August 2025

Journal of Management Sciences Aug. 2025
Metrics of Supply Chain Resilience: Structural Change-Points (SCP) and Weighted Cumulative Loss (WCL)

Mengfei LI¹) Xiaole WU¹) Yang CHEN²) Jinyan ZHU³)
¹)(School of Management, Fudan University, Shanghai, China 200433)
²)(School of Computer Science, Fudan University, Shanghai, China 200433)
³)(Information Networking Institute, Carnegie Mellon University, Pittsburgh, USA 15213)

Abstract
Against the backdrop of an evolving global political and economic landscape, supply chain resilience has emerged as a critical research topic for both industry and academia. Addressing the limitations of existing resilience measurement methods and responding to the need for unified, dynamic, non-probabilistic indicators that encompass multiple dimensions of resilience, this paper proposes two nonparametric metrics for supply chain resilience assessment: Structural Change-Points (SCP) and Weighted Cumulative Loss (WCL). SCP leverages change-point detection techniques to identify structural changes in supply chains triggered by external shocks, while WCL employs dynamic weighting functions to quantify performance losses resulting from such disruptions. Together, these metrics comprehensively characterize supply chain performance across the full "absorption-adaptation-recovery" cycle, effectively addressing the shortcomings of existing single-dimensional or static approaches. The empirical analysis uses the 2018 U.S.-China trade war as an external shock case study, combining Chinese customs and maritime shipping data to analyze resilience variations across different product supply chains and examine how factors such as network structural diversity and customer concentration affect resilience. The results demonstrate that diversified supply chain networks and dispersed customer bases significantly enhance supply chain resilience. The metric framework constructed in this paper offers strong applicability and generalizability, providing theoretical support and practical tools for enterprises to improve supply chain management capabilities and strengthen risk mitigation.

Keywords
Supply Chain; Resilience; Non-parametric Estimation; U.S.-China Trade War; Network Structure

DOI: 0
Chinese Library Classification: C93

Introduction

The rapid changes in the international political and economic environment pose severe challenges to supply chain security, making supply chain resilience a shared focus of attention for both industry and academia. However, empirical measurement methods for supply chain resilience remain limited, and how to reasonably define and measure supply chain resilience from both theoretical and empirical perspectives remains a research challenge. The cutting-edge review by Hong et al. [1] points out that supply chain resilience research still requires: (1) non-probabilistic dynamic indicators, and (2) unified indicators that encompass multiple resilience characteristics such as adaptive and restorative capabilities.

The term "resilience" originally derives from physics, representing a material's ability to absorb energy during plastic deformation and fracture. Christopher and Peck [2] first introduced this concept to the supply chain domain, defining Supply Chain Resilience (SCR) as the ability of a supply chain to recover to its original or a better state after disruption. Although fields such as economics, ecology, and environmental science have proposed distinctive resilience measurement methods [3], differences in disciplinary backgrounds and theoretical assumptions make these approaches difficult to directly transfer to the supply chain context.

In supply chain scenarios, external shocks typically generate cascading effects on overall output. Production fluctuations from upstream suppliers may force downstream firms to adopt proactive strategic responses, such as finding alternative suppliers, increasing inventory levels, optimizing procurement strategies, deepening supply chain collaboration, or adjusting technical materials. These micro-level measures precisely embody the concrete manifestations of supply chain resilience in real-world environments. Generally, highly resilient supply chains demonstrate strong absorption, adaptation, and recovery capabilities in the short to medium term: specifically, they resist shocks in the short term, delaying negative impacts on supply chain performance (absorption capability); reduce the rate of performance decline and maintain basic production capacity at the post-shock minimum performance level (adaptation capability); and recover quickly and effectively to the initial state (recovery capability). Figure 1 [FIGURE:1] illustrates the typical three-stage response process of a supply chain after a shock, where the three dimensions of absorption, adaptation, and recovery play roles at different stages.

Defining and measuring supply chain resilience in empirical research faces several challenges. Theoretical models of resilience are often complex, incorporating numerous dynamic elements that are difficult to directly observe from actual data. However, real-world supply chain data typically feature low frequency, limited availability, and insufficient observable dimensions, creating a significant gap between practical indicators and theoretical constructs. For example, Massari et al. [4] characterize supply chain resilience through agent-based models and evolutionary systems, while other studies simulate interactions among supply chain nodes through system dynamics or multi-layer network models, but such complex methods are difficult to apply directly in data-limited scenarios. Most empirical studies have had to simplify resilience definitions; for instance, Khanna et al. [5] measure resilience using supplier disruption ratios or single inventory levels, failing to comprehensively capture supply chain absorption, adaptation, and recovery capabilities, which may lead to partial and incomplete resilience assessments.

Furthermore, discrepancies between simplified resilience indicators and theoretical definitions may introduce uncertainty and bias into research conclusions. For example, organizational complexity may enhance a firm's shock absorption capacity but simultaneously constrain its ability to adjust quickly; single-dimensional resilience indicators cannot fully capture such dual effects. Therefore, comprehensively measuring the absorption, adaptation, and recovery capabilities of supply chain resilience is particularly crucial for the accuracy of causal analysis.

This paper aims to propose a systematic, comprehensive, and operationally practical method for measuring supply chain resilience, specifically designing two nonparametric statistical indicators: Structural Change-Points (SCP) and Weighted Cumulative Loss (WCL). SCP leverages change-point analysis techniques to identify structural changes in supply chains caused by external shocks in real time, while WCL employs a weighting function to conduct dynamic estimation and retrospective analysis of losses caused by shocks. Both indicators are based on time series data of key supply chain performance metrics (such as export volume or production volume) and effectively characterize supply chain performance during external shocks through continuous monitoring of dynamic changes across supply chain links.

In terms of empirical research, this paper selects the 2018 U.S.-China trade war as a case of external shock, combines customs and maritime shipping data between China and the U.S., measures and analyzes the resilience performance of various Chinese product supply chains exporting to the U.S., and subsequently identifies how product characteristics and supply chain network structures influence resilience. The empirical results confirm that diversified network structures and dispersed customer bases significantly enhance supply chain resilience.

The remainder of this paper is organized as follows: Section 2 reviews and clarifies the definitional framework of supply chain resilience; Section 3 elaborates on the construction and calculation methods of the SCP and WCL indicators; Section 4 conducts empirical analysis of the indicators using the U.S.-China trade war case and discusses the impact of supply chain network structures.

2 Resilience Definition: Literature Review and Theoretical Development

This section systematically reviews relevant research in the field of supply chain resilience to construct a clear, comprehensive, and empirically applicable definitional framework. Additionally, Section 3.4 organizes existing supply chain resilience indicators and compares their advantages and disadvantages with the metrics proposed in this paper. By tracing the evolution of the supply chain resilience concept, this section emphasizes three core dimensions of supply chain resilience: absorption capability, adaptation capability, and recovery capability. Absorption capability emphasizes the supply chain's ability to resist shocks in the short term, adaptation capability reflects the supply chain's ability to flexibly adjust during shocks, and recovery capability refers to the efficiency with which the supply chain returns to normal after a shock. This theoretical framework not only provides a solid foundation for empirical resilience measurement but also charts a clear path for the construction of subsequent indicators in this paper.

Figure 2 [FIGURE:2] intuitively demonstrates three typical performance patterns of supply chain resilience in practical contexts. With supply chain performance on the vertical axis and time on the horizontal axis, Curve A experiences a gradual decline and recovery after a shock, exhibiting the complete resilience cycle; Curve B declines simultaneously with Curve A but with a smaller magnitude, indicating stronger absorption and adaptation capabilities and better overall resilience performance; Curve C declines more rapidly with a magnitude similar to Curve A, reflecting insufficient absorption and adaptation capabilities and difficulty in securing effective time for responding to shocks. The longer the performance maintenance period after a shock, the smaller the decline magnitude, and the faster the recovery speed, the stronger the resilience.

Resilience as a multidimensional concept has been widely examined across multiple disciplines including psychology [6,7], ecology [8], and economics [9,10]. In the supply chain domain, Christopher et al. [11] proposed a classic definition focusing on recovery capability after disruption but without deeply discussing the adaptation process during disruption. Ivanov et al. [12] further emphasized the dynamic nature of resilience, arguing that supply chain resilience should also encompass the ability to maintain, adjust, and restore execution plans. Ponomarov et al. [2] defined supply chain resilience as a dynamic response process of resisting unexpected events and recovering quickly. Building on this, Hosseini et al. [13] clarified the two stages of disruption and recovery after shocks. Based on the above theoretical review, this paper divides supply chain resilience into three core dimensions—absorption, adaptation, and recovery—and analyzes their connotations in conjunction with modern supply chain development trends and corporate strategy adjustments.

Absorption capability is the supply chain's ability to resist shocks through proactive preparation, redundancy, and design strategies before risks materialize. For example, according to a survey by Nikkei, inventories of 4,353 major global industrial enterprises reached $2.1237 trillion by the end of September 2023, 30% higher than before the COVID-19 pandemic, with the purpose of better resisting supply chain disruption shocks and maintaining production continuity in the short term. Absorption capability enables supply chains to contain the negative impacts of shocks in the short term and maintain normal system functions. Absorption capability is typically defined as a system's ability to absorb shocks and minimize their impact when facing threats or disturbances [14]. Specifically, it refers to the system's capacity to maintain certain functions and service levels without complete collapse when encountering unexpected events or disruptions (such as natural disasters, cyberattacks, terrorist attacks, etc.). In practice, absorption capability may be reflected through redundant design, allowing other links to continue operating even when certain parts of the supply chain are affected, thereby maintaining overall system functionality [15]. For instance, diversified sourcing strategies can avoid dependence on single suppliers and reduce supply interruption risks; safety stock can serve as a buffer during supply chain disruptions to ensure continuous production. Additionally, refined supplier management can enhance absorption capability—by classifying suppliers and adopting different response measures based on their importance and risk levels, firms can significantly strengthen supply chain absorption capacity [16].

Adaptation capability is the supply chain's ability to adjust operations and structures after unexpected events occur to mitigate shock impacts, enabling disruption to proceed as slowly as possible and preventing complete rupture under worst-case scenarios. For example, when the pandemic caused supply chain disruptions, automotive manufacturers such as Honda reduced shock impacts by adjusting production plans, activating backup suppliers, and modifying product designs to accommodate available components, resulting in smaller production declines and avoiding complete production stoppages. When supply chains cannot rely on existing redundancy, avoiding rapid decline or total interruption becomes crucial. Adaptation capability is reflected in the operational and structural flexibility of the supply chain, enabling rapid and effective responses to sudden supply and demand changes [17]. Flexibility is the core of adaptation capability, allowing supply chains to quickly adjust network structures and operational strategies to meet changing customer demands [18]. Christopher et al. [19] consider flexibility an important component of supply chain resilience. For example, flexible production capacity and agile logistics networks can help firms effectively cope with market demand fluctuations and unexpected events.

Recovery capability is the supply chain's ability to return to its original state after a shock, potentially including the potential to improve operational efficiency through innovation and optimization during the recovery process. This process typically requires targeted adjustments to achieve operational optimization and risk response [20]. Whether a supply chain can recover to its pre-shock state is a key criterion for measuring its resilience [21–23]. Recovery capability focuses not only on whether the supply chain can return to its original state but also on its recovery speed and whether it can achieve higher operational levels through innovation and optimization during recovery. For example, after natural disasters or market upheavals, firms can quickly resume production and further enhance operational efficiency by reevaluating supply chain networks, optimizing logistics routes, and adjusting supplier selections.

In summary, this research defines supply chain resilience as a dynamic process in which a supply chain experiences performance damage and gradual recovery after encountering a shock, encompassing three dimensions: absorption, adaptation, and recovery. The stronger the supply chain resilience, the longer the duration of shock absorption, the more timely and effective the adaptation adjustments, and the faster the recovery speed. Current empirical research lacks unified, dynamic, non-probabilistic indicators that encompass multiple resilience characteristics [1], with resilience measurement often limited to single-dimensional or overly simplified metrics, such as focusing solely on supplier disruption probability or the proportion of supplier disruptions [5,13], making it difficult to comprehensively capture the multidimensional features of supply chain resilience. Therefore, constructing empirical indicators that simultaneously cover the three dimensions of absorption, adaptation, and recovery is crucial. The next section will propose two nonparametric resilience indicators suitable for empirical contexts based on the above resilience definition and compare them with existing supply chain resilience indicators from the literature in Section 3.4.

3 Resilience Metrics: SCP and WCL

This section proposes two nonparametric, non-probabilistic, unified dynamic indicators that encompass multiple dimensions of resilience—Structural Change-Points (SCP) and Weighted Cumulative Loss (WCL)—to comprehensively evaluate supply chain resilience. Traditional parametric statistical methods typically require strict assumptions about data distributions, making it difficult to effectively handle the complex dynamic characteristics of supply chain data. In contrast, nonparametric methods, by weakening distributional assumptions, demonstrate greater flexibility and universality, making them suitable for analyzing the complex and dynamic supply chain environment. These two indicators are constructed based on the following principle: when a supply chain faces external shocks, the longer the resistance phase lasts (strong absorption capability), the slower the performance decline (high adaptation capability), and the faster the recovery (good recovery capability), the stronger the resilience.

Specifically, the SCP indicator is based on structural change-point theory, which has rapidly developed in statistics in recent years, and is used to precisely identify the specific time points at which significant structural changes occur in supply chains after external shocks. WCL introduces a weighting function to dynamically weight performance losses before and after shocks, thereby nonparametrically quantifying the overall loss magnitude of the supply chain. For example, in the context of the 2018 U.S.-China trade war shock, SCP can effectively capture the time points at which tariff changes cause significant shifts in supply chain output, revealing potential delays and disruptions; WCL can quantitatively reflect the overall supply chain performance loss magnitude, providing precise evidence for corporate strategic adjustments. Both indicators are based on time series data of supply chain performance, offering effective tools for comprehensive supply chain resilience assessment.

3.1 Data Structure

To clarify indicator definitions and calculation methods, this study first specifies the data structure and notation definitions. The adopted data model exhibits high flexibility, ensuring the indicators are applicable to various supply chain scenarios.

In this study, supply chain performance is represented in the form of time series data (such as trade share, export volume, production volume, etc.), with data sources typically including government statistical departments, customs databases, and internal corporate reports. Such data can effectively reflect the supply chain impacts of policy changes, market fluctuations, and natural disasters. Let the time series data be denoted as $P_t$, representing system performance at time point $t$, where the time span is $t = 1, 2, 3, ..., T$, and the external shock occurrence time point is marked as $T_S$.

3.2 Structural Change-Points SCP

This section first introduces the structural change-point identification algorithm in Section 3.2.1, which uses a data-driven nonparametric method to precisely locate the time point $T_{cp}$ at which structural changes occur in the supply chain. Section 3.2.2 then defines the SCP indicator (Structural Change-Points, $SCP$) in detail based on this algorithm.

3.2.1 Structural Change-Point Identification Algorithm

The core of the change-point identification algorithm lies in nonparametrically determining whether and when a significant structural change has occurred in the system. This paper adopts the change-point detection method proposed by Ross et al. [24], whose advantage lies in requiring no strict assumptions about data distribution while possessing strong detection accuracy and robustness. This method compares data segments before and after each time point, determining the significance of structural changes and locating the change point $T_{cp}$ by comparing the statistic $D_t$ with a threshold $h_t$. The specific hypothesis testing forms are shown in equations (1)-(5), enhancing the generality and flexibility of change-point detection through nonparametric methods.

The null hypothesis $H_0$ is: no structural change has occurred in the time series generation process; the alternative hypothesis $H_1$: a structural shift begins at time point $T_{cp}$. The mathematical forms of the two hypotheses are as follows:
$$H_0: X_i \sim F_0(x; \theta_0), \quad i = 1, \cdots, T$$
$$H_1: X_i \sim \begin{cases} F_0(x; \theta_0) & i = 1, 2, \cdots, T_{cp} \ F_1(x; \theta_1) & i = T_{cp} + 1, T_{cp} + 2, \cdots, n \end{cases}$$
where $F(x; \theta)$ represents the distribution satisfied by the data generation mechanism of $X_i$, and $\theta$ is the potentially unknown parameter of the distribution. Under the null hypothesis $H_0$, the data generation mechanism always follows distribution $F_0$ with parameter $\theta_0$; under the alternative hypothesis $H_1$, the data generation mechanism after change point $T_{cp}$ follows distribution $F_1$ with parameter $\theta_1$.

In traditional methods, if we further assume that the distributions before and after the change point are both normal, we could use a $t$-test to detect mean changes or an $F$-test to detect standard deviation changes. To avoid excessive distributional assumptions, this paper uses the following nonparametric method for change-point hypothesis testing.

Time series data arrive sequentially; at time point $n$, historical data for times $1, 2, \cdots, n$ can be observed. The statistic $D_n$ represents the likelihood of a change point existing in the data observed up to time point $n$; the statistic $D_{k,n}$ represents the likelihood that time point $k \in (1, 2, \cdots, n)$ is a change point in the historical data observed up to time point $n$. Assuming a time series has only one change point, $D_n$ is defined as the maximum value of $D_{k,n}$:
$$D_n = \max_{k=2,...,n-1} D_{k,n}$$
The subsequent text will introduce how to use a cyclic segmentation method to handle time series with multiple change points.

To determine whether a change point exists in the time series, a threshold $h_n$ is needed, and $D_n$ is compared with this threshold. When $D_n$ exceeds the threshold, the time series is considered to contain a change point. The selection of threshold $h_n$ must satisfy the following requirements:
$$P(D_1 > h_1) = \alpha, \quad P(D_n > h_n | D_{n-1} \leq h_{n-1}, \cdots, D_1 \leq h_1) = \alpha$$
where $P(D_1 > h_1)$ is the probability of judging time point 1 as a change point based on the threshold; $P(D_n > h_n | D_{n-1} \leq h_{n-1}, \cdots, D_1 \leq h_1)$ is the probability that time point $n$ is a change point given that no change points exist before time point $n$. When the true situation conforms to the null hypothesis (no change point), the probability that the statistical test result rejects the null hypothesis and accepts the alternative hypothesis (change point exists) is controlled as $\alpha$, meaning the probability of Type I error is controlled as $\alpha$. This paper selects $\alpha$ as 0.05 in the empirical research.

The expression for $D_{k,n}$ and the determination of $h_n$ depend on assumptions about the data distribution. This paper adopts the statistic proposed by Hawkins et al. [25]:
$$D_{k,n} = \sqrt{\frac{k(n-k)}{n}} \frac{\bar{X}{k,n} - \bar{X}^{k,n}}{\hat{\sigma}$$}
where $D_{k,n}$ measures the likelihood that point $k$ is a change point in the data observed for times $1,...,n$; $\bar{X}_{k,n}$ is the mean of times $1,...,k$; $\bar{X}^$ is the estimated variance of the time series, used in the denominator to standardize the volatility level. The above formula compares whether there are significant differences between the two segments from a mean perspective by dividing the time series into before and after segments.}$ is the mean of times $k+1,...,n$; the numerator represents the difference between the two, measuring the degree of difference between the two segments; $\hat{\sigma}_{k,n

Based on equations 2, 3, and 4, the threshold $h_n$ satisfies the following formula:
$$h_n = \begin{cases} \text{[formula missing]} & \text{if } n \text{ is even} \ \text{[formula missing]} & \text{if } n \text{ is odd} \end{cases}$$

In empirical applications, the threshold $h_n$ is first selected based on data through equation 5, then the statistic $D_n$ is calculated through equations 4 and 2. If the statistic exceeds the threshold, the null hypothesis of "no change point" is rejected, and we can be confident that a change point exists in the data, with the change point time being the time when $D_{k,n}$ reaches its maximum value.

To detect a series of change points in a time series, this paper uses the above algorithm for cyclic segmentation. First, the first change point is detected through the above hypothesis testing process, then the time series is divided into two segments at the first change point time. Each segment is then treated as a new time series, and the above process is repeated in each segment until no new change points emerge.

This algorithm can effectively detect structural changes in time series and identify change point locations. When applying the algorithm, hypothesis testing can be performed for each time point to identify whether significant structural changes exist. A time series may exhibit a series of change points, with the change point identification results recorded as vector $\vec{T}{cp}$, where $T^i$ represents the $i$-th change point.

3.2.2 Structural Change-Point Indicators

where $T_{cp}^i$ represents the $i$-th change point. Based on the above change-point algorithm, this paper defines the Structural Change-Point indicator $SCP$ to comprehensively measure supply chain resilience. First, the first change point in a single supply chain, $\Delta SCP$, measures the duration that the supply chain can maintain its original structure after a shock, directly reflecting the strength of absorption and adaptation capabilities (Equation 6). Second, considering that supply chains may experience multiple structural changes, the indicator $#SCP$ is defined to measure the frequency of structural changes within a given time window. Finally, for industries or categories with multiple supply chains, the standardized indicator $SCP\%$ is defined to measure the proportion of supply chains that undergo structural changes (Equation 8). These three indicators expand progressively, providing different levels of resilience analysis perspectives and effectively supporting intra-industry and cross-industry supply chain resilience comparisons and evaluations.

Based on the first change point of a single supply chain, $\Delta SCP$ is used to measure the time that the supply chain can maintain its structure unchanged after a shock event:
$$\Delta SCP = T_{cp}^1 - T_S$$
where $T_{cp}^1$ represents the first significant structural change point identified through the change-point algorithm, at which system performance undergoes its first significant structural shift, and $T_S$ is the external shock occurrence time. $\Delta SCP$ measures the time length from shock occurrence to structural transformation, reflecting the supply chain's absorption and adaptation capabilities. The stronger the absorption capability, the longer the system maintains its original state; the stronger the adaptation capability, the longer the time required for significant transformation. Figure 3 is a schematic diagram of a supply chain performance time series with a single change point: before and after the shock, the system has two relatively stable states (a high pre-shock state and a low post-shock state). The transition between these two stable states is the "structural change," and the time point at which this structural change occurs is the "structural change point."

Supply chains may have multiple structural changes after a shock. To further incorporate this characteristic, $#SCP$ is used to measure the number of structural changes in a supply chain within a period after the external shock:
$$#SCP = |{i | T_{cp}^i \subset U(T_S, \delta)}|$$
where $T_{cp}^i$ represents the time point of the $i$-th structural change point, $U(T_S, \delta)$ is the time window within $\delta$ time after the shock occurrence, and $|\cdot|$ counts the number of elements. This indicator can measure the frequency of structural changes within a specified time range for a supply chain.

For industries with multiple supply chains, $SCP\%$ is used to characterize the proportion of products that undergo structural changes. Assuming an industry has $N$ supply chains, we calculate the proportion of supply chains that experience structural changes within each time window $\delta$:
$$SCP\% = \frac{\sum_{j=1}^{N} \mathbb{I}(#SCP_{j,\delta} > 0)}{N}$$
where $\mathbb{I}(\cdot)$ is the indicator function, $#SCP_{j,\delta}$ is the $#SCP$ calculated for the $j$-th supply chain with $\delta$ as the time window according to Equation 7; the numerator sums the number of supply chains among the industry's $N$ supply chains that generate structural change points within the time window; dividing by the denominator $N$, the total number of supply chains in the industry, yields the proportion of products undergoing structural changes. In the empirical research of this paper (as shown in Figure 7 [FIGURE:7]), $\delta$ is selected as one month, i.e., calculating the proportion of product supply chains that experience structural change points in each month for a specific industry.

These three indicators progress layer by layer. $SCP\%$ can be used to measure industrial resilience and understand overall industry trends by measuring the proportion of changed supply chains within a time window, which has important practical value for comparing industrial chains. An industrial chain (such as the electronics and electrical appliances industrial chain) often contains supply chains for multiple products, resulting in multiple $\Delta SCP$ and $#SCP$ values that are difficult to compare; however, $SCP\%$ can integrate change points across multiple supply chains in an industrial chain, providing a standardized indicator to support cross-industrial chain comparisons. The frequency and density of change points determined by $SCP\%$ can provide valuable insights into overall industry trends and structural adjustments.

The SCP indicator can be used for both horizontal comparison of historical shock events and vertical analysis of resilience differences among supply chains under specific shocks, possessing strong theoretical and practical value. For example, Figure 6 [FIGURE:6] in the empirical section of this paper focuses on the two major shock events of the pandemic and trade war, comparing their impact magnitudes on Chinese supply networks exporting to the U.S.; simultaneously, Figure 9 [FIGURE:9] compares the response degrees of capital goods, intermediate goods, and consumer goods under trade war tariff shocks. Particularly in external shock environments, the SCP indicator enables real-time monitoring of supply chains, rapidly identifying structural changes, thereby helping firms dynamically adjust supply chain strategies and resource allocations to enhance resilience levels in risk response.

3.3 Weighted Cumulative Loss WCL

The Weighted Cumulative Loss (WCL) indicator assesses the overall loss level of a supply chain after negative events through nonparametric methods. Negative shocks typically manifest as distinct performance decline intervals in supply chain performance time series. WCL quantifies the magnitude of performance loss caused by shocks through dynamic weighted analysis of this "settlement interval." Specifically, the area under the supply chain performance curve after a shock reflects loss from negative impacts, while the residual area obtained after adjusting calculation weights through the weighting function embodies the capability retention of the supply chain post-shock.

The construction of WCL particularly emphasizes the importance of temporal factors. When supply chain links face external shocks, reaction speed and adaptation capability directly determine the extent of shock diffusion and overall loss. For example, supply chain nodes with poor resilience may collapse rapidly after negative shocks and propagate negative impacts downstream, while nodes with higher resilience can effectively delay and reduce negative impacts on the overall system. Therefore, a weighting function kernel() is introduced to dynamically adjust weights at different time points, assigning higher weights to losses in the early stages of shock while gradually reducing weights for impacts in subsequent stages.

The WCL calculation formula is defined as follows:
$$WCL = 1 - \frac{\sum_{i=0}^{a} \text{kernel}1(p})}{\sum_{j=1}^{b} \text{kernel2(p$$})

where $T_S$ represents the external shock occurrence time, $p_{T_S+i}$ represents supply chain performance at the $i$-th time point after the shock; the numerator represents the weighted sum of post-shock supply chain performance, while the denominator serves as the weighted benchmark for the pre-shock stable state; parameters $a$ and $b$ represent the analysis time windows after and before the shock, respectively. To ensure model effectiveness, we assume the supply chain is in a stable state without trends before the shock, and selected performance indicators $p_t$ (such as market share) should be trend-free. If the data contains trends, trend-predicted values should replace actual data $p_{T_S-j}$ in the denominator.

The weighting function kernel() satisfies the condition that total weights sum to 1, so the WCL value range is [0, 1]. Drawing on the concept of depreciation functions in economics, the post-shock weighting function kernel1 is typically set as linearly decreasing to reflect the importance of early-stage losses while reducing sensitivity to analysis window length. Time windows $a$ and $b$ should preferably be consistent, but in practice, $a$ may be shorter due to data limitations, while $b$ should cover complete economic or seasonal cycles. Continuous linearly decreasing weighting functions are commonly used weighting function types in statistics, and Figure 4 [FIGURE:4] intuitively illustrates WCL.

In this paper's empirical analysis, we set $b = 12$ months to cover seasonal fluctuations within a year, using equal-weight averaging to estimate the pre-shock stable state; we set $a = 11$ (i.e., 12 months, with $i$ starting from 0) as the post-shock analysis window, using a linearly decreasing weighting pattern. Simultaneously, the X-13 algorithm is adopted to seasonally adjust the time series to eliminate interference from cyclical fluctuations. The adjusted WCL calculation formula is specifically:
$$WCL = 1 - \frac{\sum_{i=0}^{11} \frac{c-i}{c} p_{T_S+i}}{\sum_{j=1}^{12} p_{T_S-j}}$$
where the numerator uses linearly decreasing weights to calculate post-shock performance, and the denominator is the simple average of pre-shock supply chain performance.

WCL is widely applicable in empirical research related to supply chain resilience, capable of deeply revealing how firm characteristics and supply chain structures affect resilience performance and providing scientific evidence for corporate resilience management strategies.

3.4 Comparison with Supply Chain Resilience Indicators in the Literature

Based on the cutting-edge review by Hong et al. [1], this section discusses the advantages of SCP and WCL relative to common resilience indicators in existing supply chain resilience research—including network connectivity, recovery curves (such as Time to Recover TTR, performance decline magnitude), Time to Survive TTS, and profit loss models based on system evolution. These indicators provide a foundational framework for quantitative resilience assessment but still have limitations in practical applications.

This paper proposes nonparametric, non-probabilistic, unified dynamic indicators that encompass multiple resilience characteristics, advancing existing supply chain resilience indicators in the literature.

Traditional network connectivity indicators, such as Largest Connected Component (LCC) [26] or shortest path analysis, primarily focus on structural integrity after node/edge attacks. However, these methods only reflect structural properties, ignore the functional roles of nodes, and their static analysis neglects disturbance evolution processes, failing to capture the temporal dimension of resilience. The indicator system proposed in this paper, particularly the Structural Change-Point (SCP) indicator, based on nonparametric statistical methods, directly reflects the dynamic evolution of supply chain structural states through real-time monitoring of key performance changes and change-point identification. This introduction of a dynamic perspective enables SCP to accurately locate the time points of structural changes caused by disturbances, thereby compensating for the inability of traditional static network connectivity indicators to describe node functional heterogeneity and time-varying characteristics.

Recovery curve-related indicators, such as Time to Recover (TTR) and performance decline magnitude, have been widely used in quantitative supply chain resilience analysis [27]. Recovery curve indicators focus on supply chain system performance after disturbances, such as recovery speed and performance loss magnitude. Although these indicators can effectively reflect system recovery phase characteristics, their limitation lies in insufficient attention to the disturbance absorption and adaptation phases, evaluating supply chain performance changes only holistically or at certain local stages, lacking real-time monitoring and sensitivity to continuous supply chain state changes. In contrast, the WCL (Weighted Cumulative Loss) indicator, through its dynamic weighting function design, not only encompasses performance loss magnitude but also emphasizes the dynamic change process of losses over time, providing continuous and detailed performance monitoring. Specifically, by assigning larger weights to early disturbance stages, the WCL indicator can more effectively quantify the supply chain's rapid response capability in the initial disturbance phase and its long-term recovery performance, thereby comprehensively and continuously evaluating supply chain dynamic adaptability and recovery capability.

The Time to Survive (TTS) indicator emphasizes the maximum duration that a supply chain can maintain services after disruption of specific nodes or links, thereby identifying network bottleneck nodes [28]. This indicator performs outstandingly in identifying supply chain weaknesses and risk management, but practical applications often face difficulties in data collection, subjective bias, and insufficient consideration of node functional heterogeneity. Especially in complex networks, survival time measurements for different nodes often cannot accurately reflect overall network resilience performance. The SCP indicator demonstrates advantages in this regard by directly monitoring the overall structural change time nodes of supply chain performance, objectively revealing the dynamic characteristics of network structure evolution with disturbances, without relying on individual node survival time estimates, effectively avoiding errors from subjective assessments.

Profit loss models based on system evolution, such as the stochastic profit loss model proposed by Birge et al. [29], although theoretically combining network structure and inventory management to provide a stochastic resilience measurement approach, rely on overly strong rational enterprise assumptions [1] and have high requirements for parameter assumptions and probability distributions, making it difficult to obtain sufficiently accurate data support in reality. The WCL and SCP indicators adopt nonparametric statistical methods, weakening strong distributional assumptions about data, making them more suitable for supply chain environments with limited or low-frequency data, significantly enhancing indicator practicality and operability. Meanwhile, WCL quickly achieves performance loss assessment through simple linear weighting, while SCP precisely captures specific time points of dynamic supply chain structural changes using statistical change-point methods. The two complement each other, providing a set of empirical assessment tools with both flexibility and robustness.

The concepts of proactive flexibility [30,31] and reactive flexibility [32] in network topology design also occupy important positions in supply chain resilience research. Proactive flexibility emphasizes that firms enhance resilience through preventive measures before disturbances occur, such as diversified supplier networks and redundant capacity layouts, applicable to non-systematic disturbances but with limited applicability to systematic, large-scale disturbances [1]. Reactive flexibility emphasizes firms' response and temporary adjustment capabilities after disturbances occur, but such flexibility often does not manifest before disturbances and depends on firms' creativity and rapid response capabilities during crises. However, these two network topology design concepts lack easily operational measurement indicators. The indicators proposed in this paper can be viewed as measurements of the results produced by these concepts in supply chain performance, capable of capturing the actual temporal performance of proactive and reactive flexibility from a data-driven perspective, enabling firms to more accurately assess and enhance the actual effectiveness of these two types of flexibility.

Indicators based on system performance changes over time, such as performance loss and recovery ability, provide detailed descriptions of system state evolution over time and can reflect resilience characteristics at different supply chain stages [33,34]. However, the application of such indicators is often limited by the difficulty of predicting performance changes in complex supply chain systems [1]. The SCP and WCL indicators utilize nonparametric methods, avoiding the complexity of performance prediction, and directly conduct real-time and robust monitoring and assessment of post-disturbance performance dynamic changes based on actual observed data, significantly reducing modeling and prediction difficulty and enhancing indicator feasibility and accuracy in actual management decision-making.

In summary, compared with traditional supply chain resilience indicators, SCP and WCL demonstrate clear progress and advantages in both theoretical perspective and empirical application. First, these two indicators compensate for the shortcomings of traditional static or single-dimensional indicators from a dynamic perspective, comprehensively covering the full process performance of supply chains in absorption, adaptation, and recovery under disturbances. Second, both SCP and WCL are constructed based on nonparametric statistical methods, avoiding the strict requirements of complex probability models on data quality and distributional characteristics, greatly enhancing indicator flexibility and applicability in practical contexts. Additionally, the synergistic use of the two indicators makes resilience analysis more three-dimensional and detailed, enriching the supply chain resilience assessment toolbox and providing a strong empirical foundation and methodological innovation for supply chain resilience management and decision-making.

4 Application of SCP and WCL

To deeply explore the impact of supply chain network structure on resilience, this paper utilizes comprehensive customs data on Chinese exports and U.S. imports to construct a cross-national supply chain network (as shown in Figure 5 [FIGURE:5]). Using the 2018 U.S.-China trade war as an external shock event, this paper systematically evaluates the resilience of different product supply chains by applying the Structural Change-Point (SCP) and Weighted Cumulative Loss (WCL) indicators through changes in China's export market share to the U.S.

Supply chain resilience performance is significantly influenced by network characteristics. Different product categories (such as electrical appliances and furniture) correspond to substantially different supply chain network structures, which directly lead to variations in resilience performance. This paper further extracts firm-level supply chain network characteristics from 2017 (the year before the trade war) and examines how the network attributes of portal node firms (i.e., key enterprises participating in cross-national trade, represented by square nodes in Figure 5) affect overall supply chain resilience through regression analysis.

4.1 Data Description

The data used in this paper covers customs records of China-U.S. trade from 2016 to 2022, constructing product-level monthly time series data $p_{it}$, where $i$ represents specific products (6-digit HS codes) and $t$ represents time (monthly). This paper adopts China's trade share with the U.S. calculated from trade volume (standard containers TEU) (the ratio of Chinese TEU exports to the U.S. to total U.S. global imports) as the supply chain performance indicator $p$. The data source is the Panjiva database provided by Standard & Poor's (S&P), which encompasses detailed customs data from China, the U.S., and multiple other countries, including product types, weight, TEU volume, and firm information. To ensure data accuracy, this paper follows maritime industry standards and uses TEU as the basic unit.

The initial data includes supply chain networks for 4,997 products. Given that many products have small trade scales and low transaction frequencies, screening criteria are set as average monthly trade volume exceeding 10 TEU and at least 24 months of trade activity between 2016 and 2019, yielding 3,122 product supply chain networks. Simultaneously, we exclude products with extremely low U.S. import share (less than 0.01%) or extremely high share (exceeding 80%), finally selecting 2,639 product networks for in-depth research. The trade volume of these product networks accounts for 85.84% of total China-U.S. trade and covers 90.66% of trade volume for products affected during the trade war period, demonstrating strong representativeness and effectively supporting subsequent resilience analysis.

4.2 Shock Event and Its Intensity: U.S.-China Trade War and SCP Resilience Measurement

To validate indicator effectiveness, this paper selects the 2018 U.S.-China trade war as an external shock case and uses the 2020 COVID-19 pandemic as a control to analyze and compare the impacts of these two shock events on Chinese export supply chain resilience to the U.S.

This paper uses the 2020 COVID-19 pandemic as a reference to measure the shock intensity of the trade war and compares the impacts of the trade war and pandemic on different product supply networks. This comparison is implemented through SCP by calculating the proportion of change points ($SCP\%$) within specific periods across the same supply chains facing different shocks, which can be used to compare impacts of different shock events.

Figure 6 [FIGURE:6] shows the impacts of the U.S.-China trade war and COVID-19 pandemic on Chinese supply chains exporting to the U.S. The horizontal axis represents time (from early 2017 to early 2021), and the vertical axis represents the monthly proportion of structural changes $SCP\%$, indicating the proportion of supply chains identified as experiencing significant structural changes within each month. For example, the proportion of products experiencing structural changes during the pandemic ($SCP\%$) reached a peak of 9.48% in June 2020, meaning that among more than 2,500 product networks, up to 250 networks exhibited significant structural changes that month.

By calculating $SCP\%$ with $\delta = 6$ to focus on performance six months before and after shocks, we find that the 2018-2019 U.S.-China trade war had a significant impact on Chinese supply chains exporting to the U.S. ($SCP\% = 3.44\%$), far exceeding the natural fluctuation level before the shock ($SCP\% = 2.46\%$), but not as severe as the impact during the pandemic ($SCP\% = 5.69\%$). This result indicates that although the trade war significantly affected Chinese export supply chain resilience, its overall shock intensity was less severe than the pandemic.

Furthermore, we categorize product supply chains into four groups based on tariff impact levels: unaffected by tariffs, first-round tariffs (March 24, 2018, machinery and electronic equipment, etc.), second-round tariffs (July 26, 2018, chemicals and plastic products, etc.), and third-round tariffs (August 23, 2018, various industrial and consumer goods). As shown in Figure 7 [FIGURE:7], products unaffected by tariffs showed no significant structural changes, as expected; products involved in the second and third rounds of tariffs exhibited numerous structural change points during the trade war period, approaching pandemic levels, indicating significant tariff shock impacts. Notably, products in the first-round tariffs did not show similar patterns, demonstrating that capital- and technology-intensive products have stronger resilience to trade policy changes, while products with higher standardization levels (second and third rounds) are more vulnerable to negative impacts from policy fluctuations.

4.3 Categorized Product Resilience Measurement: WCL and SCP

This paper classifies more than 2,500 product networks based on three international standards—BEC, HS, and NAICS—to systematically demonstrate and analyze supply chain resilience differences from three dimensions: economic activity, raw material attributes, and industry categories.

Referring to the Broad Economic Categories (BEC) classification standard, products are divided into 7 categories including capital goods (manufacturing tools), intermediate goods (raw materials), and consumer goods. Figure 8 [FIGURE:8] shows the average WCL values for supply chain networks of various product categories, where lower WCL indicates smaller losses and stronger resilience; Figure 9 [FIGURE:9] displays the proportion of products experiencing structural changes after trade war shocks ($SCP\%$), where lower proportions also indicate stronger resilience performance. Comparative analysis of the two figures reveals that SCP change-point density is significantly consistent with WCL loss trends, demonstrating the consistency and reliability of the two indicators in measuring resilience from different perspectives.

In the BEC classification, the transport equipment category demonstrates the strongest resilience, maintaining negative WCL values and low SCP change-point density even when facing severe trade war shocks, indicating that this category's supply chain network structure is robust and has strong resistance capabilities. Further analysis reveals that from capital goods to intermediate goods to consumer goods, WCL gradually increases, and SCP change-point density also progressively increases, showing a trend of gradually weakening supply chain resilience along the chain from capital input to final consumption.

Based on raw material attributes and processing complexity, this paper uses the HS classification standard to further subdivide product categories and deeply examine the impact of processing complexity on supply chain resilience. As shown in Appendix Figures 10 [FIGURE:10] and 11 [FIGURE:11], precision equipment and transport equipment with high processing complexity exhibit higher resilience, while mass consumer goods such as food and tobacco show weaker resilience. This demonstrates that product substitutability, supply chain network complexity, and procurement difficulty are key factors affecting supply chain resilience.

Finally, based on industrial structure characteristics, this paper employs the NAICS (North American Industry Classification System) standard for analysis (Appendix Figures 12 [FIGURE:12] and 13 [FIGURE:13]). The results indicate that high-resilience industries are typically technology-intensive or strategically critical sectors, while low-resilience industries are mostly labor-intensive or resource-dependent sectors.

Comprehensive analysis of the above classification results effectively reveals the complex dynamic characteristics of supply chain resilience under shock scenarios, highlighting the applicability and important value of the SCP and WCL indicators proposed in this paper for rapidly assessing supply chain capabilities to respond to economic fluctuations and external shocks. These indicators can provide clear decision-making evidence for enterprises and policymakers to improve supply chain resilience and sustainability.

4.4 Impact of Network Structure on Supply Chain Resilience

Supply chain network structure has direct and indirect impacts on resilience, and the synergy and balance among network breadth, depth, and link strength are crucial for supply chain stability and sustainability. In-depth analysis of this relationship can provide important evidence for supply chain strategic planning.

Table 1 [TABLE:1] presents descriptive statistics for the dependent variable $Resilience$ and supply chain network structure-related independent variables. This study uses 2017 China-U.S. import and export data (the year before the trade war) to construct independent variables to explore how network structure affects supply chain resilience under 2018 tariff shocks. Resilience is defined as:
$$Resilience_i = (1 - WCL_i) \times 100$$
For intuitive comparison, resilience is defined as the complement of Weighted Cumulative Loss (WCL) multiplied by 100. The analysis sample includes over 1,900 product networks affected by the trade war, focusing on examining the network attributes of portal enterprises, specifically divided into two levels: global network (superscript $W$) and China-U.S. network (superscript $US$). Selected key network attributes include:

InDegree: The number of suppliers connected to a node, reflecting network resource diversity and redundancy. InDegree represents the number of sources from which a node in the supply chain obtains goods or services from different suppliers. It reflects the breadth of a firm's connections in the network and resource diversity. Higher InDegree means a firm can quickly find alternative suppliers during supply chain disruptions, thereby enhancing its anti-interference capability. This paper represents the total number of countries where Chinese firms in product network $i$ source goods globally as $InDegree_i^W$.

InWeight: The trade value (logarithm of USD) of goods or services a node receives from suppliers, reflecting supplier dependence and risk exposure. InWeight is the total volume or value of goods or services a node receives from all suppliers, using 2017 data. Larger weights indicate higher dependence on foreign suppliers. This paper uses trade value (in USD, logarithmically transformed) as the weight measure between China and the world, denoted as $InWeight_i^W$.

OutDegree: The number of customers served by a node, representing market diversity. A broader customer base helps disperse market risk and reflects a firm's connections to downstream markets. This paper records the total number of countries where Chinese firms in product network $i$ have customers globally as $OutDegree_i^W$, and the average number of customer firms in the U.S. for Chinese firms in product network $i$ as $OutDegree_i^{US}$.

OutWeight: The total trade volume of goods or services a node provides to customers, revealing market dependence intensity. Larger trade volumes mean higher risk exposure. Similar to InWeight, OutWeight reveals the strength of connections between firms and their customers. This paper calculates OutWeight between China and the world ($OutWeight_i^W$) and between China and the U.S. ($OutWeight_i^{US}$).

OutWeight Variance: The variance of customer trade volume distribution, characterizing customer concentration risk. High variance means high customer concentration, revealing potential risks from excessive customer concentration. Unbalanced weight distribution may mean firms are overly dependent on certain specific customers, making them more sensitive to market changes.

To quantify the impact of network structure on resilience, this study constructs the following multiple linear regression model:
$$Resilience_i = \beta_0 + \beta_1 \cdot InDegree_i^W + \beta_2 \cdot InWeight_i^W + \beta_3 \cdot OutDegree_i^W + \beta_4 \cdot OutWeight_i^W + \beta_5 \cdot OutDegree_i^{US} + \beta_6 \cdot OutWeight_i^{US} + \beta_7 \cdot OutWeightVar_i^{US} + \gamma \cdot ControlVariables + \epsilon_i$$

Column (1) of Table 2 [TABLE:2] presents baseline results; all results use robust standard errors. Columns (2)-(5) add product economic activity characteristics, raw material attribute characteristics, and industry category characteristics as control variables. Appendix Table 3 [TABLE:3] uses 2016 network structure as independent variables, and consistent results demonstrate the robustness of the analysis.

The results show that global InDegree ($InDegree_i^W$) and global OutDegree ($OutDegree_i^W$) are significantly positively correlated, indicating that diversity of supplier and customer countries/regions can effectively improve resilience and reduce disruption risk. Higher InDegree enhances firm flexibility in responding to supply disruptions, while customer diversification reduces market fluctuation impacts. Global weighted OutDegree ($OutWeight_i^W$) and U.S. OutWeight variance ($OutWeightVar_i^{US}$) are significantly negatively correlated, showing that excessive dependence on international markets and customer concentration both increase risk exposure and weaken resilience. U.S. market customer diversity ($OutDegree_i^{US}$) also significantly enhances resilience, demonstrating the importance of market diversification in resisting trade policy shocks.

$InDegree_i^W$: This variable shows significant positive correlation in all models, indicating that the number of suppliers in a supply chain is beneficial for improving its resilience. Higher InDegree means connections with more suppliers, thereby enhancing firm flexibility and risk resistance when facing external shocks. This positive correlation can be further understood from several aspects. Diversity and Redundancy: When firms source raw materials or products from multiple suppliers, supply chain diversity increases. This diversity can serve as a "redundancy" buffer against supply disruptions, enabling firms to adjust procurement strategies more flexibly. For example, when a supplier in Country A cannot deliver, the industry can quickly shift to a supplier in Country B, thereby reducing production interruption risk. Negotiation Advantage: More internationalized suppliers mean the industry may have stronger negotiation positions in the supply chain. Firms can reduce costs through competitive procurement and achieve more favorable terms among suppliers in different countries. This not only helps optimize cost structures during normal times but also retains more negotiation space when responding to external shocks. Geographic Diversity and Risk Dispersion: Firms with high InDegree establish connections with suppliers in different geographic regions, which further enhances supply chain resilience. For example, when natural disasters or political instability occur in one region, firms can rely on suppliers in other regions to continue operations, thereby avoiding overall supply chain paralysis.

$OutDegree_i^W$ and $OutWeight_i^W$: These show positive and negative correlations respectively, indicating that foreign customer diversity is beneficial for supply chain resilience, but greater dependence on foreign markets also brings larger risk exposure. $OutDegree_i^W$ represents customers in more countries, meaning the firm has stronger market diversity that disperses market risk. Through multiple sales channels, firms can avoid excessive sales dependence on a single market, thereby reducing negative impacts from market fluctuations. For example, when demand declines in one region, firms can maintain sales through customers in other regions, keeping the supply chain stable. $OutWeight_i^W$ represents more foreign trade volume, which expands the firm's international risk exposure and makes it more susceptible to changes in the international situation. Firms need to reasonably balance the stability of domestic circulation with risks from international trade to improve supply chain resilience.

$OutDegree_i^{US}$: Diversified U.S. customer bases are beneficial for resilience. The significant positive correlation of $OutDegree_i^{US}$ emphasizes the importance of diversified customers in the U.S. market. When firms in an industry have multiple U.S. customers, they can better cope with market fluctuations and adjust sales strategies more flexibly when facing trade friction or tariff policy changes.

$OutWeightVar_i^{US}$: This shows significant negative correlation in all models, indicating that OutWeight variance is inversely proportional to supply chain resilience. Excessively high OutWeight variance means unbalanced weight distribution, which may indicate over-dependence on a few large customers, increasing customer concentration risk. Once these customers reduce orders or switch to competitors, the firm's production and sales will be severely affected. This concentration risk may limit the firm's adaptation capability, making it slow to respond to market changes. Firms need diversification strategies. To enhance supply chain resilience, firms may need to balance sales weights by dispersing their customer base. This can be achieved by increasing the number of small customers or expanding business in multiple markets, thereby reducing dependence on a single large customer and enhancing supply chain robustness.

4.5 Discussion

The results of this study indicate that link diversity and weight distribution balance in supply chain network structure are two key factors determining supply chain resilience. Link diversity, manifested as broad distribution of suppliers and customers, helps enhance supply chain adaptation capability and risk resistance; balanced weight distribution reduces over-dependence on individual suppliers or customers, thereby preventing local risks from diffusing throughout the entire supply chain.

Regression analysis results further validate the importance of diversified network structures in supply chain management. Connections with multiple international suppliers enable firms to quickly activate alternative options when supplier disruptions occur, effectively reducing operational interruption risks; similarly, a broad global customer base enhances firms' ability to cope with market fluctuations. When demand fluctuates in one region, firms can rely on other markets to maintain overall business stability, and this diversity strategy significantly improves firms' resistance to external shocks.

In contrast, the impact of weight distribution is more complex. Firms with larger global trade volumes ($OutWeight_i^W$) are exposed to higher international risks and exhibit poorer resilience performance; while higher variance in U.S. market customer weight distribution ($OutWeightVar_i^{US}$) indicates excessive customer concentration, weakening firms' market adaptability and risk resistance capabilities. Therefore, firms need to reduce dependence on single markets or customers through balanced weight distribution to improve overall supply chain resilience performance.

The key to supply chain design lies in effective balance between diversification and centralization. While diversification strategies can improve supply chain resilience, excessive diversification may lead to increased management complexity and operational costs; whereas centralization, while helpful for efficiency improvements, may amplify systemic risks. Therefore, firms need to dynamically optimize supply chain structures based on their own characteristics and market environments to achieve appropriate balance between resilience and operational efficiency.

Based on this research, we propose the following recommendations to enhance supply chain resilience:

Supplier and Customer Diversification Management: Actively expand supplier and customer networks to reduce dependence on single entities. Expanding supply and market channels can enhance firm flexibility when facing shocks, reducing negative impacts from supply disruptions or market fluctuations.

Weight Distribution Optimization: Monitor and balance weight distributions among suppliers and customers to avoid over-dependence on key nodes. Through rational weight allocation, firms can effectively reduce local risk diffusion and enhance adaptability to external environmental changes.

Dynamic Adjustment and Risk Management: Regularly assess supply chain structures, identify key nodes, weak links, and potential risks, and implement dynamic adjustments. Establish comprehensive emergency response mechanisms, such as backup supplier systems and logistics solutions; utilize data analysis tools to continuously monitor supply chain performance, promptly detect and correct anomalies; flexibly adjust inventory and production plans according to market demand to maintain supply chain agility and stability.

Conclusion

This paper proposes two nonparametric statistical indicators—Structural Change-Points (SCP) and Weighted Cumulative Loss (WCL)—to construct a comprehensive and dynamic supply chain resilience assessment framework, addressing issues in current supply chain resilience measurement methods such as non-dynamism, probabilistic nature, single-dimensionality, and excessive assumptions about data distributions.

The research first theoretically clarifies the definition of supply chain resilience, emphasizing the dynamic absorption, adaptation, and recovery capabilities of supply chains after encountering external shocks. It then designs and validates the SCP and WCL indicators, where the SCP indicator, based on change-point detection technology, real-time identifies structural changes caused by external shocks and can effectively measure supply chain absorption and adaptation capabilities; the WCL indicator quantifies the cumulative loss of supply chain performance as shocks occur through dynamic weighting functions, emphasizing the importance of early-stage losses.

The empirical study uses the 2018 U.S.-China trade war as a case study, employing customs and maritime shipping data between China and the U.S. to conduct in-depth analysis of supply chain resilience. The study finds that network structure diversity and customer concentration are key factors significantly affecting supply chain resilience. Supply chains with diversified network structures and dispersed customer markets demonstrate stronger shock resistance; capital-intensive and technology-intensive products exhibit higher resilience, while products with high standardization levels are more susceptible to policy fluctuations.

The main contribution of this research lies in providing a set of nonparametric dynamic indicators that overcome the limitations of traditional supply chain resilience measurement methods, making resilience assessment more practically relevant and operational. Meanwhile, the broad applicability of the SCP and WCL indicator system enables it to provide clear empirical evidence for enterprises and policymakers to optimize supply chain management strategies and resource allocation, improving overall supply chain risk resistance and sustainable development capabilities.

Future research can further explore the applicability of this indicator system under more external shock scenarios and expand studies on supply chain resilience characteristics across different countries, industries, and firm sizes to continuously enrich and improve the theoretical framework and practical application methods of supply chain resilience. Future research can also further expand this indicator system to enable it to delve from supply chain-level resilience to node-level resilience under limited data conditions, thereby more precisely locating resilience weaknesses.