1 Introduction

People love inspiring and encouraging stories, which fosters the increasing popularity of disruptive innovation. Christensen (1997) published his remarkable book The Innovator’s Dilemma and creatively proposed the disruptive innovation theory to explain how startups defeat powerful and well-managed incumbent enterprises. The most classic case study used in the book is the hard drive industry in America. Briefly, in the literature, the process of successful disruptive innovation is typically illustrated in Fig. 1 and interpreted as follows. In the beginning, 14-inch hard drives are the only type of products sold in the market and improved in capacity at a certain speed. Then the cheap but inferior products of 8-inch hard drives enter as disruptive innovations in the low-end market, which is ignored by the powerful incumbent enterprises that sell 14-inch hard drives. What is surprising is that the initially inferior products finally catch up with the mainstream customers’ demand in capacity after a few years, and leave the originally powerful incumbent companies disrupted. This phenomenon reoccurred in the ensuing hard drive enterprises. Many other industries used as cases in the book are claimed to experience a similar pattern, such as steel, motorcycle, accounting software, etc.

Fig. 1
figure 1

A classic case of disruptive innovation—hard drives (Christensen 1997)

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Disruptive innovation intrigues both scholars and practitioners all over the world, whereas increasing popularity accelerates the exposure of its theoretical issues. One of the hotly discussed and fundamental issues is its ambiguous definition (Adner 2002; Bower and Christensen 1995; Christensen 1997, 2006, 2014; Danneels 2004; Ganguly et al. 2010; Govindarajan and Kopalle 2006; Klenner et al. 2013; Markides 2006; Nagy et al. 2016; Tellis 2006). Christensen (2006) clarified that the word “disruptive” has many different connotations and is widely misinterpreted, which may be the source of the confusion. He is very open to criticism and claims that the word is not properly chosen to name the phenomenon (Christensen 2014). Indeed, the theory has been enriched and stronger during the past twenty years. However, readers who turn to Christensen’s work for a clear-cut definition may disappointingly find the boundaries of disruptive innovation are vague (Weeks 2015). That is to say, the real identity of disruptive innovation is still behind the mist.

A variety of factors involved in the process of disruptive innovation are supposed to be critical attributes of disruptive innovation. In summarization, lower price, initially inferior technology, value network, oversupply, asymmetric incentives, relativity, and complementary technology are the frequently used theoretical components linked closely to disruptive innovation (Bower and Christensen 1995; Christensen 1997, 2006; Christensen et al. 2002). These components sufficiently constitute a successful story (interpretation) of disruptive innovation. Undoubtedly, success needs various factors, but the nature or definition of disruptive innovation should not be based on success. Otherwise, disruptive innovation would become a happy-ending story. More crucially, it may lead us to presume that unless the incumbent companies are already disrupted, or we can’t identify a disruptive innovation, which is exactly what the scholars criticized as the post hoc definition. Defining disruptive innovation post hoc merely offers us hindsight, and logically disables the predictive use of the theory. The ambiguous or post hoc definition of disruptive innovation incurs accumulative confusion and criticism. The radical causation is that the nature of disruptive innovations is not unveiled.

However, it is extremely challenging to find some unsuccessful cases of disruptive innovations and further conduct a comprehensive analysis combining both the successful and unsuccessful disruptive innovations to extract their common nature. The fact is that the cases we are able to use are normally pertinent to the outstanding disruptive enterprises, because they are standing out enough to catch attention. As Barney (1997) pointed out that some companies are more fortunate than others when choosing technologies. These lucky survivors are more eye-catching, and thus are more readily found plausible theories to explain their success. But how to build a theory that allows failure upon the cases of success? We probably find an approach that could help us out of the theoretical dilemma. Our philosophy is inspired by reductionism. Since a variety of theoretical components are involved in the theory of disruptive innovation, we question which component is more fundamental than another and doubt the necessity of each component. If one component is more fundamental than all the others, it is reasonable to postulate this component should be imperative, and it is certainly the very nature of disruptive innovation. To decipher the nature of disruptive innovation, reorganizing the entangled or scattered theoretical components frequently used in the relevant research literature is very necessary. This study follows “Occam’s razor” principle while reorganizing the disruptive innovation theory (Hopp et al. 2018). That is, the improvement of disruptive innovation theory is mainly based on “subtraction”. On the basis of existing research, using as few theoretical elements as possible to construct a theory that is logically self-consistent and does not lose explanatory power.

This research contributes to the existing literature from the following aspects: (1) analyzing key driving forces for disruptive innovation and theoretical deficiencies by sorting out existing literature and cases, and utilizing the interpretative structural modeling to reorganize the original disruptive innovation theory, which contributes to a more coordinated and streamlined theoretical framework; (2) proposing the “duality” as the nature of disruptive innovation that distinguishes it from other types of innovation, which prevents the limitations of post hoc analysis and the “survivorship bias”; (3) providing an extendable and adjustable systematic framework for future theoretical development, which is conducive to the formation of theoretical consensus or the focus of academic discussion; (4) providing the theoretical reference and analysis for authorities to effectively identify disruptive innovation and formulate policies for scientific and technological innovation.

The rest of this paper is organized as follows. Section 2 analyzes the key influencing factors of disruptive innovation and introduces the concept of duality. Section 3 reorganized the theory framework of disruptive innovation utilizing the interpretative structural model. Section 4 concludes the research.

2 The factor analysis of disruptive innovation

Disruptive innovation is a complex dynamic process involving many factors. The existing literature explores the influencing factors of disruptive innovation from various perspectives. For example, the research from a micro-individual perspective shows the characteristics of managers will affect enterprises’ seizure of disruptive innovation. This type of research focuses on incumbents and explores how these enterprises respond to the challenge of disruptive innovation in terms of managers’ inertia, experience, ability, and perception of disruptive innovation (Adner 2002; Bergek et al. 2013; Dewald and Bowen 2010; Gilbert and Bower 2002; Henderson 2006; Osiyevskyy and Dewald 2015; Wan et al. 2015). Some research has discussed from the industrial level or the national economic level (Pinkse et al. 2014; Ruan et al. 2014; Si and Chen 2020; Wan et al. 2015). These analytical perspectives are actually further extensions of Christensen’s theory at the macro or micro level. It is certainly meaningful to study the impacts of these factors on disruptive innovation; however, given the lack of systematization, coordination and streamlining of disruptive innovation theory, as well as the risk of misuse and misunderstanding of the disruptive innovation concept (Christensen 2006; Christensen et al. 2016), this study concentrates on key driving forces directly used to explain market changes in the original disruptive innovation theory to avoid introducing redundant concepts and potential contradictions.

2.1 The main influencing factor analysis

2.1.1 Oversupply

Oversupply is an important theoretical component and provides the basis for other factors of disruptive innovation theory (Christensen and Raynor 2013; Christensen 2006). According to Christensen’s theory, the 8-inch hard drives were a disruptive innovation relative to the 14-inch ones. Figure 2 displays trajectories between the 14-inch and 8-inch hard drives, which are denoted as \(L1\) and \(L2\) respectively, there is the line \(L3\) representing the real demand of the market. With this group of lines, Christensen explained why the startups disrupted the incumbents in the 1980s. The 14-inch hard drives heavily overshoot the market demand, which leads to the “oversupply”. Although the 8-inch hard drives as disruptive innovation start from low-end market, they just need to grow faster than the real demand for hard drive capacity to satisfy the consumers’ demand and encroach on the market share of incumbent enterprises, which the intersection of \(L2\) and \(L3\) represents.

Fig. 2
figure 2

The pattern of oversupply

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2.1.2 Price and technological performance

The low price and low quality are reckoned as important characteristics of disruptive innovations (Benzidia et al. 2021; Christensen and Raynor 2013; Christensen 2006; Christensen et al. 2016, 2018). Hard drive capacity is an important performance indicator, and it is also a key factor affecting product prices. Smaller hard drives also typically have smaller storage capacities and therefore sell for less. In the case of oversupply of incumbent companies’ product performance, smaller-sized hard drives have attracted consumers in the mainstream market by virtue of their price advantages, thus successfully “disrupt” incumbent enterprises. In the same vein, the 5.25-inch hard drives disrupt the 8-inch ones, then the former were disrupted by the 3.5-inch hard drives after a few years. This pattern depicted in Fig. 2 may lead people directly to think that disruptive innovation means the fiascos of incumbents. After all, incumbents are severely alienating themselves from the demand, while the startups are unhesitatingly heading towards what the mainstream customers actually need (Christensen 1997, 2006; Christensen et al. 2002).

2.1.3 Complementary technology

In the reflective review, Dan and Chieh (2008) pointed out that the commercialization of potential disruptive technologies would not succeed with the absence of complementary technologies. It is true for the hard drive case. Hard drives in small sizes would not be adopted quickly unless portable electronic products are booming. When hard drives are first launched on the market, main customers are users of mainframe computers. These customers are very persistent in the pursuit of computer performance but do not pay much attention to the volume of hard drives. In fact, the engineers who first produce prototypes of smaller hard drives come from mature incumbent companies, but they do not invest resources in large-scale production because performances of these hard drives cannot meet the needs of the target customers. The rise of smaller hard drives is due to the development of large-scale integrated circuits, and the miniaturization of CPUs has made small and micro-electronic products, such as laptops gradually go out of the laboratory. This also allows small-size hard drive manufacturers to find a clear target market. In other words, if integrated circuit technology has not developed to a certain extent to give birth to miniaturized processors, these disruptors in the hard drive industry may not appear. It is the emergence of complementary technologies that can form a new market that incumbent companies have never set foot in, enabling small-size hard drive manufacturers to take root and develop.

2.1.4 Value network

Value network is a vital concept in disruptive innovation theory. The proposition of value network is mainly to explain the behavior of incumbent enterprises in disruptive innovation. Although some incumbent enterprises have strong R&D capabilities and first manufacture engineering machines with disruptive potential, they did not mass-produce them; while other incumbent enterprises are aware of the threat of latecomers and the potential of disruptive innovation, but they are unable to quickly adjust their R&D strategies and take effective measures. According to Christensen’s (1997) opinions in The Innovator’s Dilemma, the value network is a kind of environment in which enterprises understand consumer demand and product value, allocate resources, participate in market competition, and propose and solve problems. Although the definition of value network is relatively loose, it can be seen that value network is actually a large framework for enterprises to make decisions. The formation of this framework has a lot to do with the development history of enterprises. It was gradually formed and remained relatively stable through the continuous trial and error of enterprises. Incumbent enterprises have become survivors and leaders in the industry and have formed stable relationships with certain types of customers. The demand characteristics of such customers play a subtle role in shaping the enterprise’s value network. Therefore, even if incumbent enterprises first develop engineering machines with disruptive potential, they will be limited by the value network and lack the motivation to allocate resources for mass production; and when the incumbent enterprises realize the huge potential and threat of disruptive innovation, they are also subject to the value network and cannot imitate and followed up in time.

2.1.5 Relativity

Christensen (2006) clarified and enhanced his theory by introducing “relativity”. “Relativity” means disruptive innovations are relatively disruptive rather than absolutely. For instance, to Schwab and Ameritrade’s business models, the online stock brokerage is a sustaining innovation, while it is a disruptive innovation to Merrill Lynch’s. Hence, creatively introducing something new to the original value network could be either sustaining or disruptive. It depends on different reference value networks: if an innovation improves the value factors traditionally valued by a company or industry, it undoubtedly is sustaining innovation; instead, if an innovation adds a brand-new value factor that was never valued before, it is disruptive innovation.

2.1.6 Asymmetric incentives

As incumbent enterprises have invested lots of resources in improving hard drive capacity that results in diminishing marginal returns, they have to sell products at a higher price and focus on high-end customers to support the business model of high R&D investment. On the contrary, for disruptive enterprises, the shortage of resources prevents them from focusing on the improvement of a single value dimension of products. Hence they have to introduce other selling points to attract consumers in order to make up for the insufficiency in a single value dimension. Thus, disruptive enterprises operate at a relatively low cost and gain benefits in the low-end market. However, benefits of the high-end market are also very attractive to disruptive enterprises, thus forming asymmetric incentives. Such asymmetric incentives force incumbent enterprises to stay in the high-end market, while disruptive enterprises can not only grab benefits from the low-end market but also gradually encroach on the high-end market.

2.2 The introduction of duality

The explanatory power of the oversupply theory is not sufficient when considering only one value dimension. In Fig. 2, the 8-inch hard drives (\(L2\)) and the demand line (\(L3\)) intersect at point \(B\); draw the perpendicular line \(L4\) of the vertical axis through B, and denote the intersection point of the \(L4\) and \(L1\) as \(C\). Evidently, point \(B\) marks the disruption’s occurrence. Oddly, point \(C\) is horizontally on the left of \(B\), which means product \(C\) has the same capacity as product \(B\). However, product \(C\) is an outdated product once produced by the incumbent company. The incumbent enterprises are disrupted by latecomers with “outdated products”. It is not inconsistent with the reality. Realistically, incumbents normally do not give up the old products immediately when the newest products are launched but apply the limiting pricing strategy to prevent intruders: reducing the price of old products and simultaneously selling the latest product at a higher price, and thus it shrinks the niche for potential competitors. For instance, Apple may lower the price of iPhone 7 when it begins to sell iPhone 8. In addition, the capacity of the hard drive is an important performance indicator. In the 1980s, the capacity of hard drives was only tens to hundreds of megabytes. With the development of semiconductor technology, the capacity of hard drives has reached the terabyte level, which is more than one million times that of the past. The hard drive industry still has not stopped pursuing capacity. It can be observed in Fig. 3, which exhibits obviously the technological trajectories of hard drives all evolve to the upper right, that is, the pursuit of capacity is the same no matter what sizes of hard drives are. Therefore, “oversupply” is not enough to explain the success of disruptive innovation.

Fig. 3
figure 3

The development of two dimensions of hard drives

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This research attempts to add a new value dimension to the analysis and re-examine the explanatory power of “oversupply”. Keep the vertical axis in Fig. 3 unchanged, and replace the horizontal axis with the “portability” of hard drives to obtain Fig. 4. It can be seen from the case of hard drives that disruptive products have better portability than mainstream products. On the whole, the portability and capacity of hard drives are constantly improving. No matter in the value network of disruptive innovation or sustaining innovation, hard drive capacity is an important performance indicator. The original concept of value network is full of tacit and flexible knowledge, as it is derived from the concept of technological paradigm invented by Dosi (1982), who was actually inspired by Kuhn’s (2012) “paradigm” of science. But Kuhn didn’t even define the renowned concept for the paradoxical reason that paradigm by its nature is not a concept that can be clearly defined (Chalmers 1999). The value dimensions are the specific reflection of the value network in terms of products or technologies. Enterprises follow their own value network to understand market demand and product value, and allocate resources in R&D, production, and sales, which are finally reflected in products of different types and value perceived by consumers. For example, the capacity and portability of hard drives are two different value dimensions. As Christensen and Raynor (2013) mentioned, when you disassemble a product, what you see is not the combination of various components, but the structure of the enterprise. An enterprise effectively forms a certain organizational structure for R&D and production based on value network. Such an abstractive value network can be represented by the value dimension.

Fig. 4
figure 4

The shortcut of disruptive innovation to satisfy consumers

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Initially, the hard drives were specially made for huge and slow mainframe computers. The only pursuit of the mainframe computer users was larger storage capacity and higher speed of the hard drives irrespective of their sizes. However, downsizing the hard drives endows the hard drives with a new value factor—portability, and opened up the market for medium-range computers. The development process of hard drives reflects the improvement of disruptive innovation in two value dimensions. The continuous improvement of capacity reflects the disruptive innovation’s partial inheritance of traditional value dimensions; while the improvement of portability reflects its pursuit of new value dimensions. Christensen and Raynor (2013) and Utterback and Acee (2005) also pointed out that the attribute set of new products or technologies can be regarded as the combination of core attributes and additional (new) attributes. Adner (2002) decomposed the attributes of disruptive innovation into two dimensions to build a computational model and believed that the competition between disruptive innovation and existing technologies is the competition in two different dimensions. When analyzing the innovation of a product, the attributes can be simply summarized into two dimensions, one of which represents the basic attribute and the other represents the new attribute. If the former (capacity) is excluded, disruptive innovation will lose its basis for existence. If the latter (portability) is removed, it will degenerate into ordinary ones and lose the symbolic characteristics of disruptive innovation. This study refers to two processes above as the “inheritance” and “expansion” of the original value network by disruptive innovation, respectively. Inheritance means that disruptive innovation does not abandon the recognition of the original value network; while expansion means that disruptive innovation introduces new value compared with the original value network. The value network of disruptive innovation has duality. The evolution of disruptive innovations can be vividly described by biological evolution: inheritance means that offspring acquire heritable traits from their parents, while expansion means that offspring produce new mutations relative to their parents. This is in line with Dosi’s technological trajectories and paradigms. Dosi (1982) argued that technology should undergo market selection in order to survive and evolve. The same goes for disruptive innovation. For latecomers, it is not easy to find new value dimensions recognized by the market. In many cases, so-called innovations simply become victims of market choices, and only those surviving disruptive innovations can achieve the public’s attention.

The “inheritance” and “expansion” of the original value network make disruptive innovation possess “duality”; thus it has an asymmetric advantage over mainstream products. From the perspective of market demand, the two value dimensions of disruptive innovation correspond to different preferences of consumers. In Fig. 4, \({U}_{1} ,{U}_{2} {U}_{3}\) and \({U}_{4}\) are indifference curves, the utilities represented by the four curves satisfy the inequation\({U}_{1}< {U}_{2}<{U}_{3}<{U}_{4}\). \(\overrightarrow{B\mathrm{^{\prime}}A\mathrm{^{\prime}}}\) is the technological trajectory of the incumbent enterprises. It has a lower portability and only improves hard drives in the storage capacity. Assume that its portability is fixed at 2, around about 15 units need to be gained in capacity to reach \({U}_{4}\) from\({U}_{1}\). Another trajectory is \(\overrightarrow{HG}\), which also vertically improves in capacity but with a higher portability. It is horizontally fixed at 5 (more portable), it merely needs about 6 units’ gain in capacity to penetrate from \({U}_{1}\) to\({U}_{4}\). Due to the diminishing marginal effects of utility and returns, technologies that improve on the single value dimension are inefficient in both satisfying consumer demands and research and development. It can be seen in the figure that hard drive manufacturers have a strong recognition of the capacity, and they rely heavily on the improvement of hard drive capacity, which results in the phenomenon that smaller hard drives successfully encroach on the market of large hard drives appears repeatedly in hard drive industry. That is, disruptive enterprises become new incumbent enterprises, which in turn are disrupted by subsequent disruptors.

From the analysis above, we can see that the development of hard drive technology does not give up the continuous improvement of capacity after the introduction of portability, and consumers are willing to give up a part of hard drive capacity in exchange for more portability, which shows that the oversupply of hard drive capacity is relative to new value dimensions. Without the emergence of new value dimensions, oversupply cannot provide an effective explanation for the success of disruptive innovations. Given that the value dimension is the specific presentation of the value network in products, the value network should play a more fundamental role in the theory of disruptive innovation than oversupply, that is, the prerequisites of oversupply are the change of the value network and the expansion of the value dimension. Moreover, the duality of disruptive innovations provides the basis for their relativity. Since innovation itself is a latecomer in time and has differences in characteristics. Relativity should be a universal attribute of innovation. Innovations are usually discussed without explicitly referring to what they are being compared with. However, when discussing disruptive innovation, it is necessary to clarify its reference objects. Disruptive innovation has the potential to open up new markets and encroach on traditional markets because of the duality. The impacts of disruptive innovation can be accurately analyzed only when the influencing objects are clarified. For example, Kodak is one of the most successful film camera manufacturers in the world, but its challenge comes from digital camera technology; while the threat to digital camera manufacturers comes from the rise of smartphones. Smartphones do not intend to attack digital camera manufacturers, but the market of digital cameras has been severely squeezed by the development of mobile phone cameras. Compared with digital cameras, smartphones have introduced a new value dimension of communication functions. The encroachment of the former on the latter’s market can effectively be analyzed and understood using the duality and relativity of disruptive innovations.

3 The reorganization of disruptive innovation theory

3.1 ISM analysis process

Interpretive structural model (ISM) is a qualitative and quantitative analysis method commonly used in the hierarchical analysis of system structure. ISM is a group learning process where structural models are generated in order to portray complex subjects of a system through a carefully designed pattern using graphics and sentences (Sinaga et al. 2019). It decomposes the complex system into several subsystem elements and constructs a multi-level hierarchical structure model upon data processing techniques and information from experts in order to obtain a consistent matrix using the established procedure (He et al. 2021). ISM can help system analysts clarify the relationship and hierarchy between different system elements (Ali et al. 2020; Jain and Qureshi 2022; Malone 1975; Singh and Kant 2008) and be widely used in modern system engineering analysis. Analysts only need to understand the direct relationship between two factors in the system to begin the analysis process of ISM. The specific process is as follows:

1. Define the factor set. Label factors and define the set \(E=\{{e}_{1},{e}_{2},{e}_{3},...,{e}_{n}\}\) after determining the factors contained in the system. \({e}_{i}\) is the symbolic representation of the corresponding factors in the system.

2. Construct adjacency matrix. The adjacency matrix \(A=\{{a}_{ij}{\}}_{n\times n}\) is used to represent the relation between factors \({e}_{i}\) and \({e}_{j}\) (\({e}_{i}, {e}_{j}\in E\)) in the set:

$$A={\left[\begin{array}{ccccc}{a}_{11}& {a}_{12}& {a}_{13}& \dots & {a}_{1n}\\ {a}_{21}& {a}_{22}& {a}_{23}& \dots & {a}_{24}\\ {a}_{31}& {a}_{32}& {a}_{33}& \dots & {a}_{3n}\\ \vdots & \vdots & \vdots & \ddots & \vdots \\ {a}_{n1}& {a}_{n2}& {a}_{n3}& \dots & {a}_{nn}\end{array}\right]}_{n\times n}$$

where \({a}_{ij}\) satisfies:

$$\begin{array}{l}{a}_{ij}=\left\{\begin{array}{l}1,\quad {e}_{i} \,\text{is related to} \,{e}_{j} \\ 0, \quad { e}_{i} \,\text{is not related to} \,{e}_{j}\end{array}\right.\end{array}$$
(1)

3. Calculate the reachable matrix. The reachable matrix \(M=(A+I{)}^{k}\), \(I\) is identity matrix. \(k\) is a positive integer that satisfies the following conditions:

$$(A+I{)}^{k-1}<(A+I{)}^{k}=(A+I{)}^{k+1}$$
(2)

Equation (2) is Boolean logic operation: \(0+0=0, 0+1=1, 1+0=\mathrm{1,1}+1=1, 0\times 0=0, 0\times 1=0, 1\times 0=0, 1\times 1=1\). The reachable matrix \(M\) not only exhibits the direct relation between factors in the set \(E\), but also shows the indirect relation. For any \({m}_{ij}\) in the matrix, \({m}_{ij}=1\) indicates that factor \({e}_{i}\) can connect \({e}_{j}\) through some edges; and \({m}_{ij}=0\) means that \({e}_{i}\) cannot establish directed connection with \({e}_{j}.\)

4. The hierarchy division. The hierarchy can be divided by the calculated reachable matrix \(M\). The reachable set \(R({e}_{i})\) and antecedent set \(A({e}_{i})\) can be calculated from the reachable matrix \(M\), and the reachable set and antecedent set is verified to see whether Eq. (3) is satisfied. The factors that satisfy for Eq. (3) are the first layer \({\mathcal{L}}_{1}\) factors of the system. After removing the factors of the first layer and continuing the calculation according to Eq. (3), the system is analyzed layer by layer to obtain the structural relationship of the system.

$${\mathcal{L}}_{\mathrm{n}}=\{{e}_{i}|{\mathcal{R}}_{i}={\mathcal{R}}_{i}\cap {\mathcal{A}}_{i}\}$$
(3)

3.2 The factor analysis of disruptive innovation based on ISM model

Disruptive innovation involves complex micro and macro factors, and there exist redundant and competing concepts. Therefore, it is necessary to simplify the theory and capture the nature of disruptive innovation. This study uses the value network to comprehensively represent various internal factors of enterprises. For example, the value network embodies factors, such as managers, resource allocation, R&D strategy, organizational structure and scale. In addition, since the construction of the adjacency matrix of the ISM needs to obtain the direct correlation between various factors, macro-environmental factors (such as policies, regulations and social influence, etc.) are not included in the ISM. Try to avoid “loop” when constructing the model, and thus the connection and structure between various factors can be expressed through a clear directed graph. Seven core factors involved in disruptive innovation theory are introduced in Sect. 2.1, and another important factor of duality is added in Sect. 2.2. To make the structure of the ISM model clearer, these factors need to be properly decomposed. Firstly, “duality” is decomposed into “first value dimension” and “second value dimension”. These two value dimensions reflect the core characteristics that distinguish disruptive innovation from sustaining innovation. Different combinations of these two value dimensions will affect the performance and price of the products. For instance, storage capacity is the most critical value dimension that affects the performance and price of hard drives, and the increase in portability means that the size of hard drives is reduced, and the storage capacity and price will decline accordingly (when the storage density remains unchanged). Christensen argued that incumbent enterprises are oversupplied with hard drive performance driven by the excessive pursuit of storage capacity that exceeds the actual demand of mainstream consumers. Correspondingly, the phenomenon can be termed “undersupply” that disruptive innovations fail to meet mainstream customer demand for storage capacity when they enter the market. The oversupply and undersupply make products have obvious differences in price, thus forming “price advantage” and “price disadvantage”. The model ultimately explains the encroachment of technologies or products into markets, referring to the classification of Schmidt and Druehl (2008), the market is divided into the existing market, low-end market and new market. Thus, thirteen factors are obtained in total, which is denoted as set \(E =\) {first value dimension \({e}_{1}\), second value dimension \({e}_{2}\), relativity \({e}_{3}\), oversupply \({e}_{4}\),undersupply \({e}_{5}\), price disadvantage \({e}_{6}\), price advantage \({e}_{7}\), low-end market \({e}_{8}\), new market \({e}_{9}\), existing market \({e}_{10}\), complementary technology \({e}_{11}\), value network \({e}_{12}\), asymmetric incentives \({e}_{13}\)}. The following adjacency matrix \(A\) can be obtained by sorting out direct relations between each factor:

The reachable matrix \(M\) can be calculated based on Eq. (2) and adjacency matrix \(A\):

The calculation results of system structure analysis are shown in Tables 1, 2, 3, 4, 5, 6, 7 (The numbers indicate subscripts corresponding to factors).

Table 1 Results of the first layer calculation
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Table 2 Results of the second layer calculation
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Table 3 Results of the third layer calculation
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Table 4 Results of the fourth layer calculation
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Table 5 Results of the fifth layer calculation
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Table 6 Results of the sixth layer calculation
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Table 7 Results of the seventh layer calculation
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The system structure can be divided into seven levels, as shown in Table 8. Figure 5 is obtained based on the corresponding factors of \(E\).

Table 8 The results of hierarchy division
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Fig. 5
figure 5

Multi-layer structure diagram

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3.3 The theory framework of disruptive innovation

To clearly show the hierarchical structure and interrelationships of various factors of disruptive innovation theory, all factors can be placed in a three-dimensional space according to ISM layers, as shown in Fig. 6. The thirteen factors are divided into seven layers. The seventh layer is the value network, which is the starting point of the whole theory. The value network embodies enterprises’ values for products or technologies, which forms the internal organization structure, management philosophy, resource allocation method, etc. The value network is the reflection of enterprises' essential characteristics, which map to technologies or products manifest as two value dimensions, i.e., the first value dimension and the second value dimension in the second layer. Given the development of the hard drive industry in the United States, the earliest customers of hard drives were users of mainframe computers, and the customers who own mainframes are usually from universities, research institutes, or large enterprises. These customers are most concerned about computer performance. Hence the storage speed of hard drives has become the value pursued by these customers. This leads to hard drive enterprises tending to invest resources in the value dimension of improving the storage speed, which is the so-called first value dimension. The more enterprises improve the storage speed of hard drives, the more difficult it is to improve the portability, i.e., the second value dimension. From the perspective of technological evolution, an enterprise that is good at sustaining innovation is a highly “differentiated” organization. The organizational structure and the understanding of technologies or products are all in the service of developing hard drives with faster storage speeds. In fact, the competition among hard drive enterprises was quite fierce at that time, which also intensified the resource inclination of incumbent enterprises on the first value dimension.

Fig. 6
figure 6

The relations between theoretical factors of disruptive innovation

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For disruptive enterprises, because they are less competitive relative to incumbent enterprises, the differentiation degree is inferior. They are not caught in the path dependence of value networks like incumbent enterprises. The disadvantage of disruptive enterprises in the first value dimension can only be compensated in other dimensions, such as improving the hard drive portability. Under the technical conditions at that time, the R&D cost required to increase the density of hard drives is very expensive, and the cheapest measure to miniaturize hard drives is to reduce their capacity. The incumbent enterprises own strong technological strength but have not fully understood the value of miniaturized hard drives. Although disruptive enterprises are committed to the development of small hard drives, they have not given up on the pursuit of storage speeds. In the market, when the pair of mutually restrictive value dimensions of storage speed and volume appears, it is faced with a situation of weighing between the two. Thus, the fifth layer of “relativity” appears.

Since the birth of hard drives, the capacity has increased tens of thousands of times. As software complexity increases, the demand for hard drive performance enhances. Purely from the perspective of hard drive capacity or storage speed, there is no existence of technological “oversupply”. In Christensen’s case, the so-called enterprises’ oversupply of hard drive capacity is relative. For example, miniaturized electronic products could not be equipped with huge hard drives in emerging markets of ATMs, cash registers, and vehicle computers due to the limitation of physical space. In these scenarios, the miniaturization of hard drives is more advantageous than the larger capacity and higher storage speed. But in view of mainframe users, these miniaturized hard drives are not attractive. Therefore, relative to different markets, the relative advantages of sustaining innovation and disruptive innovation are different. Therefore, oversupply or undersupply are both based on the relativity of the value dimension.

The oversupply and undersupply mentioned here refer to the first value dimension. The first value dimension is the core value dimension in which incumbent companies compete, occupying large amounts of resources in R&D, production, and sales. The reduction in the first value dimension of disruptive innovation gives it an advantage in price; therefore, the price of sustaining innovation is a relative disadvantage. Given resource input and product price, sustaining innovation with technological oversupply and price disadvantage can only further focus on existing customers and move toward the high-end market (Christensen and Raynor 2013; Christensen 2006). Conversely, disruptive innovation with technological undersupply but low prices have the potential to attract customers in the lower-end market. In the case of the hard drive industry, electronic products are in the “democratized” stage. Therefore, the low price of disruptive innovation has also won it the emerging market of electronic products. This is exactly the phenomenon reflected by asymmetric incentives in the second layer. It is worth noting that latecomer enterprises do not fully understand the potential target market when developing small hard drives; small hard drives are required by the market benefits from the further development of integrated circuit technology (Christensen and Raynor 2013; Dan and Chieh 2008). Thus, the development of complementary technologies creates conditions for the formation of new markets.

Above all, the value network in the seventh layer in Fig. 6 reflects the disposition of enterprises, while two value dimensions in the sixth layer are its reflection at the technology or product level. Enterprises need to consider resource allocation in these two value dimensions, while consumers in the market need to make trade-offs based on their heterogeneous preferences. Then relativity derives, which exhibits asymmetric advantages and disadvantages in terms of price, performance, and incentives, making sustaining innovation and disruptive innovation diffuse in various markets. Figure 6 can be simplified to get Fig. 7. The value network is located at the enterprise level, which is equivalent to the enterprise’s “genotype”, and the value dimension structure of the technology provided by the enterprise is the "phenotype", which determines the specific status of disruptive innovation and sustaining innovation in terms of price, technological performance, etc., and affects the share distribution of enterprises in different sub-markets, showing different market encroachment phenomenon. Therefore, the dual value dimension of disruptive innovation gives it the potential to encroach on different sub-markets at the same time. From a logical perspective, if the second value dimension is deleted, innovation has only a single value dimension and can only meet the demand of the existing market. This is the motivation for incumbent enterprises to pursue sustaining innovation. On the contrary, if the first value dimension of disruptive innovation is deleted and only the second value dimension is retained, it will have nothing to do with existing products and lose the meaning of discussing relativity. Innovation itself is a relative concept (Guttentag and Smith 2017; Nagy et al. 2016). Therefore, having two value dimensions (duality) is a necessary condition for the existence of disruptive innovation, and it is also the key to explaining the disruptive innovation phenomenon. Hsu and Cohen (2021) also demonstrated the dual role of disruptive market encroachment.

Fig. 7
figure 7

The key factors and relations of disruptive innovation theory

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4 Conclusions

The disruptive innovation theory has widely spread in academia and industry since Christensen proposed disruptive innovation two decades ago. Although the theory depth has been greatly developed through the efforts of researchers, the problems of concept redundancy and conflicts in the theory have not been completely resolved. To obtain a streamlined and systematic theory, this study first analyzes the market phenomenon induced by disruptive innovation. The market phenomenon is the explicit manifestation of disruptive innovation that Christensen first observed, and it is also the target that theory ultimately needs to explain or predict. In fact, there are many factors that affect disruptive innovation, but external factors need to affect the development of things through internal factors. Therefore, the explanation of the phenomenon needs to return to the basic characteristics of the disruptive innovation itself, and establish a causal relation between characteristics and the market phenomenon. On the basis of the value network, relativity, oversupply, asymmetric incentives, price advantage and other factors in the original disruptive innovation theory, this study adopts the ISM in system engineering to construct the relationship and hierarchy between disruptive innovation factors.

The analysis shows that theoretical factors of disruptive innovation can be organized into seven layers. The value network in the seventh layer is the entrance of the system, which exhibits that the essence of disruptive innovation is rooted in the value network of the enterprises. The latecomers have introduced a new value dimension while recognizing the value dimension pursued by the mainstream market. In the context of disruptive innovation, the enterprise value network manifests itself as two value dimensions. These two value dimensions reflect the different perceptions of innovation value between disruptive enterprises and incumbent enterprises, which lead to differences in resource allocation, market positioning, and technology supply between the two types of enterprises. The value network and duality form the fundamental level of the theoretical framework. The middle-level factors such as relativity, oversupply, undersupply, price advantage, price disadvantage, and asymmetric incentives are derived from the fundamental level. Furthermore, the external factor of complementary technologies is located at the highest layer of the mesosphere, next to the market level. The market level refers to the potential market phenomenon caused by disruptive innovation, i.e., impacting the existing market, encroaching into the low-end market and opening up the new market. It can be found from the streamlined theory framework disruptive innovation initiated by latecomer enterprises and the sustaining innovation led by incumbent enterprises are the results of enterprises carrying out R&D in different value dimensions. Sustaining innovation focuses on the original value network, which explains the advantages of incumbent enterprises in maintaining existing markets and the disadvantages in opening new markets. Disruptive innovation introduces a new value dimension and expands the original value network to a higher dimension, thus avoiding the direct competition with incumbent enterprises in the initial and growth stages, and giving it the potential to open up new markets. Innovations that simply occupy the low-end market cannot be regarded as disruptive innovations. Disruptive innovation originating in the low-end market is an expedient measure for latecomers with limited resources. Its essence lies in having two value dimensions (duality), i.e., the traditional one and the new one, which endows disruptive innovation with the potential to encroach on existing markets and open up new markets at the same time. Consistent with Schumpeter’s definition of innovation as “executing a new combination of production factors”, the analysis of this study shows that the nature of disruptive innovation is the implementation of a new combination of value dimensions, and does not involve the presupposition of market outcomes triggered by disruptive innovation. Thus, the theoretical flaw of post-hoc identification is avoided.