Computing systems reliability: models and analysis
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Waloddi Weibull, a Swedish physicist, introduced this distribution in It is a generalization of an exponential distribution suitable for modeling lifetimes having constant, strictly increasing, and strictly decreasing hazard functions. Procedure: 1. Collect the failure data.
Get the best fit for the data to a Weibull distribution:. For example, halogen and compact fluorescent bulbs use a different technology to extend life. Further, rating of incandescent long-life light bulbs may proceed as follows:. However, this distribution has a very long tail:. Observe that for the constant failure rate exponential model, a Weibull distribution can be used:. Combine series or parallel component reliabilities to give an equivalent reliability and reduce the system. See the following examples:. Examine the two different configurations of the following 4-component system with identical components.
The component failure rate is:. Moral: We get the greatest gain in reliability by making a system redundant at the lowest level possible. Generally, it is better to make modules redundant than to duplicate the system. Same functional parameters.
Computing system reliability models and analysis cell engineering
Interfaces between parallel subsystems increase complexity of design which decreases reliability. The Parts Count reliability model assumes that the system is in series; this model underestimates the reliability of redundant systems. For redundant systems, the Parts Count model is used to estimate the reliability of the series subsystems and interfaces. Reliability is then computed while considering the redundancy structure. Note: In some cases the interface reliability may dominate the redundant subsystem reliability and determine the overall system reliability.
In this case the simplex system may be more reliable than the redundant system. The Voter compares the outputs of all N modules and outputs the majority. The NMR system will generally have an odd number of modules, so. The voter compares input signals or numeric values and picks the middle value as its output. Normal operation is as follows:. Extra hardware increases reliability for the short term but once redundancy is used up there is simply more hardware to fail and reliability decreases quickly.
For redundant systems MTTF may not be an appropriate measure of reliability. It is necessary to look at R t in relation to mission time. System reliability is determined by 3 parallel modules in the first stage, a voter in the last stage, and a parallel voter-module in the intermediate stage. Failed modules accumulate in an NMR system until they become the majority and the system fails. The system life can be extended by purging all of the failed modules. This can be accomplished through Hybrid Redundancy using spares , or through Adaptive Voting also called Change Voting.
In essence, the failed module s must be detected first. This configuration is often used with TMR systems. If more than a few spares are switched, the complexity increases to a point where its reliability dominates the system reliability. Say we have 3 programmers write code and then vote on the results. In a TMR system, each program could execute on a completely different set of hardware.
However, software is labor-intensive and very expensive to produce.
SIAM Journal on Scientific and Statistical Computing
N-ary programming significantly increases this cost, does not protect against specification errors, and introduces timing and coordination problems since each of the programs is not identical to the others. In adaptive voting, the voted output is compared with the module outputs. When a module fails, it is removed along with one other module this is to keep an odd number of modules. The voter is then changed to select the majority of the remaining modules.
This approach can be combined with hybrid redundancy in order to switch good modules back in. Voting particularly TMR is used in many fault-tolerant, very-high-reliability computer systems. In general, A and B can be different i. A can be an on-line power source while B can be a generator. It should be noted that B can fail while in its standby mode, or the switch could fail. Examine the following simple case. A sequence of failures forms a process that starts over each time a device fails and a new one is switched in.
Continuous distributions used for this purpose include exponential, Weibull, log-normal, and generalized gamma. Discrete distributions such as the Bernoulli, Binomial, and Poisson are used for calculating the expected number of failures or for single probabilities of success.
Advances in System Reliability Engineering - 1st Edition
The same continuous distributions used for reliability can also be used for maintainability although the interpretation is different i. However, predictions of maintainability may have to account for processes such as administrative delays, travel time, sparing, and staffing and can therefore most complex. The probability distributions used in reliability and maintainability estimation are referred to as models because they only provide estimates of the true failure and restoration of the items under evaluation.
Ideally, the values of the parameters used in these models would be estimated from life testing or operating experience. However, performing such tests or collecting credible operating data once items are fielded can be costly. As a result, that estimates based on limited data may be very imprecise. Testing methods to gather such data are discussed below.
We first highlight the research gap in early reliability prediction and then discuss the related works in Section 2. In the case where the k -out-of- n components are not identical, the reliability must be calculated in a different way. Filling stations are not very ubiquitous, and the economy may not support many trained mechanics for automotive repairs. Similar to the work by [ 7 , 11 ], as described previously, these values were inferred from analogous components with similar operations and input obtained from a domain expert the wheelchair developer. If you choose a system distribution, the argument given should be a Boolean expression referencing which components need to work or fail to make the system work or fail. Based on the result shown in Table 2 and Fig 10 , it can be seen that the component reliability gradually decreased as the iteration number increased.
RAM are inherent product or system attributes that should be considered throughout the development lifecycle. The discussion in this section relies on a standard developed by a joint effort by the Electronic Industry Association and the U. Government and adopted by the U. Department of Defense GEIA that defines 4 processes: understanding user requirements and constraints, design for reliability, production for reliability, and monitoring during operation and use discussed in the next section.
Understanding user requirements involves eliciting information about functional requirements, constraints e. From these emerge system requirements that should include specifications for reliability, maintainability, and availability, and each should be conditioned on the projected operating environments.
RAM requirements definition is as challenging but as essential to development success as is the definition of general functional requirements. System designs based on user requirements and system design alternatives can then be formulated and evaluated.. Reliability engineering during this phase seeks to increase system robustness through measures such as redundancy, diversity, built-in test, advanced diagnostics, and modularity to enable rapid physical replacement. In addition, it may be possible to reduce failure rates through measures such as use of higher strength materials, increasing the quality components, moderating extreme environmental conditions, or shortened maintenance, inspection, or overhaul intervals.
Design analyses may include mechanical stress, corrosion, and radiation analyses for mechanical components, thermal analyses for mechanical and electrical components, and Electromagnetic Interference EMI analyses or measurements for electrical components and subsystems. In most computer based systems, hardware mean time between failures are hundreds of thousands of hours so that most system design measures will be to increase system reliability are focused on software.
The most obvious way to improve software reliability is by improving its quality through more disciplined development efforts and test. Methods for doing so are in the scope of software engineering but not in the scope of this section. However, reliability and availability can also be increased through architectural redundancy, independence, and diversity.
Redundancy must be accompanied by measures to ensure data consistency, and managed failure detection and switchover.
Within the software architecture, measures such as watchdog timers, flow control, data integrity checks e. System RAM characteristics should be continuously evaluated as the design progresses. Where failure rates are not known as is often the case for unique or custom developed components, assemblies, or software , developmental testing may be undertaken assess the reliability of custom-developed components.
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Markov models and Petri nets are of particular value for computer-based systems that use redundancy. Evaluations based on qualitative analyses assess vulnerability to single points of failure, failure containment, recovery, and maintainability. Analyses from related disciplines during design time also affect RAM.
Human factor analyses are necessary to ensure that operators and maintainers can interact with the system in a manner that minimizes failures and the restoration times when they do occur.
There is also a strong link between RAM and cybersecurity in computer based systems. On the one hand defensive measures reduce the frequency of failures due to malicious events. Many production issues associated with RAM are related to quality. The most important of these are ensuring repeatability and uniformity of production processes and complete unambiguous specifications for items from the supply chain.
Other are related to design for manufacturability, storage, and transportation Kapur, ; Eberlin Large software intensive systems information systems are affected by issues related to configuration management, integration testing, and installation testing. Depending on organizational considerations, this may be the same or a separate system as used during the design. After systems are fielded, their reliability and availability to assess whether system or product has met its RAM objectives, to identify unexpected failure modes, to record fixes, to assess the utilization of maintenance resources, and to assess the operating environment.
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In order to assess RAM, it is necessary to maintain an accurate record not only of failures but also of operating time and the duration of outages. Systems that report only on repair actions and outage incidents may not be sufficient for this purpose. An organization should have an integrated data system that allows reliability data to be considered with logistical data, such as parts, personnel, tools, bays, transportation and evacuation, queues, and costs, allowing a total awareness of the interplay of logistical and RAM issues.
These issues in turn must be integrated with management and operational systems to allow the organization to reap the benefits that can occur from complete situational awareness with respect to RAM. Reliability Testing can be performed at the component, subsystem, and system level throughout the product or system lifecycle.
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