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60-722: The Siemens S200 is a high-floor light rail vehicle (LRV) manufactured by Siemens Mobility in Florin, California , beginning service in 2016. The S200 succeeds earlier Siemens high-floor LRV models, including the SD-100/SD-160 and the SD-400/SD-460 . Its low-floor counterpart is the Siemens S700 . The S200 is designed specifically for the North American market, and is built to the specifications of each individual operator. The S200

120-457: A Weibull distribution , log-normal distribution , or a hypertabastic distribution , the hazard function may not be constant with respect to time. For some such as the deterministic distribution it is monotonic increasing (analogous to "wearing out" ), for others such as the Pareto distribution it is monotonic decreasing (analogous to "burning in" ), while for many it is not monotonic. Solving

180-412: A conditional probability , where the condition is that no failure has occurred before time t {\displaystyle t} . Hence the R ( t ) {\displaystyle R(t)} in the denominator. Hazard rate and ROCOF (rate of occurrence of failures) are often incorrectly seen as the same and equal to the failure rate. To clarify; the more promptly items are repaired,

240-634: A different specification than in San Francisco's fleet. High-floor High-floor describes the interior flooring of commuter vehicles primarily used in public transport such as trains , light rail cars and other rail vehicles, along with buses and trolleybuses . Interior floor height is generally measured above the street surface or above the top of the rail. High-floor designs usually result from packaging requirements: mechanical items such as axles, motors, crankshafts, and/or transmissions, or luggage storage spaces are traditionally placed under

300-522: A flat floor ranging between 760 and 1,370 mm (30 and 54 in) above the top of the railhead (ATOR). To enhance accessibility and optimize dwell times , railway platform heights at stations are sometimes standardised to allow level boarding for commuters on high platforms. According to one definition, level boarding means the gap between the platform and the floor of the track varies by no more than 76 mm (3 in) horizontally and 16 mm ( 5 ⁄ 8  in) vertically. Level boarding

360-500: A new underground light rail line is equipped with platforms for low-floor trams and will be permanently operated with low-floor vehicles. This form of design and construction will avoid the need for subsequent rebuilding of stops on tram routes, even though both cities already have underground lines with high-floor platforms. Buses in the UK were traditionally step-entrance built, however this has created problems for people who use wheelchairs as

420-434: A railcar more rapidly if they do not have to climb stairs to enter, reducing dwell time at a stop, and reducing overall travel time. In addition, high-platform railcars have more floor space for passengers if space is not required for stairways, and wheelwells needed to accommodate train bogies . Because bilevel rail cars have two passenger levels within a standard height rail car, the lower level, where passengers board,

480-400: A time interval Δ t {\displaystyle \Delta t} = ( t 2 − t 1 ) {\displaystyle (t_{2}-t_{1})} from t 1 {\displaystyle t_{1}} (or t {\displaystyle t} ) to t 2 {\displaystyle t_{2}} . Note that this is

540-815: Is a new design by Siemens for the North American market, building upon its previous models. Siemens entered the North American light rail market in the late 1970s with the Siemens–Duewag U2 , which was initially built in Düsseldorf , West Germany . The U2's successors in the high-floor LRV market were manufactured in Florin, California, along with low-floor designs including the SD660 and the S70/S700 . Calgary Transit selected Siemens to manufacture 60 light rail vehicles in 2013, to replace part of its initial fleet of U2 trains. The S200

600-582: Is also capable of showing advertisements, although it has not been implemented yet. Some of these features (LCD information screens, security cameras, LED exterior signs) have been implemented on the refurbished Siemens SD-160 cars as part of mid-lifecycle refurbishment. Siemens have designated the S200 light rail vehicles for San Francisco as S200 SF, and the San Francisco Municipal Transportation Agency internally designates them as

660-717: Is also known as stepless entry since passengers do not have to negotiate a staircase to board the passenger car. For newly constructed routes, routes primarily located in tunnels, or routes with a dedicated right of way and enough space, high platforms are usually preferred, since high-floor vehicles are cheaper to manufacture, and have better operating characteristics. High platforms do have significant advantages beyond level boarding for wheelchair accessibility. Physically disabled passengers (e.g. those using wheelchairs or who have difficulties climbing stairs) also benefit, as do travelers pulling wheeled luggage or small folding shopping carts. Even physically non-disabled passengers can board

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720-430: Is generally lower than a conventional high-floor car. Hence level boarding with a bilevel car is accomplished using a lower platform, as low as 460 mm (18 in) ATOR. Because tram/light-rail/streetcar vehicles often share loading gauge sizes with heavy rail vehicles, these passenger vehicles usually also use high floor designs. Existing tram/streetcar/light-rail networks generally feature low platforms as many of

780-479: Is that the use of large positive numbers (such as 2000 hours) is more intuitive and easier to remember than very small numbers (such as 0.0005 per hour). The MTBF is an important system parameter in systems where failure rate needs to be managed, in particular for safety systems. The MTBF appears frequently in the engineering design requirements, and governs frequency of required system maintenance and inspections. In special processes called renewal processes , where

840-557: Is the city railway in Cologne; in the mid-1990s, it was decided to divide that city's partially high-platform network into two separate networks: high-floor and low-floor. In contrast with some light rail underground lines, which are often provisionally equipped with low platforms or with tracks laid on raised ballast, there are new developments in the German cities of Düsseldorf (Wehrhahn line) and Dortmund (east–west line). In each of these cities,

900-571: Is the most common unit in practice. Other units, such as miles, revolutions, etc., can also be used in place of "time" units. Failure rates are often expressed in engineering notation as failures per million, or 10 , especially for individual components, since their failure rates are often very low. The Failures In Time ( FIT ) rate of a device is the number of failures that can be expected in one billion (10 ) device-hours of operation. (E.g. 1000 devices for 1 million hours, or 1 million devices for 1000 hours each, or some other combination.) This term

960-436: Is used particularly by the semiconductor industry. The relationship of FIT to MTBF may be expressed as: MTBF = 1,000,000,000 x 1/FIT. Under certain engineering assumptions (e.g. besides the above assumptions for a constant failure rate, the assumption that the considered system has no relevant redundancies ), the failure rate for a complex system is simply the sum of the individual failure rates of its components, as long as

1020-674: The California Public Utilities Commission investigated the issues. The investigation into the coupler issues found that maintenance technicians were overtightening an adjustment screw in the couplers, which placed additional stress on the shear pins, which then failed. Maintenance procedures were revised, and redesigned brackets and spacers were installed in the couplers. Two-car and three-car trains resumed service in June 2019, but were again withdrawn in December 2019 after issues with

1080-614: The Chase Center , and full service on the Central Subway . The first S200 LRV for the Muni Metro entered service on November 17, 2017, and the final LRV of the 219-vehicle order is expected to be delivered in 2025. One of the primary concerns for the LRV4 fleet in San Francisco was improving the mean distance between failures (MDBF) compared to the existing Breda LRV2/3 fleet. The Breda fleet

1140-595: The emergency stop button on San Francisco's older LRVs when requiring a quick stop, because of the sometimes faulty nature of their braking systems. Emergency braking in the S200 LRVs was found to be effective, but applying the emergency brakes disables anti-lock braking , leading to flat spots on wheels as they grind against the rails. The braking system on the S200 LRVs was redesigned in late 2019 to incorporate additional track brakes , and modifications were completed in 2020. Calgary Transit's S200 LRVs, which it refers to as

1200-494: The LRV4. San Francisco's S200 LRVs succeed prior LRV designs from Boeing-Vertol ( LRV1 ) and AnsaldoBreda (LRV2 and LRV3). SFMTA ordered 175 LRVs in September 2014 at a total cost of $ 648 million. Additional S200 LRVs were ordered in 2015, 2017, and 2021. The S200 trains will replace the entire Muni Metro fleet, and will provide additional capacity for service expansions. These expansions include additional game day service to

1260-550: The LRV4. The issues, involving doors, couplers, and brakes, drew widespread media attention. In response, the San Francisco Municipal Transportation Authority delayed a $ 62   million payment to Siemens. The issues with the LRV4 fleet, combined with the high failure rate of SFMTA's older trains, caused delays and overcrowding on multiple services. On April 12, 2019, a passenger on the N-Judah line

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1320-997: The S200 cars are narrower than the existing Tokyu trains. The plan was first announced in January 2023, and the deal was finalized in May 2023, after the RTA received a grant from the Federal Transit Administration . The S200s are expected to begin service in Cleveland in 2026. In May 2023, Metro announced its intention to acquire 48 vehicles to replace its aging fleet of SD-400 light rail vehicles. The S200 vehicles for St. Louis will be equipped with batteries for operation on tracks without overhead lines, allowing for flexibility in future expansions. Multiple defects were reported in April 2019 with San Francisco's fleet of S200 trains, which it refers to as

1380-461: The S200 is a high-floor design, designed for level boarding . The design is customized for each operator, to account for varying platform heights, loading gauges , and service requirements. All S200 vehicles are powered by direct current , collected from overhead lines with a pantograph . In September 2013, 60 light rail vehicles were ordered, costing $ 200 million, for the Calgary CTrain ;

1440-874: The Series 9, experienced minor issues in October 2016. Software glitches in some newly-introduced S200 trains activated a safety mode, which reduced their service speed from 80 to 40 km/h (50 to 25 mph). The trains' doors were too slow to open, also causing delays. The issues were resolved by Siemens staff in Calgary, and the S200 cars continued in service. In the aftermath of the April 2019 incidents in San Francisco's S200 fleet, Calgary City Council transportation committee chair Shane Keating requested that Calgary Transit review its S200 fleet for similar issues. Calgary Transit officials highlighted their maintenance and inspection procedures, and emphasized that their trains' doors are built to

1500-420: The brakes, or have major transmission problems in a new vehicle. In practice, the mean time between failures (MTBF, 1/λ) is often reported instead of the failure rate. This is valid and useful if the failure rate may be assumed constant – often used for complex units / systems, electronics – and is a general agreement in some reliability standards (Military and Aerospace). It does in this case only relate to

1560-545: The buses are not wheelchair accessible, as well as being somewhat difficult for passengers with reduced mobility and parents who may be carrying prams and pushchairs. Despite low-floor buses first being phased into the UK in 1994, a large number of step-entrance buses remained in use as well as being manufactured. However with the popularity of low-floor buses expanding by the late 1990's due to their easy accessibility for elderly passengers with reduced mobility, passengers with disabilities and parents carrying prams and pushchairs,

1620-525: The couplers were damaged. At the Board of Supervisors meeting in April 2019, Muni officials also reported that the wheels on the LRV4s required resurfacing before their expected end-of-life because of the use of emergency brakes, which are engaged once a week on average. At any given time, only half (or fewer) of the LRV4s were available for service because of wheels with flat spots caused by emergency braking. Muni and

1680-410: The differential equation for F ( t ) {\displaystyle F(t)} , it can be shown that A decreasing failure rate (DFR) describes a phenomenon where the probability of an event in a fixed time interval in the future decreases over time. A decreasing failure rate can describe a period of "infant mortality" where earlier failures are eliminated or corrected and corresponds to

1740-481: The discrete case nor in the continuous case. Increasing failure rate is an intuitive concept caused by components wearing out. Decreasing failure rate describes a system which improves with age. Decreasing failure rates have been found in the lifetimes of spacecraft, Baker and Baker commenting that "those spacecraft that last, last on and on." The reliability of aircraft air conditioning systems were individually found to have an exponential distribution , and thus in

1800-630: The door sensor system under warranty, and normal operation resumed in June 2019. In a separate incident on April 12th, a two-car train of LRV4 cars was found with a faulty shear pin in its couplers . The S200's coupler shear pins allow the couplers to retract inwards in a collision, working in tandem with an anti-climber on the front of the train, which protects the train operator and passengers. The faulty shear pins put trains at risk of unintentionally separating in service, and Muni responded by running trains with only one car. More extensive inspections in May 2019 showed that approximately 1 ⁄ 3 of

1860-866: The end of their economic or maintainable life. To get around this, a wheelchair compliant step-entrance bus introduced by Wrightbus, the Eclipse SchoolRun was produced in 2006, fitted with a wheelchair lift to allow wheelchair-bound passengers onto the bus, but no further wheelchair compliant step-entrance bus designs were produced. Due to the Terms Of The Disability Discrimination Act requiring all buses in public service to be wheelchair accessible, non-compliant step-entrance single deckers and their low floor counterparts were outlawed after 31 December 2015, with non-compliant step-entrance double deckers and their low floor counterparts following suit after 31 December 2016, however exemptions apply for

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1920-514: The existence of a failure distribution , F ( t ) {\displaystyle F(t)} , which is a cumulative distribution function that describes the probability of failure (at least) up to and including time t , where T {\displaystyle {T}} is the failure time. The failure distribution function is the integral of the failure density function , f ( t ), The hazard function can be defined now as Many probability distributions can be used to model

1980-413: The failure distribution ( see List of important probability distributions ). A common model is the exponential failure distribution , which is based on the exponential density function . The hazard rate function for this is: Thus, for an exponential failure distribution, the hazard rate is a constant with respect to time (that is, the distribution is " memory-less "). For other distributions, such as

2040-454: The flat region of the bathtub curve , which is also called the "useful life period". Because of this, it is incorrect to extrapolate MTBF to give an estimate of the service lifetime of a component, which will typically be much less than suggested by the MTBF due to the much higher failure rates in the "end-of-life wearout" part of the "bathtub curve". The reason for the preferred use for MTBF numbers

2100-435: The following: Although the failure rate, λ ( t ) {\displaystyle \lambda (t)} , is often thought of as the probability that a failure occurs in a specified interval given no failure before time t {\displaystyle t} , it is not actually a probability because it can exceed 1. Erroneous expression of the failure rate in % could result in incorrect perception of

2160-458: The initial "future fleet" delivery of 68 LRVs, where seats are placed along the long sides of the car, rather than lateral seating, where seats face the front and back of the vehicle. The longitudinal seating creates wider aisles, is preferred by advocates for the disabled, provides more room for standing passengers, and may accommodate bicycles on board, as the bicycle policy only allows folding bikes on board. However, in "future fleet" of 68 LRV4s,

2220-697: The insurance, finance, commerce and regulatory industries and fundamental to the design of safe systems in a wide variety of applications. Failure rate data can be obtained in several ways. The most common means are: Given a component database calibrated with field failure data that is reasonably accurate , the method can predict product level failure rate and failure mode data for a given application. The predictions have been shown to be more accurate than field warranty return analysis or even typical field failure analysis given that these methods depend on reports that typically do not have sufficient detail information in failure records. The failure rate can be defined as

2280-404: The interior floor of these vehicles. The term is used in contrast with low-floor designs, which offer a decreased floor and entry height above the street surface. Since low-floor designs generally were developed after high-floor vehicles, the older high-floor design is sometimes also known as conventional or the “traditional” design. A rail vehicle of conventional or high-floor design usually has

2340-597: The light rail vehicles used on the Blue , Green , and Waterfront lines. GCRTA's S200 vehicles will include steps at the front and back doors for boarding and alighting at street-level light rail stations and stops. These doors will also have manually operated trapdoors for use on the Red Line , which exclusively uses high-level platforms. The introduction of S200 LRVs for the Red Line will require modifications at Red Line stations, as

2400-544: The limited use of non-compliant heritage buses on vintage bus services, as well as Transport For London's Heritage Routemasters due to their service being overlaid on the high-frequency low-floor Route 15. In San Francisco , the Muni Metro light-rail system, which has both on-street and underground stations, uses a combination of high and low platforms, and the vehicles feature retractable stairs to accommodate both platform types. For on-street stations, stairs are deployed within

2460-499: The long benches were flat and lacked the individual seating pockets used in the Breda longitudinal benches. In a November 2019 report, Muni provided details for a retrofit of the already-delivered "future fleet": half the flat longitudinal benches will be replaced with single transverse seats, and the other half will be replaced with individual longitudinal seats. For the "replacement fleet" of 151 cars, 50 will be delivered with seating to match

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2520-419: The mean time between critical failures (MTBCF), even though the mean time before something fails is worse. Suppose it is desired to estimate the failure rate of a certain component. A test can be performed to estimate its failure rate. Ten identical components are each tested until they either fail or reach 1000 hours, at which time the test is terminated for that component. (The level of statistical confidence

2580-462: The measure, especially if it would be measured from repairable systems and multiple systems with non-constant failure rates or different operation times. It can be defined with the aid of the reliability function , also called the survival function, R ( t ) = 1 − F ( t ) {\displaystyle R(t)=1-F(t)} , the probability of no failure before time t {\displaystyle t} . over

2640-611: The order was later slightly expanded to 63 LRVs at a cost of $ 201.6 million. The first car was delivered on January 6, 2016. Later, an additional 6 cars were ordered. The first of this order was delivered in May 2019 and was put into service on July 11, 2019. In February 2020, 15 more LRVs were ordered bringing the total fleet to 84 S200 LRVs. The new cars feature a host of new and upgraded technologies. Heated floors and triple-pane windows were added to combat Calgary's harsh winter climate, as well as sloped entryways to eliminate moving ramps found on older trains. A new speaker system adjusts

2700-462: The pooled population a DFR. When the failure rate is decreasing the coefficient of variation is ⩾ 1, and when the failure rate is increasing the coefficient of variation is ⩽ 1. Note that this result only holds when the failure rate is defined for all t ⩾ 0 and that the converse result (coefficient of variation determining nature of failure rate) does not hold. Failure rates can be expressed using any measure of time, but hours

2760-541: The production of step-entrance buses slowed, with the last ever non-compliant step-entrance bus design being the double-decked East Lancs Pyoneer in 1997. The production of step-entrance buses in the UK almost fully ceased by 31 December 2000, with the legal requirement for new buses produced to be wheelchair accessible, which forced bus manufacturers to concentrate on making low-floor buses, however bus operators were still allowed to order secondhand non-compliant step-entrance buses and run them on their services until they reach

2820-458: The retrofitted "future fleet" of 68; the remaining 101 will have double transverse seats instead of the single transverse seats. The seats also will be lowered, enabling riders shorter than 5 ft 4 in (163 cm) to rest their feet on the floor. The Greater Cleveland Regional Transit Authority intends to acquire 24 S200 vehicles to replace heavy rail vehicles used on the Red Line , with an option to acquire 36 additional units to replace

2880-542: The retrofitting of high platforms on existing routes, while still providing improved accessibility. Although low-floor vehicles began to be developed in the 1920s, the first low-floor tram is generally recognized as the Duewag / ACM Vevey design of 1984 deployed in Geneva, providing a floor height of 480 mm (19 in) ATOR. Tourist coaches generally have very high floors, sometimes greater than 1,000 mm (39 in) above

2940-697: The road surface, in order to have ample room for luggage under the floor. Since boarding must be allowed directly from flat ground, long and steep staircases are needed. Transit buses also use high floors to provide mechanical clearances for solid axles, but the use of dropped axles has enabled the creation of low-floor buses and by 2008 in the United States, the majority of new transit bus orders were for low-floor types. Today, in Germany, all rapid transit railways, most commuter trains , and many light rail vehicles operate as high-floor networks. A notable exception

3000-484: The shear pins resumed. The later issues with shear pins were attributed to stresses on the couplers brought on by San Francisco's hilly terrain. Siemens provided new shear pins under warranty until it completed a redesign of the system, and the shear pin issues were resolved by the end of 2021. The investigation into the wheel issues found faults in the design of the brake system on the S200 LRVs, and also highlighted issues with operator training. Operators were trained to use

3060-443: The situation where λ( t ) is a decreasing function . Mixtures of DFR variables are DFR. Mixtures of exponentially distributed random variables are hyperexponentially distributed . For a renewal process with DFR renewal function, inter-renewal times are concave. Brown conjectured the converse, that DFR is also necessary for the inter-renewal times to be concave, however it has been shown that this conjecture holds neither in

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3120-607: The sooner they will break again, so the higher the ROCOF. The hazard rate is however independent of the time to repair and of the logistic delay time. Calculating the failure rate for ever smaller intervals of time results in the hazard function (also called hazard rate ), h ( t ) {\displaystyle h(t)} . This becomes the instantaneous failure rate or we say instantaneous hazard rate as Δ t {\displaystyle \Delta t} approaches to zero: A continuous failure rate depends on

3180-440: The stations or stops are in the streets. The high construction/conversion cost of high platforms and the difficulty of making high platforms compatible with other features of the urban landscape are a significant obstacle to converting tram networks these into urban or commuter rail networks with high platforms. These problems were a major motivation for the development of low-floor trams , which allow transit operators to avoid

3240-471: The time to recover from failure can be neglected and the likelihood of failure remains constant with respect to time, the failure rate is simply the multiplicative inverse of the MTBF (1/λ). A similar ratio used in the transport industries , especially in railways and trucking is "mean distance between failures", a variation which attempts to correlate actual loaded distances to similar reliability needs and practices. Failure rates are important factors in

3300-415: The units are consistent, e.g. failures per million hours. This permits testing of individual components or subsystems, whose failure rates are then added to obtain the total system failure rate. Adding "redundant" components to eliminate a single point of failure improves the mission failure rate, but makes the series failure rate (also called the logistics failure rate) worse—the extra components improve

3360-538: The vehicle to allow boarding from low platforms; as the trains move underground, the stairs rise until they are flush with the floor to allow boarding from high platforms. Mean distance between failures The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system. For example, an automobile's failure rate in its fifth year of service may be many times greater than its failure rate during its first year of service. One does not expect to replace an exhaust pipe, overhaul

3420-442: The volume output depending on the number of passengers in each car. Dynamic interior LED lights adjust to become brighter when it is dark and dimmer when light is shining through the windows. The end doors were moved back to improve passenger flow and include LED lights to indicate if a door can be opened or if it is closing/locked. New infotainment systems were added alongside LED info signs to display next stop and line information. It

3480-508: Was able to achieve an MDBF of 2,000–5,500 miles (3,200–8,900 km) in fiscal years 2005 and 2006; the contract with Siemens called for a MDBF of 25,000 miles (40,000 km). When they were initially placed in service, the Siemens LRV4 had a MDBF of 5,000 miles (8,000 km), improving to 17,000 miles (27,000 km) by January 2020. Ridership surveys and SFMTA staff recommendations resulted in an all-longitudinal seating configuration for

3540-477: Was designed for service in Calgary, whose CTrain system uses high platforms for level boarding. The second customer, the San Francisco Municipal Railway , uses a combination of high platforms and street-level stops for its Muni Metro system. This distinct environment prompted the inclusion of retractable stairs in San Francisco's S200 trains, which entered service in 2017. The basic design of

3600-404: Was dragged along a platform after her hand became stuck in a door. The passenger was thrown down to track level after freeing her hand, and was seriously injured. The April 2019 incident was the fourth reported incident where passengers were trapped by doors on the LRV4. As a temporary measure, the rear doors on S200 trains were locked shut to prevent additional trapped passengers. Siemens redesigned

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