Qualitative/quantitative reasoning, fault

Since perfect knowledge of the model is rarely a reasonable assumption, soft computing methods, integrating quantitative and qualitative modeling information, have been developed to improve the performance of observer-based schemes for uncertain systems [36], Major contributions to observer-based approaches can be found in [39, 56] as well, where fault isolation is achieved via a bank of observers, while identification is based on the adoption of online universal interpolators (e.g., ANNs whose weights are updated on line). As for the use of observers in the presence of advanced control techniques, such as MPC or FLC, in [44] an unknown input observer is adopted in conjunction with an MPC scheme. 

Fault tree analysis is a technique by which the system safety engineer can rigorously evaluate specific hazardous events. It is a type of logic tree that is developed by deductive logic from a top undesired event to all subevents that must occur to cause it. It is primarily used as a qualitative technique for studying hazardous events in systems, subsystems, components, or operations involving command paths. It can also be used for quantitatively evaluating the probability of the top event and all subevent occurrences when sufficient and accurate data are available. Quantitative analyses shall be performed only when it is reasonably certain that the data for part/component failures and human errors for the operational environment exist. 

Whilst some comparative experimental evidence on the effectiveness of techniques such as testing and fault tolerance is available [FAA 1982 Knight and Leveson 1986b], the assessment, measurement and prediction of the contribution of formal methods to safety is a subject largely unresearched. There are two major reasons for this. First, there is very little experiment data. This is because there are relatively few instances of use of formd methods for safety-critical systems and even in these cases there is no systematic data collection [Bowen and Stavridou 1992]. But perhaps more fundamentally, quantitative evidence is sometimes perceived as inappropriate for qualitative improvement techniques such as formal methods. The two major schools of thought concerning risk analysis and assessment, qualitative and quantitative, are often at odds with each other. The quantitative school believes that probabilities are primarily reflections of the actual frequency of events, thus are objective and can be used for pr ictions of future events. 

There Is a need for a system to easily understand and effectively classify hazardous events. The methodology should provide solutions that meet simple as well as reasonable complex processes in a qualitative manner. For unusuallycomplexand/orunusuallysever consequences, quantitative methods such as fault tree or event tree analysis should be employed. 

The reason for such diversity in methods of determining SILs is probably due to the difficulties of arriving at reliable and credible estimates of risk in the wide variety of situations faced in industries. Whilst a quantitative risk assessment is desirable it may be worthless if the available data on fault rates is minimal or subject to huge tolerances. Qualitative methods allow persons to use an element of judgment and experience in the assessment of risk without having to come up with numerical values that are difficult to justify. 

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