MTBF Definition and Calculation

Plasticity is the theory describing the deformation of a solid material undergoing non-reversible changes of shape in response to applied forces. Unlike elasticity, where deformation is recovered upon unloading, plastic deformation is permanent. The theory involves a yield criterion to define the onset of plasticity, a flow rule to describe the evolution of plastic strain, and a hardening rule.

The bathtub curve is a graphical model illustrating three phases of a product's life in terms of failure rate. It starts with a high but decreasing 'infant mortality' rate, followed by a low, constant 'useful life' rate, and concludes with an increasing 'wear-out' rate. MTBF calculations using a constant failure rate (\(\lambda\)) are typically only valid during the central 'useful life' phase.

The fundamental building block of modern digital electronics is the transistor, specifically the MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor). It operates as an electronically controlled switch. By applying a voltage to its gate terminal, the flow of current between its source and drain terminals can be turned on (representing a '1') or off (representing a '0'), enabling the implementation of logic gates.

For repairable systems, Mean Time Between Failures (MTBF) is the sum of Mean Time To Failure (MTTF) and Mean Time To Repair (MTTR). The formula is \(MTBF = MTTF + MTTR\). MTTF represents the average operational time before a failure, while MTTR is the average time taken to repair the system. This distinction is critical for understanding system availability.

For a system of components in series, where any single failure causes system failure, the overall failure rate is the sum of individual rates. The system's MTBF is the reciprocal of this sum: \(MTBF_{system} = (\sum_{i=1}^{n} \lambda_i)^{-1} = (1/MTBF_1 + 1/MTBF_2 + ... + 1/MTBF_n)^{-1}\). This implies the system's MTBF is always less than the lowest individual component's MTBF.

Developed by French engineer Pierre Bézier for Renault in the 1960s, UNISURF was one of the first true 3D CAD/CAM systems. Its core innovation was the use of what are now known as Bézier curves and surfaces. These are parametric curves defined by a set of control points, allowing for the intuitive and mathematical creation of complex freeform shapes for car bodies.

The Weissenberg effect is a phenomenon in viscoelastic fluids where the fluid climbs up a rotating rod inserted into it. This is contrary to the behavior of Newtonian fluids, which are pushed outwards by centrifugal force, forming a vortex. The effect is caused by normal stress differences that develop in the fluid under shear.

A Pourbaix diagram, also known as a potential/pH diagram, is a thermodynamic chart that maps the stable equilibrium phases of an aqueous electrochemical system. It graphically shows the conditions of potential (\(E_H\)) and pH under which a metal is immune (thermodynamically stable), passivated (forms a stable protective film), or susceptible to corrosion (forms soluble ions).

Digital circuits are categorized into two main types: combinational and sequential logic. In combinational logic, the output is a pure function of the present input values only (e.g., an adder). In sequential logic, the output depends not only on the current inputs but also on the past sequence of inputs, as these circuits have memory elements (e.g., a flip-flop).

The Deborah number is a dimensionless quantity in rheology, used to characterize the fluidity of materials. It is the ratio of the relaxation time, which is an intrinsic property of the material, to the characteristic time scale of the experiment or observation. The formula is \(De = \frac{t_c}{t_p}\), where \(t_c\) is the relaxation time and \(t_p\) is the observation time.

Repeatability assesses precision under identical conditions, while reproducibility assesses precision when one or more conditions change, such as the operator, instrument, or location. Reproducibility variance is always greater than or equal to repeatability variance. This distinction is crucial for understanding measurement variability, especially in inter-laboratory comparisons where conditions are inherently different.

Cleanrooms utilize two primary airflow principles to control contamination. Turbulent (or non-unidirectional) flow involves mixed air streams, suitable for less stringent classes (ISO 6-9). Laminar (or unidirectional) flow uses parallel, constant-velocity air streams to sweep particles out of the environment, essential for high-purity applications like ISO 1-5, preventing cross-contamination and ensuring rapid particle removal.

CMOS (Complementary Metal-Oxide-Semiconductor) is the dominant technology for constructing integrated circuits. It uses complementary pairs of p-type and n-type MOSFETs to build logic gates. Its primary advantage is very low static power consumption, as one transistor in the pair is always off during steady state, resulting in minimal current flow except during switching transitions.

Molecular electronics explores using individual molecules or nanoscale molecular collections as fundamental electronic components. This approach aims to build circuits at the ultimate limit of miniaturization, far beyond traditional silicon-based technology. Key components include molecular wires, switches, and rectifiers, leveraging quantum mechanical properties like electron tunneling through molecular orbitals for their function.