Triple Modular Redundancy Voter Circuit Improvement

Summary

Redundancy has been fashionable approach to design a fault tolerance system. Because the hardware in a digital system are getting decrease in value and software program redundancy will devour extra time and assets, hardware redundancy is helpful mechanism to enhance the reliability of the system. Whereas an energetic hardware redundancy is used to detect the faults within the hardware element and get better the system from these defective elements, passive hardware redundancy is mainly used to masks the faults within the hardware module. Triple Modular Redundancy is appropriate instance of hardware redundancy approach the place three similar practical elements are used and voting mechanism will take majority of inputs because the output of the system. Nevertheless, a single level failure within the TMR will impede to enhance the reliability of the system. This report will focus on on totally different mechanisms to enhance the voter circuit of triple modular redundancy. A report presents a element evaluation on totally different methods and comparability amongst these approach on foundation value and complexity to implement in triple modular redundancy to enhance voter circuit.

Introduction

A failure of any elements in a important system might result in catastrophic occasions like a human or financial loss. The divergent of a results of a non-critical system from its anticipated output could have little or no impact on the throughput of the system in comparison with that of a important system [1]. So, it's crucial to make sure that each element is out there at on a regular basis and performing as it's anticipated and produce the specified output.  With an implementation of fault tolerance mechanism in a important system, there is a rise within the availability and reliability of a system’s elements. A fault tolerant system is designed in such a manner that it will probably detect the failures of elements and isolate the defect elements from the present system and produce the specified output with out interrupting the stream of the system. A fault tolerance system could be carried out by means of hardware redundancy and software program redundancy. Because the hardware redundancy is relatively decrease than software program redundancy, it has grow to be a well-liked approach to design a fault tolerance system [2].

A triple modular redundancy is without doubt one of the methods to construct fault tolerance system because it will increase the reliability of the system by means of implementation of two out of three voting mechanism approach [3]. The voting mechanism has performed a big function in triple modular redundancy approach as it's going to resolve an precise output out of three elements. The bulk outputs from the three elements would be the precise output of the voting circuit. Regardless of its skill to generate consensual output from the three modules, the presence of single level failure i.e. the failure of the voting circuit itself might result in inconsistency within the output the general methods. This report features a thorough description on fault tolerance, hardware redundancy, and triple modular redundancy approach. Moreover, the report primarily targeted on a mechanism to keep away from the only level failure i.e. voting mechanism within the triple modular mechanism approach.

Background

The idea of fault, errors and failure performs essential function whereas bettering the dependability of the system. Many of the instances, these three phrases are used interchangeably in fault tolerance. Nevertheless, every time period has their very own which means and profitable implementation of fault tolerance design should deal with every of those phrases.

Fault

It may be outlined because the defect or flaws within the hardware or software program element of the system. Whether it is hardware element, fault is taken into account because the defects whereas whether it is software program element, it's thought-about as the issues within the software program system. Faults are mainly thought-about as the basis of the failure of the methods, so, it's essential to keep away from any form of the faults whereas integrating hardware or software program of the system. On foundation of the period, fault could be everlasting, transient or intermittent fault.  Whereas everlasting fault happens as a consequence of failure of elements, bodily harm of hardware or design and don't repair by themselves together with time, transient faults happen for brief time frame and don't re-occur constantly. In the meantime, intermittent fault strikes in between fault and fault free operations within the system. Each transient and intermittent faults are occurred steadily in comparison with that of everlasting faults within the system [4].

Error

In the meantime, errors happen when output from the system is deviated from the anticipated output. So, when there's fault within the hardware elements or software program elements, there will probably be inconsistency within the end result from the elements. Principally, error signifies the state that's invalid to the system specification and mustn't exist [5,6].

Failure

It may be outlined because the incapacity of the system to supply desired outcomes as specified within the system specification. When error happens, a system will probably be in undesirable state and the end result from the system will probably be totally different from the anticipated one. The system habits will probably be modified which is taken into account because the failure of the system [5,6].

fault

Error

Failure

Determine 1 Circulate of Fault, Error and Failure within the System

Redundancy

Redundancy is without doubt one of the environment friendly methods to realize fault tolerance mechanism within the digital system. As its identify counsel, redundancy is mainly an addition of hardware and software program assets, data or time in a system greater than it required to carry out their regular operation. There are 4 redundancy methods and they're:

  1. Software program Redundancy
  2. Time Redundancy
  3. Data Redundancy
  4. Hardware Redundancy

 

Software program Redundancy

Whereas the bodily defects within the hardware elements can barely re-occurred as soon as it's found and restore, fixing bugs within the software program applications will create larger probability to create different errors within the coding. Regardless of the presence of various software program improvement course of, there are probabilities to develop error susceptible software program as a consequence of novice builders, lack of testing or insufficient money and time for the total part improvement of the software program. N-version programming is without doubt one of the software program fault-tolerance approach the place a program writes for N instances and execute in parallel to take majority output as a ultimate output of this system. Whereas this system is an efficient to masks the errors in this system, will probably be pricey and tough to keep up all of the model of the code. Likewise, a use of watchdog timers and timeouts, time redundancy for program or self-checking within the software program allowed to detect the faults within the software program. When a software program runs for a number of instances and in contrast the outcomes, it's attainable to determine the faults or bugs in this system.

Time Redundancy

The idea of time redundancy is to run this system multiples instances within the presence of identical hardware configuration and examine the produce outcomes. It reduces the expense on costly hardware addition and likewise keep away from parallel execution of the applications. Since a program could be run a number of instances in the identical modules and examine the outcomes to determine errors or faults, it's going to environment friendly in contrast hardware and software program redundancy approach. Apart from that, it's appropriate for transient or intermittent faults as a frequent run of applications in identical module will assist to get majority output because the precise output of the system. Nevertheless, one of many appreciable disadvantages of time redundancy is the requirement of huge period of time to determine the faults and defects within the system in comparison with hardware and software program system [8].

Data Redundancy

Right here, there will probably be an addition of additional data together with knowledge to make sure to integrity of the knowledge modifications throughout a storage or transmission. An error-detecting codes and correcting codes, and self-checking circuits are fashionable mechanism for data redundancy. Parity code is broadly used for error-detection within the reminiscence of the pc system. A parity bit is generated by a parity generator and knowledge is encoding by means of computation of its parity. When there's modifications within the computed parity bit with saved parity bit, there is a sign of knowledge modifications and error sign is distributed to the processor of invalid reminiscence knowledge. Alternatively, knowledge that are encoded with error-correcting codes incorporates each errors and enough redundancy to get better the specified knowledge. In the meantime, self-checking circuit will produce legitimate output phrase when there's legitimate enter and when there's existence of fault, it's going to produce invalid output code to detect the fault within the system [7].

Hardware Redundancy

Hardware redundancy could be achieved by means of the addition of additional hardware to the system. Because the hardware elements are getting cheaper with development of expertise, it may be thought-about as appropriate mechanism to realize reliability within the system. Other than that, it additionally doesn't require proceed commentary and won't take extra time to determine and masks the error in comparison with different redundancy methods. For instance, an addition of processors, knowledge or reminiscence buses, energy and even reminiscences can simply obtain hardware redundancy. There are generally three approaches to acquire hardware redundancy methods and they're as comply with

  1. Passive Redundancy
  2. Lively Redundancy
  3. Hybrid Redundancy

Passive redundancy is accountable for hiding and masking the faults within the hardware elements fairly than detecting these faults. It should produce the end result primarily based on polling mechanism and supply the right output from the system regardless of the present of faults within the elements. When there are multiples faults than polling circuit can cowl, then it can't cover the faults and failure of the system is imminent. Triple modular redundancy and N modular redundancy are the acceptable instance of fault tasking approach by means of use of redundant hardware within the system [9].

Determine 2 N-modular hardware Redundancy

Equally, energetic hardware redundancy is used to detect the faults within the elements and get better from these defective elements. There are use of various methods for fault detections and computation with duplication is without doubt one of the methods the place two duplicate modules execute similar computation in parallel and with use of comparator outcomes are in contrast. If the outcomes will not be equal between two modules, an error sign will probably be produced.

After the detection of faults, no extra exercise is carried out till the system get better from the fault.

Determine three Comparability with Duplication

In the meantime, in standby Sparing approach, a single module out of N modules will function and accountable for the output of the system whereas remaining n-1 modules will stay as a spare. When there's failure of working module, spares will probably be switched and begin to function. Subsequently, a standby sparing system having N modules will tolerate N-1 faults within the modules. Moreover, Pair and spare approach mix each comparability approach and sparing approach to enhance fault detects and get better. There's a use of two modules in parallel and when there's error after comparability, it's going to determine defected module and changed it's going to spare modules. Other than these methods, timer mechanism can be utilized for error detection [10,11].

Apart from energetic and passive redundancy methods, hybrid redundancy approach, which incorporates options from each earlier methods, is one other hardware redundancy approach to determine faults within the elements and get better from these faults. One of many approaches of hybrid redundancy approach is duplex-triplex structure the place two duplication with comparability approach together with TMR is used to masks the errors, detect the faults and take away these faults from the system to supply fascinating output. One of many main disadvantages of hybrid redundancy is that the strategies that are used to implement it are pricey [12].

Triple Modular Redundancy

The idea of Triple Modular Redundancy is especially primarily based on redundancy of hardware elements of the system. It's extremely used to make system extra dependable and proceed to carry out their operations in opposition to the delicate errors. When an error happens in sequential circuits, which signifies to the totally different storage within the system comparable to registers, reminiscences, flip-flips and counters, there will probably be a change within the saved state in several storage and result in the execution of this system totally different from the anticipated one. To reduce results of soppy errors, TMR is designed in microprocessors in order that errors won't halt the stream of this system.

Determine four Triple Modular Redundancy Approach

The generalization of TMR approach in N modular redundancy approach. Whereas there's presence of n modules within the N modular redundancy approach, TMR could have three similar practical hardware items to carry out the operation. The idea of the TMR design is to make use of three duplicate modules which is able to take identical enter. All of the operation throughout the module is identical for all three of these modules, so, using enter knowledge is identical of all three instances. On the highest of the similar modules, there's apply of voting mechanism to get majority output because the precise output of the system. So, voter circuit will take all three outputs of the hardware unit because the enter to the unit and majority of enter will contemplate because the precise output of the system. For instance, contemplate there are three hardware modules A, B and C within the system. All three modules are functionally similar, and all are provided with zero enter. Amongst three modules, two produce output end result as 1 whereas one module produces zero as output. When all three outputs from module enter into voter Logic, E, it's going to carry out some calculation to resolve majority output from the modules, which on this case will probably be 1 and regarded 1 because the output of the element. Since inputs within the voter logic are binary and variety of inputs are in odd numbers, will probably be simpler to calculate majority inputs within the voter machine [13].

The essential goal of Triple Modular Redundancy is to masks the errors exist within the practical unit of the system. So, it may be thought-about because the passive hardware redundancy approach to realize the reliability of the system. The bulk logic gate also referred to as voting logic consists of straightforward AND-OR circuit. Think about a, b and c are three inputs from the modules to the logic gate, then it may be outlined as ab V bc V ac. Moreover, mathematically, the reliability of any system, R, could be calculated because the sum of the chances of success and fail occasions i.e.

R(system) = Rmthree + 3RM2(1- RM) = 3RM2 – 2 RMthree

Right here, the fundamental assumptions are made, and they're voting circuit doesn't fail, failures of three modules are unbiased from one another, system won't fail if none of three modules fails or precisely one module fails at a time. Nevertheless, the foremost drawback of triple modular redundancy approach is its single level failure. Whereas there could be made an assumption that voter circuit by no means fails however when it does, the reliability of entire system will probably be compromised. When all three modules are working completely, the failure of voter circuit may end up totally different output from the system fairly than precise appropriate output produce by the practical unit [15].

Literature Evaluation

The aim of fault tolerance system is to keep away from a failure of the general system regardless of present faults within the totally different elements. Redundancy has been a big approach to guarantee fault tolerance design within the digital system. Amongst a number of redundancy methods, hardware redundancy is consistently used to enhance the reliability of the digital methods. Whereas energetic hardware redundancy is helpful to detect faults and restoration, passive hardware redundancy is helpful to cover faults in hardware elements. TMR is a passive hardware redundancy approach the place faults are hidden, and solely appropriate knowledge are handed as output from the system [16].

V.M et al (2005) had mentioned on the choice approach to triple modular redundancy approach known as Lowered Triple Modular Redundancy. It mainly operates on lookup-table which is achieved after expertise mapping stage. Quite than utilizing three similar total design, they most popular for the triplicating first and third class of the lookup desk and there's a use of tri buffer-based majority voters to get the output from the system. The target of their analysis is to deal with single occasion failure, which primarily occurred to due extra charged induced from the radiation. Because of this, it's extremely influential to alter the interior state of the information, totally on reminiscence components like routing configuration bits and search for desk entries. So, such errors might result in change in bits in reminiscence or desk entries and fully produce sudden output from the system. With the assistance of spare flip-flops of CLBs in combinational circuits, numerous insensitive LUTs are duplicated. They described a serious drawback of utilizing Triple Modular Redundancy approach is an extreme space overhead. Their proposed approach, RTMR, simply required 99.61% of further variety of LUTs, which is sort of 100% much less that of LUTs required in regular TMR. Regardless of using a smaller variety of further LUTs in RTMR, it was capable of present excessive degree of SEU immunity [17].

One other proposed method to enhance Triple modular redundancy is cascaded TMRs. They're primarily utilized in areas like pipeline course of, Poly-Si TFT. Since there's use of a number of levels of TMR design to construct the cascaded TMR, it is usually generally known as Multi-stage TMR. The construction is designed in a such manner that one output from the TMR would be the three inputs for the one other TMR. It may be thought-about dependable if no less than two inputs from every stage is present appropriate worth and finish voter produce the correct output. With use of a number of voters, it will probably impede the only level failure exist within the unique Triple modular redundancy approach. Whereas an unique TMR has single voter, it can't present dependable end result on the failure of voting system whereas cascaded triple modular redundancy approach can present dependable end result regardless of failure of voter.

Determine 1 Classical Cascaded Single Voter TMR Module

Whereas unique cascaded TMR consists of single level failure one voter, new proposed approach consists of a number of voter per stage. When there's use of single voter within the TMR, there are strict rule to realize the reliability of the system. In the meantime, when there's use of a number of voters in every stage of the TMR, it's going to enhance the price of designing and finally violate the cost-effective design. So, Yi, Chung and Kim (2015) proposed new cost-effective cascaded Triple modular redundancy which is able to enhance the fee effectiveness of the design and likewise guarantee there's loosen within the guidelines to convey the reliability to the system [18].

In the meantime, the idea of TMR is to masks the defective module within the system. When there's one defective module within the system, it will probably proceed to work and supply desired end result. So as to execute the identical activity on the identical hardware after the detection of TMR failure or exchange the hardware, reload and restart, Shin and Kim (1994) proposed an adaptive restoration methodology by optimally selecting both RSHW or RHWR on foundation of their value effectiveness. They used Bayes theorem to replace gather data of every state within the TMR system after every voting end result. When there's TMR failure, the anticipated value of RSHW will calculated on foundation of all of the likelihoods and people outcomes are in contrast with RHWR. After persevering with enhance within the variety of unsuccessful RSHWs, everlasting TMR failure will probably be elevated and ultimately there's enhance in the price of RSHW. As greater than 90% faults within the system are generally known as transient faults or non-permanent faults and round 2% faults are everlasting faults, a easy re-execution of the duty will probably be an efficient course of to get better from many of the TMR failures. Such re-execution of activity will assist to eradicate hardware value come up as a consequence of alternative of huge chunk of hardware failures, cut back restoration time come up by means of the alternative of hardware, system configuration and system restart. The adaptive methodology of RSHW calculate the state with all attainable likelihoods state within the system and later gauge the RSHW or RHWR primarily based on their anticipated value when the system reaches in one of many estimated states.  When the variety of unsuccessful RSHWs exceeds the utmost variety of RSHWs allowable or estimated value of RSHW exceed that of RSHW, then RHWR will probably be invoked [19].

Moreover, Patooghy et.al (2006) mentioned on distributed voting mechanism to beat the present downside of the only level failure within the Triple Modular Redundancy. Their concepts utilized using time redundancy and disagreement detector options to beat the problem. A way is experimented with vertex2Pro and Vertex4 Xilinx FPGA to display the reliability and enhance imply time failure of a TM system. They highlighted regardless of the proceed analysis to enhance the voting circuit within the TMR system, lots of these works are primarily based on sure degree of assumptions which makes present downside easy however unrealistic. One frequent instance of such assumption is lots of researches are primarily based on neglecting the only level failure to enhance the reliability of the system. Their proposed methodology would masks the everlasting and transient faults which occurred within the voter of a TMR system with assist of time redundancy, Triple modular redundancy with disagreement detector and use of n spares voter within the system. The variety of spare voters used within the system will assist to resolve what number of faults it will probably cowl within the system. One of many advantages of their proposed methodology is that distribution of determination between voter and disagreement detector. Nevertheless, one of many disadvantages of their proposed methodology is definite degree of delay to supply the output as a consequence of comparability between distributed determination maker [20].

The usage of phrase voter over standard voter has their very own benefit to make sure the information integrity. Mitra and McCluskey (2000) has mentioned on phrase voter and introduced their implementation with examine to little by little voting design in standard voter system. They'd in contrast space and delay overhead of word-voter design with little by little voter. The usage of word-voter must enhance the capabilities of Triple modular system to guard in opposition to common-mode and a number of module failures. There may be vital of additional hardware to construct the phrase voter which is an order of 1 2-input logic gate and three XNOR gates for every output of the system. In the meantime, the phrase voter design could be modified to ensure that knowledge outputs with out the error sign in absence of additional gate.

Determine 2 TMR system with Phrase Voter

Determine three voting mechanism in TMR

Right here, the above to determine explaining the voting mechanism for each little by little voting mechanism and phrase voting mechanism. Whereas little by little voting mechanism will thought-about every little bit of the enter to search out the errors within the defective module, word-wise voting mechanism will take each of the inputs and in comparison with discover the errors within the module [21] .

Whereas TMR helps to enhance the reliability of methods, it’s single level failure i.e. voting logic failure might trigger the failure of an total system. Sadeghi, Soltan, and Khayyambashi [22] has argued that regardless of a easy construction of TMR mannequin, an existence of voter logic as a weaker level will result in a failure of the general system. When there's a fault in a single hardware element, a voter can masks these faults by producing appropriate output from the system. Nevertheless, if there are any faults on a voter, it's going to produce an inconsistent and incorrect output which may result in the failure of a system. Subsequently, they've proposed to make use of three voters as a substitute of 1 voter in order that the chance of voter logic failure will probably be diminished and a failure of 1 voter could be coated by different two voters within the system.

Because the reliability of a voter should be excessive to enhance the general reliability of the system, an assumption of voter at all times produces an accurate end result or stay fault free weaken to supply fault tolerance design. Moslem and Václav [23] have proposed novel fault tolerant voter circuit design utilizing wired-logic to make voter itself to tolerant faults and assist the reliability of a system. An open drain CMOS NAND gate, which includes solely 2 series-connected n-channels are used to make fault-tolerant voter. Moreover, novel voter circuit design could be expanded for N- modular redundancy system the place N is odd integer and larger than or equal to 5.

Whereas there are totally different strategies that are proposed to enhance the reliability of methods and make fault tolerant voter circuit, some proposed strategies elevated the complexity with use of a number of multiplexer and precedence encoders. In the meantime, different proposed strategies are lack of inextensibility as a consequence of which such module will solely assist on explicit fashions fairly than generalized mannequin. A novel fault tolerant voter circuit has diminished the complexity in its design and additional assist for generalized hardware redundancy strategies.

Analysis Methodology

Triple modular redundancy methodology has been helpful approach to enhance the reliability of the system. Whereas TMR has skill to masks the fault exist in of the module, it won't capable of decrease the fault exist within the voter circuit. Additionally it is known as single level failure within the TMR system and failure of voter circuit can compromise the reliability of the system. This report has carried out main analysis on bettering the voter circuit of the Triple modular redundancy system. In the meantime, the report additionally performs the secondary analysis on bettering the reliability of triple modular redundancy system with consideration of TMR failure, and so forth.

The issue assertion of the report clearly states that voter circuit within the triple modular system fails can result in the failure of the system. Voter circuit is used to supply an output from nearly all of the enter to the voter. Since there's use of three similar modules within the TMR with offering identical enter on every of these modules, voter circuit can obtain both identical enter from all of the modules or can obtain no less than two totally different enter from three modules. The report has recognized totally different assumptions which are made whereas designing the triple modular redundancy and elaborate and eradicated these assumption to determine precise approach that might assist to enhance the voter circuit of the system. Primarily, analysis finds a number of the assumptions frequent on totally different implementation approach and they're as comply with

  1. Voter circuit by no means fails
  2. There will probably be no faults on two modules directly, which implies just one module can have fault to implement TMR design

Each of those assumptions have made important function in designing easy Triple Modular Redundancy system.

Since a analysis is a qualitative analysis, it has described totally different terminology related to TMR approach. The distinguish between fault, error and failures in digital system adopted by totally different redundancy methods comparable to hardware, software program, time and knowledge redundancy approach helps to enlist the benefit and drawback of every redundancy approach. The analysis illustrated that hardware redundancy is extra frequent follow to construct reliability in digital system in comparison with that on software program redundancy. As hardware gadgets are cheaper together with development in expertise, it may be helpful to design fault tolerance system. Alternatively, software program redundancy required a number of instances run of identical program in parallel, which is able to devour each assets and time to search out the faults in this system and repair these bugs. Moreover, analysis additionally identifies time redundancy could be helpful to keep away from using further hardware and wish of parallel run of this system. Nevertheless, because it executes a number of instances of this system to determine the bugs in this system, it's going to delay total execution of this system.

In the meantime, to enhance the voter circuit, this report has measured the fee effectiveness and complexity of proposed design to enhance reliability of the voter circuit. A literature overview from totally different papers have been noticed as part of the survey to determine the potential design to enhance the voter circuit of Triple modular redundancy system. As well as, analysis report has in contrast the theoretical data of various papers fairly than accumulating pattern knowledge and making use of numerical system to match the end result. Primarily based on outcomes from totally different papers, advantages and downsides of every design is recognized and categorised to decide on acceptable design methodology to resolve a difficulty related to the only level failure. Whereas the paper has tried to reduce pointless assumptions however has not fully keep away from all of the assumptions exist whereas designing the system.

End result

The report has reviewed a number of analysis papers associated to reliability of triple modular redundancy. It's noticed that triple modular redundancy has less complicated construction to design and successfully deal with the fault masking of hardware elements. The commentary of outcomes from totally different papers derived that the assumptions comparable to no failure of two hardware elements directly and easily voting logic won't ever fail has weaken the reliability of triple modular redundancy approach. In the meantime, a analysis additionally finds regardless of many of those proposed methods are viable to enhance voter, a complexity, inextensibility, and dependency on the opposite elements make tough to implement. By evaluating above components, a novel fault-tolerant voter circuit design is appropriate to enhance voter logic because it overcomes the complexity, inextensibility, and dependency and capable of present reliability to the TMR system. It has diminished the complexity required to extend the reliability of the voter circuit as there's solely use of twelve transistors and one pull-up resistor for a voter. Moreover, the dependency as a result of community on one gate within the voter to supply the ultimate output can also be diminished.

Determine 1 Reliability Comparability between traditional voter and novel voter

With use of open-drain NAND gates, which consists of solely 2 series-connected n-channels, a easy and dependable voter circuit could be generated.

Conclusion and Future Work

Conclusion

Hardware redundancy is helpful to enhance the reliability of the system. Though the construction of triple modular redundancy is straightforward and price efficient, a single level failure i.e. voter circuit might trigger the failure of the general system. In the meantime, totally different methods have been proposed to enhance the reliability of the triple modular redundancy, nonetheless, many of those methods have been primarily based on assumptions that no two modules will fail on the identical time and voter circuit won't ever fails. The report has carried out element evaluation on some methods which will probably be helpful to enhance the voter circuit within the system.

Future Work

This analysis stays targeted on bettering voter circuit of the triple modular redundancy. The report research a number of literature overview papers to evaluation the approach to enhance the voter mechanism in order that the reliability of the triple modular redundancy won't compromise as a result of single level failure within the TMR. An extra detailed analysis and carry out the evaluation by means of assortment of knowledge will present sheer data concerning appropriate approach to enhance reliability of the system. Though the report has carried out value and complexity evaluation to pick acceptable approach for voter, use of numerical knowledge will additional proof to pick acceptable mechanism.

Reference

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[9] SADEGHI, M., SOLTAN, H., & KHAYYAMBASHI, M. (2015). The examine of hardware redundancy methods to offer a fault tolerant system. Cumhuriyet Science Journal, 36(four), 236-245.

[10] Oliveira, D. A., Rech, P., Quinn, H. M., Fairbanks, T. D., Monroe, L., Michalak, S. E., … & Carro, L. (2014). Trendy GPUs radiation sensitivity analysis and mitigation by means of duplication with comparability. IEEE Transactions on Nuclear Science, 61(6), 3115-3122.

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[12] Lee, S., Lee, S., Lee, Okay.-C., & Kim, M.-H. (2017). Analytical hybrid redundancy system for the fault tolerance of superior driver help methods. Proceedings of the Establishment of Mechanical Engineers, Half D: Journal of Vehicle Engineering, 231(12), 1660–1665. https://doi.org/10.1177/0954407016684265

[13] Anjankar, S. C., & Kolte, M. T. (2014). Fault Tolerant and Correction System Utilizing Triple Modular Redundancy. Worldwide Journal of Rising Engineering Analysis and Know-how, 2(2), 187-191.

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[15] Rahman, M., Rafique, S., & Alam, M. (2017). A Fault Tolerant Voter Circuit for Triple Modular Redundant System. Journal of Electrical and Digital Engineering, Vol5, (5), 149-159.

[16] V. M. Noor Mohammad, Vikram Chandrasekhar, V. Kamakoti, “Lowered triple modular redundancy for tolerating seus in sram-based fpgas”, Proceedings of NASA Worldwide Convention on Army Functions in Programmable Logic Gadgets (MAPLD) September 2005, september 2005.

[17] Yi, H. J., Chung, T. S., & Kim, S. (2015). A Reliability Evaluation of Cascaded TMR Programs. In Data Science and Functions (pp. 369-376). Springer, Berlin, Heidelberg.

[18] Shin, Okay. G., & Kim, H. (1994). A time redundancy method to TMR failures utilizing fault-state likelihoods. IEEE Transactions on Computer systems, 43(10), 1151-1162.

[19] Patooghy, A., Miremadi, S. G., Javadtalab, A., Fazeli, M., & Farazmand, N. (2006, September). An answer to single level of failure utilizing voter replication and disagreement detection. In Reliable, Autonomic and Safe Computing, 2nd IEEE Worldwide Symposium on (pp. 171-176). IEEE.

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