Triple modular redundancy

The general case of TMR is called N-modular redundancy, in which any positive number of replications of the same action is used. The number is typically taken to be at least three, so that error correction by majority vote can take place; it is also usually taken to be odd, so that no ties may happen. == Majority logic gate ==

3-input majority gate The 3-input majority gate output is 1 if two or more of the inputs of the majority gate are 1; output is 0 if two or more of the majority gate's inputs are 0. Thus, the majority gate is the carry output of a full adder, i.e., the majority gate is a voting machine. For a TMR system with a single voter of reliability (probability of working) and three components of reliability , the probability of it being correct can be shown to be . Voter The majority gate itself could fail. This can be protected against by applying triple redundancy to the voters themselves. In a few TMR systems, such as the Saturn Launch Vehicle Digital Computer and functional triple modular redundancy (FTMR) systems, the voters are also triplicated. Three voters are used – one for each copy of the next stage of TMR logic. In such systems there is no single point of failure. Even though only using a single voter brings a single point of failure – a failed voter will bring down the entire system – most TMR systems do not use triplicated voters. This is because the majority gates are much less complex than the systems that they guard against, so they are much more reliable. By using the reliability calculations, it is possible to find the minimum reliability of the voter for TMR to be a win. ==Chronometers==

To use triple modular redundancy, a ship must have at least three chronometers; two chronometers provided dual modular redundancy, allowing a backup if one should cease to work, but not allowing any error correction if the two displayed a different time, since in case of contradiction between the two chronometers, it would be impossible to know which one was wrong (the error detection obtained would be the same of having only one chronometer and checking it periodically). Three chronometers provided triple modular redundancy, allowing error correction if one of the three was wrong, so the pilot would take the average of the two with closer reading (vote for average precision). There is an old adage to this effect, stating: "Never go to sea with two chronometers; take one or three." Mainly this means that if two chronometers contradict, how do you know which one is correct? At one time this observation or rule was an expensive one as the cost of three sufficiently accurate chronometers was more than the cost of many types of smaller merchant vessels. Some vessels carried more than three chronometers – for example, HMS Beagle carried 22 chronometers. {{cite web In the modern era, ships at sea use GNSS navigation receivers (with GPS, GLONASS & WAAS etc. support) – mostly running with WAAS or EGNOS support so as to provide accurate time (and location). == In popular culture ==

• In Arthur C. Clarke's science fiction novel Rendezvous with Rama, the Ramans make heavy use of triple redundancy. • In the popular anime Neon Genesis Evangelion, the Magi are a set of three biological supercomputers that must agree with a 2/3 majority vote before delivering a decision. • In the film Minority Report, 3 "precogs" are used to predict impending homicides, using a triple modular redundancy. In the plot, this system fails, causing a false positive: an innocent man is wrongly accused of murder. == See also ==