###### Abstract  
Advancement of IoT and ICT provide infrastructure to manage, monitor and control Cyber-Physical Systems (CPS) through timely provision of real-time information from the shop floor. Although real-time information in CPS such as resource failures can be detected based on IoT and ICT, improper response to resource failures may cripple CPS and degrade performance. Effective operations of CPS relies on an effective scheme to evaluate the impact of resource failures, support decision making needed and take proper actions to respond to resource failures. This motivates us to develop a methodology to assess the impact of resource failures on operations of CPS and provide the decision support as needed. The goal of this study is to propose solution algorithms to analyze robustness of CPS with respect to resource failures in terms of the impact on temporal properties. Given CPS modeled by a class of discrete timed Petri nets (DTPNs), we develop theory to analyze robustness of CPS by transforming the models to residual spatial-temporal network (RSTN) models in which capacity loss due to resources is reflected. We formulate an optimization problem to determine the influence of resource failures on CPS based on RSTNs and analyze the feasibility to meet the order deadline. To study the feasibility to solve a real problem, we analyze the computational complexity of the proposed algorithms. We illustrate the proposed method by application scenarios. We conduct experiments to study efficiency and verify computational feasibility of the proposed method to solve a real problem. c 2020 May 20219 9 July 202113 July 2021  
operations and robustness of CPS. Robustness of CPS can be achieved only if the real-time information provided by IoT and ICT are timely and properly used to support decision making and respond to the changing environment. For example, real-time information from the shop floor--such as resource failures [6]--can be detected in CPS. However, real-time resource failures information from IoT and ICT is useful only if an effective scheme to evaluate the impact of, and deal with, resource failures is available. In the literature, design issues of CPS include robustness, security and cost effectiveness [7]. Study on the impact of resource failures on CPS is less explored. This motivates us to develop a methodology to assess the impact of resource failures on operations and temporal properties of CPS. The goal of this study is to propose a method for modeling and analysis of CPS, in order to pave the way for developing an effective strategy to handle resource failures in CPS. To evaluate the impact of resource failures on CPS, we will study the robustness of CPS in the context of manufacturing systems in this paper. The robustness property is concerned with the influence of resource failures on the operations and performance of CPS. In make-to-order manufacturing, meeting the deadline of orders is an important issue. Resource failures often cripple the operations of manufacturing systems and may lead to delays in fulfillment of orders. Therefore, the robustness property of CPS with respect to resource failures to be studied in this paper is concerned with how the orders will be influenced due to resource failures. In classical control theory, robustness addresses the issue about whether the desired system property can be maintained in the presence of uncertainty. The problem to be studied in this paper is to investigate the effects of resource failures on operations of CPS and the fulfillment of an order with multiple product demands and deadlines. The problem setting of this paper is different from that of [8], in that multiple types of product demands are considered in this study whereas the work of [8] considers a single type of product demands. The objective of this study is to propose a solution algorithm to analyze robustness of CPS with respect to resource failures, based on a class of discrete timed Petri net (DTPN) model that extends the one in [8].