Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a mechanical or electronic system during normal system operation. MTBF can be calculated as the arithmetic mean (average) time between failures of a system. The term is used for repairable systems while mean time to failure (MTTF) denotes the expected time to failure for a non-repairable system.
In economics, the marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as output is increased by an infinitesimal amount. As Figure 1 shows, the marginal cost is measured in dollars per unit, whereas total cost is in dollars, and the marginal cost is the slope of the total cost, the rate at which it increases with output. Marginal cost is different from average cost, which is the total cost divided by the number of units produced.
An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel electrolyte covers the surface of this oxide layer, serving as the cathode or negative plate of the capacitor. Because of their very thin dielectric oxide layer and enlarged anode surface, electrolytic capacitors have a much higher capacitance-voltage (CV) product per unit volume than ceramic capacitors or film capacitors, and so can have large capacitance values. There are three families of electrolytic capacitor: aluminum electrolytic capacitors, tantalum electrolytic capacitors, and niobium electrolytic capacitors.
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, producing rapid propagation and typically complete fracture of the structure.
Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high direct current densities are used, such as in microelectronics and related structures. As the structure size in electronics such as integrated circuits (ICs) decreases, the practical significance of this effect increases.
A product's service life is its period of use in service. Several related terms describe more precisely a product's life, from the point of manufacture, storage, and distribution, and eventual use. Service life has been defined as "a product's total life in use from the point of sale to the point of discard" and distinguished from replacement life, "the period after which the initial purchaser returns to the shop for a replacement". Determining a product's expected service life as part of business policy involves using tools and calculations from maintainability and reliability analysis. Service life represents a commitment made by the item's manufacturer and is usually specified as a median. It is the time that any manufactured item can be expected to be "serviceable" or supported by its manufacturer.
A contour line of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value.
An isoquant, in microeconomics, is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs. The x and y axis on an isoquant represent two relevant inputs, which are usually a factor of production such as labour, capital, land, or organisation. An isoquant may also be known as an “Iso-Product Curve”, or an “Equal Product Curve”.
Burn-in is the process by which components of a system are exercised before being placed in service. This testing process will force certain failures to occur under supervised conditions so an understanding of load capacity of the product can be established.
Failure 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.
In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible level of production, and the result is a cost curve. Profit-maximizing firms use cost curves to decide output quantities. There are various types of cost curves, all related to each other, including total and average cost curves; marginal cost curves, which are equal to the differential of the total cost curves; and variable cost curves. Some are applicable to the short run, others to the long run.
Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time.
Enzyme assays are laboratory methods for measuring enzymatic activity. They are vital for the study of enzyme kinetics and enzyme inhibition.
A highly accelerated life test (HALT) is a stress testing methodology for enhancing product reliability in which prototypes are stressed to a much higher degree than expected from actual use in order to identify weaknesses in the design or manufacture of the product. Manufacturing and research and development organizations in the electronics, computer, medical, and military industries use HALT to improve product reliability.
A tantalum electrolytic capacitor is an electrolytic capacitor, a passive component of electronic circuits. It consists of a pellet of porous tantalum metal as an anode, covered by an insulating oxide layer that forms the dielectric, surrounded by liquid or solid electrolyte as a cathode. Because of its very thin and relatively high permittivity dielectric layer, the tantalum capacitor distinguishes itself from other conventional and electrolytic capacitors in having high capacitance per volume and lower weight.
In statistics, the exponentiated Weibull family of probability distributions was introduced by Mudholkar and Srivastava (1993) as an extension of the Weibull family obtained by adding a second shape parameter.
A prediction of reliability is an important element in the process of selecting equipment for use by telecommunications service providers and other buyers of electronic equipment, and it is essential during the design stage of engineering systems life cycle. Reliability is a measure of the frequency of equipment failures as a function of time. Reliability has a major impact on maintenance and repair costs and on the continuity of service.
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime. Sometimes complementary cumulative distribution functions are called survival functions in general.
The Fei–Ranis model of economic growth is a dualism model in developmental economics or welfare economics that has been developed by John C. H. Fei and Gustav Ranis and can be understood as an extension of the Lewis model. It is also known as the Surplus Labor model. It recognizes the presence of a dual economy comprising both the modern and the primitive sector and takes the economic situation of unemployment and underemployment of resources into account, unlike many other growth models that consider underdeveloped countries to be homogenous in nature. According to this theory, the primitive sector consists of the existing agricultural sector in the economy, and the modern sector is the rapidly emerging but small industrial sector. Both the sectors co-exist in the economy, wherein lies the crux of the development problem. Development can be brought about only by a complete shift in the focal point of progress from the agricultural to the industrial economy, such that there is augmentation of industrial output. This is done by transfer of labor from the agricultural sector to the industrial one, showing that underdeveloped countries do not suffer from constraints of labor supply. At the same time, growth in the agricultural sector must not be negligible and its output should be sufficient to support the whole economy with food and raw materials. Like in the Harrod–Domar model, saving and investment become the driving forces when it comes to economic development of underdeveloped countries.
Power system operations is a term used in electricity generation to describe the process of decision-making on the timescale from one day to minutes prior to the power delivery. The term power system control describes actions taken in response to unplanned disturbances in order to provide reliable electric supply of acceptable quality. The corresponding engineering branch is called Power System Operations and Control. Electricity is hard to store, so at any moment the supply (generation) shall be balanced with demand. In an electrical grid the task of real-time balancing is performed by a regional-based control center, run by an electric utility in the traditional electricity market. In the restructured North American power transmission grid, these centers belong to balancing authorities numbered 74 in 2016, the entities responsible for operations are also called independent system operators, transmission system operators. The other form of balancing resources of multiple power plants is a power pool. The balancing authorities are overseen by reliability coordinators.
