This definition also follows on from the work of Sood & Tellis which applied a subsampling approach to analyse different types of 'multiple S-curves', and subsequently concluded that technologies tend to follow more of a step-function, with long periods of static performance interspersed with abrupt jumps in performance, than a classical S shape. In this study, stagnation periods were recorded where technology performance during a given subsample had an upper plateau longer in duration than the immediately preceding growth phase, whilst the subsequent jump in performance in the year immediately after the plateau was almost double the performance during the entire plateau \cite{Sood_2005}. Other studies, including the work of Chang and Schilling, classify multiple S-curves based on whether successive curves intersect or are disconnected (see Fig.  \ref{402288} and \cite{Chang_2010,Schilling_2009}).

Anomalies associated with scientific and technological crisis

Up till now, only substitution patterns associated with technological failure have been discussed. However, previous studies have identified that technological disruptions are not just the result of the existing technology being deemed to have 'failed'. In this sense Edward Constant argued that a feature common to all technological revolutions was the emergence of 'technological anomalies', which could be traced to either scientific or technological crisis. The first, and most common cause of these technological anomalies results from functional failure, where:
"either the conventional paradigm proves inappropriate to "new or more stringent conditions", or an individual intuitively assumes that (s)he can produce a better or a new technological device" \cite{II_1973}
Alternatively, technological anomalies can arise as a result of presumptive technological leaps:
"The demarcation between functional-failure anomaly and presumptive anomaly is that presumptive anomaly is deduced from science before a new paradigm is formulated and that scientific deduction is the sole reason for the sole guide to new paradigm creation. No functional failure exists; an anomaly is presumed to exist, hence presumptive anomaly" \cite{II_1973}
Whilst technological revolutions may originate from either scientific or technological crisis, a critical  area of commonality lies in the anomaly-crisis process observed in both conditions:
"in both science and technology anomaly causes certain individuals to reject the conventional paradigm and to create  new paradigms, and, in each, crisis may lead to revolution" \cite{II_1973}
The type of crisis that emerges is dependent on which type of anomaly precedes it. Scientific crisis can occur irrespective of whether an alternative theoretical framework exists or not when a persistent, unresolved, scientific anomaly successfully refutes an established theory. In this condition the crisis is directly linked to the anomaly. However, technological anomaly and crisis are rarely so logically driven, and can arise in conditions where existing technological paradigms are still performing favourably. This is illustrated by the turbojet revolution of the 1930s and 1940s where piston-engine developments had provided remarkable performance improvements and continuing success, but were superseded by scientific advances that were directly responsible for the radical technological changes that followed. In addition, in order for a technological anomaly to provoke a technological crisis, a convincing alternative paradigm must exist, so that the relative functional failure of the conventional system is observable. As such, the alternative technological paradigm instigates the crisis, whilst the technological anomaly may only be seen as speculation or as a limiting condition to the normal technology \cite{II_1973}.

Modes of substitution

Based on the definitions of functional failure and presumptive anomaly described in sections \ref{677399} and \ref{646617}, this study examines the ability to distinguish between these two modes of substitution from analysis of historical scientific and technological data. Table \ref{table:technology_categories} uses these definitions and performance evidence obtained from literature to classify a sample set of technologies according to the mode of substitution observed.