Risk management of PPP project in the preparation stage based on Fault Tree Analysis

The risk management of PPP(Public Private Partnership) project can improve the level of risk control between government departments and private investors, so as to make more beneficial decisions, reduce investment losses and achieve mutual benefit as well. Therefore, this paper takes the PPP project preparation stage venture as the research object to identify and confirm four types of risks. At the same time, fault tree analysis(FTA) is used to evaluate the risk factors that belong to different parts, and quantify the influencing degree of risk impact on the basis of risk identification. In addition, it determines the importance order of risk factors by calculating unit structure importance on PPP project preparation stage. The result shows that accuracy of government decision-making, rationality of private investors funds allocation and instability of market returns are the main factors to generate the shared risk on the project.


Introduction
The rational assessment of shared risk about the public-private partnership project (hereinafter referred to as "PPP project") is the basis of risk-response and risk-allocation mechanism [1] . The PPP project has a significant impact on regional economic and social development. At the same time, it is also the primary means of government to guide private investment. Due to the internal and external factors, PPP project involves many risks, which mainly involves risk losses, considerable uncertainties and increased risk events by the main investment part [2] . Therefore, it is necessary to identify the risk factors, improve the effectiveness of risk management, grasp the key points of risk management, and allocate resources rationally to reduce risk losses in the pre-project preparation stage. Besides, fault tree analysis (hereinafter referred to as "FTA") is a tree describing directed logic of accident and a logical deductive analysis tool, which is used to analyze the phenomenon, cause and result about accident, so as to find out the measures to prevent the accidents [3] . Consequently, in this paper, FTA method is used to analyze and assess the risk factors of PPP project in the preparation stage.

Literature review
At present, there are two main kinds of risk-sharing methods for PPP projects: one is to confirm the risk-sharing ratio of each project through questionnaire and expert interview statistics. The tendency of risk is reflected by comparing the mean. The other is to establish mathematical models to seek the optimal solution of risk-sharing so as to determine the number of key risk-sharing between government and private sector. Consequently, there are both advantages and disadvantages of two methods. The former is easy to operate, but it can not define the specific commitment number of shared risk in the government sector and private sector. While the latter can determine the amount of shared risk quantitatively. However, the model building process is complicated. What's more, most cases need to discard some conditions, and it is different from the real PPP project. Thus, the conclusions of reliability should be verified [4] . In addition, Thomas et al. proposed a fuzzy fault framework tree and Delphi method on the basis of risk probability and impact assessment, which included the process of key risk modeling and expert judgment system in the general case [5] . Besides, Zhang and Zou developed fuzzy analytic hierarchy process (AHP) model to evaluate the risk environment of joint venture. However, as an emerging model, it appears to have many problems about PPP mode in China, such as delaying approvals, financing problems, lacking of market returns, project uniqueness, legal change, government credit and other risks [7] . Due to lacking of operational experience in the government and the private sector in PPP project, lots of projects failed to be identified and evaluated effectively [8] . Consequently, it is essential for government sectors and private investors to use scientific tools to assess the risk of PPP project and to provide a scientific basis for decision-making in the pre-preparation phase. Therefore, the purpose of this paper is to identify and assess the risks in PPP projects from the four perspectives of government sectors, private investors, macroeconomics and external environment. Moreover, this paper focus on finding out the main causes that lead to the occurrence of PPP projects so as to reduce the risk probability of different subjects and make risk assessment more closer to reality on the basis of uncertainty conditions.

The risk analysis process of PPP project
From a practical point of view, PPP project risk includes the probability of events and the seriousness of consequences. Thus, the analysis process can be divided into risk identification, risk estimation and risk assessment.

Risk identification
Risk identification, namely, identify all factors that may affect the progress of project to classify statistically and propose risk list. Hence, risk factors can be defined by checklist method and expert survey methods [9] . According to PPP research report in 2016, it pointed out that China has implemented more than 8,000 PPP projects, which involve water plants, power plants, bridges, tunnels, roads transportation, hospitals, sewage disposal and other fields [10] . As shown in Table 1, it summarizes the representative PPP projects and major risk factors for failure. From the statistics of the reasons for failure, a half of the PPP project failures are related to the lack of government credit, insufficient market returns, public opposition, market demand changes and project uniqueness. They account for a high proportion, so special attention should be paid to such issues in PPP cooperation projects.

Risk Estimation
Identified risk factors may determine the number and probability of risk losses and it is necessary to find out the relation among them. the probability and the magnitude of loss to determine the degree of correlation is essential in the risk assessment. There are a lot of methods of risk estimation, such as planning evaluation technology(PERT), analytic hierarchy process(AHP) and fuzzy comprehensive evaluation, etc., which are analyzed the risk of PPP project from possibility of occurrence, severity of impact and controllable degree on the preparation phase [11] .

Risk assessment
According to the estimation results, the appropriate methods are used to evaluate the risk factors of PPP projects and to determine the importance of factors and the level of risk, which can summarize the results of qualitative analysis so as to propose risk management recommendations for government departments and private investors to develop PPP risk management strategy in the project preparatory stage.

The construction of fault tree for PPP project
Bell Labs applied the method of Fault Tree Analysis (FTA) to militia missile launch control system and the research made great success in 1961. It is a method for reliability, security analysis and risk evaluation of large complex systems. At present, FTA has been widely used in aerospace, nuclear, electronics, machinery, chemical, mining and other fields [13][14][15] . On the whole, the FTA method not only can link the relevant factors of system failure analysis, but also can find the system fault spectrum and weak links easily. What's more, the system failure probability and other reliability parameters can be determined quantitatively in order to provide quantitative data to assess and improve the reliability of system. The basic steps of FTA method are shown in Figure1.

Project Overview
Yinxiang River Cultural Tourism Zone is located in the south of Shigu Town, Weibin District, Baoji City, Shaanxi Province. It has a total planned area of 67 square kilometers. Additionally, the planning area about the first centralized control area of Yinxiang River (hereinafter referred to as "Yinxiang river treatment area") is 9 square kilometers, of which construction area is 758 acres. Yinxiang river control area of 9 square kilometers is the scope of project. On the whole, the construction of project is divided into three parts, including infrastructure and public facilities construction (about RMB 1.272 billion), franchise facilities construction (about RMB 116 million), land acquisition and resettlement house construction (about RMB 1.141 billion). In addition, the initial investment is estimated about RMB 2.529 billion and its total construction period is 5 years. Besides, the project is started in 2016 and should be put into use in 2020.

The identification and analysis of project risk factors
Based on the long-term stability of cooperative relation between government and private investors, taking the risk management ability, project return mechanism and market risk management ability into account, it should be allocated the risk reasonably between government and social investors. Firstly, due to land acquisition and demolition, the residents of resettlement, and archaeological heritage protection risk in the development process, the government departments is responsible for pre-formalities and administrative approval risks for the construction projects.
Secondly, the private investors are mainly responsible for operation risk and financial risks of the project, such as rising interest rates or financing costs, broken capital chain, construction timing less than expected, insufficient operating income and other risks.
Finally, the risk of force majeure should be shared by the two parties. At the same time, policy and legal risks, which is beyond the scope of government controllable legal changes and policy changes risk, should be shared by the two parties as well.

The construction of fault tree
There are many risks in PPP project. In the process of risk identification, the risk factors of whole system can be identified and decomposed one by one on the basis of project cycle, so that the network analysis and calculation can be carried out smoothly. And then, the risk factors that can be eliminated by general measures should be removed. According to the basic idea and principle of fault tree rendering, a part of the fault tree is shown in Figure 2. Especially, the fault tree consists of 13   Macroeconomic risks X 9 Supporting facilities M 4 External environmental risks X 10 Project quality problem M 5 Reputational risk X 11 Tender risk M 6 Construction risk X 12 Contract risk M 7 Operational risk X 13 License acquisition risk M 8 Decision risk X 14 Financing risk M 9 Engineering risk X 15 Project overruns M 10 Financial risk X 16 Company management risk M 11 Managing risk X 17 Quality of service M 12 Public relations risk X 18 Project uniqueness risk M 13 Force majeure risk X 19 Inflation X 1 Lack of government credit X 20 Interest rate change X 2 Government corruption X 21 Legal changes X 3 Land acquisition risk X 22 Political factor risk X 4 Geological risk X 23 Natural factor risk X 5 Residents opposed the cut set that contains the bottom event is arbitrarily removed so that it does not become cut sets, namely, such cut set is a minimum cut set. According to the fault tree, the minimum cut set can be obtained by Boolean algebra method.  21  20  19  18  17   16  15  14  12  10  9  10  9  8  7  6  5  4  3  2  1   21  13  20  19  18  11  10  9  8  7  6  5   4  3  2 From the above results, we can get the conclusion that the top event is the union of n = 94 intersection, which is the minimum cut set of the fault tree, corresponding to the 23 fault occurrence patterns of the top event.

5.4.2.
Minimum path set. The minimum path set of the fault tree is solved by the method to find the minimum cut set of the dual tree. Moreover, the minimum path set is solved by using the properties of dual system. There are three minimum path sets in the fault tree, and there are three paths in which the top event does not occur. Therefore, three kinds of processing schemes can be developed to make ensure that the top event does not occur. (1). Besides, the importance of the structure is also calculated. And then, it can be sorted according to the size of coefficient about the structure importance. The coefficient is greater, the top event has a greater impact on the bottom event .
The structural importance of calculation results is: (   11  12  13   3  4  5  6  16  17  19  20  22  23   1  2  7  8  9  10  14  15  18  21 probability of the bottom events, the risks of PPP projects are decomposed into the event levels, and then the probability of the bottom events is calculated [16] . According to the calculation results, it can be concluded that the occurrence probability of the largest is X 8 = 0.1600, X 3 = X 5 = X 9 = 0.0500, and the smallest is X 1 = X 2 = X 4 = X 21 = X 22 = X 23 = 0.0010 in the 23 base events.

5.5.2
The probability of the top event. The occurrence probability of fault tree, whose the top event is P (T) = 0.2378, is calculated by using the "down method". According to the calculation of intermediate event and top event probability, we can get the conclusion that the first level intermediate event, which has the greatest impact on the top event, is M 1 (the sum of occurrence probability about "government risk" is 0.2800). In addition, the second-floor event with the greatest impact on M 1 is X 2 ("government decision error" occurs with a probability of 0.0314). Therefore, it is necessary to be controlled to "OR" connection the events with high occurrence probability. Furthermore, reducing the occurrence probability of the top event is possible, which can be controlled the bottom event about X 3 (lack of government credit), X 6 (project non-uniqueness), X 10 (insufficient market return) and X 11 (market demand change).

5.5.3
The probabilistic importance of the bottom event. Based on the probability importance analysis of the bottom events, we can see that the probability of X 8 (income insufficiency) and X 9 (supporting facility risk) is the largest. When the above 23 bottom events occur, they have the greatest impact on the top event. At the same time, these bottom events are connected with the top event by "OR gate". Consequently, the change of probability about the bottom event has great influence on the top event. Therefore, the risk warning should be taken into account seriously to ensure that the occurrence probability of the top event is the least during the project implementation. However, the bottom event for "AND" connection is exactly opposite. The higher the probability of the bottom event, the lower the importance of probability. Therefore, it should focus on the occurrence probability of the smallest "AND" connection bottom event so as to avoid the top event effectively.
As the occurrence probability of the top event about Yinxiang River PPP project is large, the probability of adjustment event is P (T) = 0.1347. Table 3 shows the probability of improved bottom event and its importance ranking. Table 3.The Ranking of Probabilistic Importance for the bottom Event Bottom event notation carried out though building the fault tree in the preparation stage. Moreover, the four types of risk sharing are also confirmed. At the same time, the risk factors of different subjects are evaluated on the basis of risk identification, and the degree of risk influence is quantified to determine the importance order of risk factors, which have an influence on PPP project in the preparation stage. These results point out that the accuracy of government decision-making, the rationality of private investors' fund allocation and the instability of market return are the main factors that generate the shared risk about project. Secondly, the risk of project incompletion, insufficient facilities, financing and projects non-uniqueness, to some extent, will hinder the smooth implementation of PPP projects and there is a great deal of uncertainty. Finally, external environmental factors, such as legal change and force majeure risk, are less likely to occur in the preparation phase of PPP project.