Where does failure collide?

Griffith's 1921 The phenomena of rupture and flow in solids introduced the idea that a solid breaks when the energy freed by a growing crack exceeds the energy needed to create new surface, so that tiny flaws, not the ideal strength of the atomic bonds, decide when a material gives way. Irwin's 1957 Analysis of stresses and strains near the end of a crack traversing a plate refined this into the stress concentrated at a crack tip, the basis of modern fracture mechanics. Here failure is the fracture or permanent yielding of a physical material under load, measured in the laboratory, and it has nothing to do with a machine that stops working, a person's motive to avoid losing, or a firm that goes bankrupt.[1][2]

Unit

One broken or yielded specimen, scaled by the stress or energy at which it fails

Recovery means

Not applicable

Measured by

Measured by tensile, fracture-toughness, and fatigue tests that record the load, stress intensity, or energy at breakage

Weibull's 1951 A statistical distribution function of wide applicability gave reliability engineering the curve now used to model how the chance of breakdown changes with age, treating failure as the moment a component stops performing its intended function. In this field failure is an event in time, summarised by a failure rate and a distribution of times-to-failure across a population of units. The referent is the loss of function of an engineered system, tracked statistically over a service life, not the cracking of a raw material, a person's fear of losing, or the collapse of a company.[3]

Unit

A single loss-of-function event in a unit, scaled by its time-to-failure

Recovery means

A repairable unit is restored by maintenance and returns to service, and its uptime is tracked as availability

Measured by

Measured by failure rate, mean time to failure, and fitted life distributions from test or field data

Atkinson's 1957 Motivational determinants of risk-taking behavior defined the motive to avoid failure, the learned disposition to feel shame and anxiety at not succeeding, as one of two forces that shape which tasks a person will attempt. In achievement psychology, fear of failure is this motivational state, later elaborated as a set of distinct threats such as shame and loss of social standing. The referent is a person's disposition in an achievement setting, rated by questionnaire, and it is unrelated to a fractured material, a component that quits working, or an insolvent business.[4]

Unit

One person's strength of the motive to avoid failure

Recovery means

Not applicable

Measured by

Measured by projective tests and self-report scales such as achievement-motive and fear-of-failure inventories

Beaver's 1966 Financial ratios as predictors of failure studied firms that could not pay their obligations and showed that accounting ratios separated failing from surviving companies years in advance, treating failure as the inability of a business to meet its debts. Altman's 1968 Financial ratios, discriminant analysis and the prediction of corporate bankruptcy combined several ratios into the Z-score, still a standard gauge of distress. Here failure is the financial collapse or insolvency of an organisation, judged by its accounts, not the rupture of a material, the breakdown of a device, or a person's motive to avoid losing.[5][6]

Unit

One firm's failure or insolvency event, scaled by financial-distress indicators

Recovery means

A firm may reorganise through bankruptcy proceedings and return to solvency, or else be liquidated

Measured by

Measured by financial ratios, discriminant and hazard models, and bankruptcy or default records