Fracture mechanicsFracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Theoretically, the stress ahead of a sharp crack tip becomes infinite and cannot be used to describe the state around a crack. Fracture mechanics is used to characterise the loads on a crack, typically using a single parameter to describe the complete loading state at the crack tip.
Failure mode and effects analysisFailure mode and effects analysis (FMEA; often written with "failure modes" in plural) is the process of reviewing as many components, assemblies, and subsystems as possible to identify potential failure modes in a system and their causes and effects. For each component, the failure modes and their resulting effects on the rest of the system are recorded in a specific FMEA worksheet. There are numerous variations of such worksheets.
Failure causeFailure causes are defects in design, process, quality, or part application, which are the underlying cause of a failure or which initiate a process which leads to failure. Where failure depends on the user of the product or process, then human error must be considered. A part failure mode is the way in which a component failed "functionally" on the component level. Often a part has only a few failure modes. For example, a relay may fail to open or close contacts on demand.
Failure rateFailure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering. 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.
Failure analysisFailure analysis is the process of collecting and analyzing data to determine the cause of a failure, often with the goal of determining corrective actions or liability. According to Bloch and Geitner, ”machinery failures reveal a reaction chain of cause and effect... usually a deficiency commonly referred to as the symptom...”. Failure analysis can save money, lives, and resources if done correctly and acted upon.
ConsistencyIn classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead.
Mechanical computerA mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment output displays. More complex examples could carry out multiplication and division—Friden used a moving head which paused at each column—and even differential analysis. One model, the Ascota 170 accounting machine sold in the 1960s calculated square roots.
Complete theoryIn mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence the theory contains the sentence or its negation but not both (that is, either or ). Recursively axiomatizable first-order theories that are consistent and rich enough to allow general mathematical reasoning to be formulated cannot be complete, as demonstrated by Gödel's first incompleteness theorem.
Test statisticA test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.
Model theoryIn mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the statements of the theory hold). The aspects investigated include the number and size of models of a theory, the relationship of different models to each other, and their interaction with the formal language itself.
