446:^
3430:.
3405:.
3346:^
3329:.
3291:.
3263:^
2683::
2664:op
2650:op
2643:10
2611:op
2594:10
2546:10
1817:.
1337:PF
1256:PF
679:,
3733:/
3724:/
3659:e
3652:t
3645:v
3578:.
3549:.
3524:.
3493:.
3465:.
3440:.
3415:.
3391:.
3367:.
3340:.
3301:.
3287::
3170:i
3159:=
3156:k
3095:,
3083:k
3079:/
3073:i
3069:u
3062:=
3046:/
3042:1
2990:)
2987:u
2984:(
2981:f
2957:)
2954:u
2951:(
2948:S
2944:/
2940:)
2937:u
2934:(
2931:f
2928:=
2925:)
2920:i
2916:u
2912:(
2885:i
2881:u
2860:)
2855:i
2851:u
2847:(
2844:S
2820:i
2791:i
2787:u
2771:,
2759:)
2754:i
2750:u
2746:(
2743:S
2736:i
2727:)
2721:i
2717:u
2713:(
2705:i
2697:=
2694:L
2661:n
2654:B
2647:n
2640:B
2619:,
2607:n
2597:d
2590:B
2568:,
2556:n
2542:B
2464:,
2458:1
2450:)
2443:)
2438:k
2434:c
2430:(
2421:1
2414:n
2409:1
2406:=
2403:k
2394:(
2389:=
2386:)
2381:n
2377:c
2362:1
2358:c
2354:(
2323:,
2317:1
2309:)
2302:)
2297:k
2293:c
2289:(
2280:1
2273:n
2268:1
2265:=
2262:k
2253:(
2248:=
2245:)
2240:n
2236:c
2232:;
2226:;
2221:1
2217:c
2213:(
2181:.
2174:)
2169:2
2165:c
2161:(
2153:+
2150:)
2145:1
2141:c
2137:(
2127:)
2122:2
2118:c
2114:(
2103:)
2098:1
2094:c
2090:(
2079:=
2076:)
2071:2
2067:c
2058:1
2054:c
2050:(
2019:,
2012:)
2007:2
2003:c
1999:(
1991:+
1988:)
1983:1
1979:c
1975:(
1965:)
1960:1
1956:c
1952:(
1941:)
1936:2
1932:c
1928:(
1920:+
1917:)
1912:2
1908:c
1904:(
1893:)
1888:1
1884:c
1880:(
1869:=
1866:)
1861:2
1857:c
1853:;
1848:1
1844:c
1840:(
1805:t
1785:c
1765:)
1762:t
1759:,
1756:c
1753:(
1750:F
1747:P
1725:2
1721:c
1712:1
1708:c
1681:,
1674:)
1669:2
1665:c
1661:(
1653:+
1650:)
1645:1
1641:c
1637:(
1627:)
1622:2
1618:c
1614:(
1603:)
1598:1
1594:c
1590:(
1579:=
1563:)
1558:1
1554:c
1550:(
1540:)
1535:2
1531:c
1527:(
1510:)
1505:2
1501:c
1497:(
1488:1
1483:+
1477:)
1472:2
1468:c
1464:(
1454:)
1449:1
1445:c
1441:(
1424:)
1419:1
1415:c
1411:(
1402:1
1396:1
1391:=
1378:)
1375:)
1370:2
1366:c
1362:(
1354:,
1349:1
1345:c
1341:(
1327:)
1322:2
1318:c
1314:(
1305:1
1300:+
1297:)
1294:)
1289:1
1285:c
1281:(
1273:,
1268:2
1264:c
1260:(
1246:)
1241:1
1237:c
1233:(
1224:1
1218:1
1213:=
1206:)
1201:2
1197:c
1188:1
1184:c
1180:(
1143:2
1139:c
1135:;
1130:1
1126:c
1102:,
1095:)
1090:2
1086:c
1082:(
1074:+
1071:)
1066:1
1062:c
1058:(
1048:)
1043:2
1039:c
1035:(
1024:)
1019:1
1015:c
1011:(
1000:=
991:)
986:2
982:c
978:(
969:1
964:+
958:)
953:1
949:c
945:(
936:1
930:1
925:=
922:)
917:2
913:c
909:;
904:1
900:c
896:(
847:2
843:c
839:,
834:1
830:c
776:t
750:e
746:/
742:1
720:t
710:e
706:=
703:)
700:t
697:(
692:T
688:R
663:.
646:1
641:=
613:T
569:T
515:T
503:.
491:t
488:d
484:)
481:t
478:(
475:R
465:0
457:=
429:)
426:t
423:(
418:T
414:R
390:T
366:)
363:t
360:(
355:T
351:f
327:t
324:d
320:)
317:t
314:(
309:T
305:f
301:t
291:0
283:=
280:}
277:T
274:{
270:E
266:=
238:T
210:.
200:)
184:(
174:=
143:.
133:)
117:(
107:=
49:(
33:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
