Natural Hazards

, Volume 64, Issue 2, pp 1707–1716 | Cite as

Hazard management and risk design by optimal statistical analysis

  • Cheng-Wu Chen
  • Kevin Fong-Rey Liu
  • Chun-Pin Tseng
  • Wen-Ko Hsu
  • Wei-Ling Chiang
Original Paper


Elicitation methods are used in decision making with respect to risk hazards to allow a researcher to infer the subjective utilities of outcomes from the observed preferences of an individual. A questionnaire method is presented, in this study, which takes into account the inevitable distortion of preferences by random errors and minimizes the effect of such errors. Under mild assumptions, the method for eliciting the utilities of many outcomes is a three-stage procedure. First, the questionnaire is utilized to elicit responses from which a subjective score is defined. Second, individual risk factors are discussed. Finally, the regression model presents individual risk preferences given the overall organizational risk culture, risk management policy, risk identification, and risk analysis. This paper addresses how company managers face risk and their tolerance of risk with respect to risk management.


Risk hazard assessment Computer aided Financial insurance 

1 Introduction

There are increasing novel methodologies are proposed to overcome the hazard problems (see Raviv 1979; Yi et al. 2010; Chen 2012a, b; Hsu 2011, 2012; Lin 2011, 2012a, b, c; Shih 2012; Tsai 2010, 2011a, b; Tseng 2011, 2012; Yang 2012 and the references therein). A proper enterprise risk management program can not only eliminate or reduce the severity of unfavorable consequences, but can also reduce the amount of financing required after an event occurs (Hoecht and Trott 2006; Kumar and Budin 2006; Wang et al. 2010; El-Gayar and Fritz 2010; Lauras et al. 2010). The general program includes risk control and risk transfer measures (Zhou et al. 2010). Risk control measures are designed to limit and avoid partial risk, while risk transfer measures are designed to deliver or share unavoidable risks with other parties. In recent years, many artificial intelligent models are proposed to solve all kinds of practical risk problems (see Chen and Chen 2010 and the references therein). Even though the improved uncertainty analysis techniques and modifications of problem formulation have led to improved efficiency of probabilistic optimization, the improvement is quite limited due to the nature of optimal natural disaster risk control strategy (Yusuf et al. 2004; Power et al. 2001; Prater et al. 2001). In this study, a new viewpoint of practical issue, risk preference, a long-time concern in the industry is increasingly recognized as a concern in the strategies of risk control and risk management agencies. Managers should also face and manage the risk. However, risk preference problems are complex due to the involvement of several factors whose values are often conflicting. In addition to the risk preference that is directly involved in risk management, it has gained an active and significant role (Tseng and Chen 2012; Lin et al. 2012). Risk preference is a personality trait related to decision making under risk. It plays a key role in survivability.

2 Methodology

In the optimal methodology (Chen 2004; Hsiao et al. 2005a, b; Chen 2006; Tseng et al. 2012), one usually assumes that the output will be publicly observed; i.e., observed by the enterprise authorities, managers, and the insurer. However, in this paper, a questionnaire is prepared and a subjective score defined firstly. Second, individual risk factors are analyzed through the data. Finally, a regression model presents the relation between overall organizational risk culture, risk management policy, risk identification, and risk analysis. These factors are correlated with individual risk preferences.

2.1 Search for available questionnaires and results

In order to build an effective questionnaire for assessing the manager’s tolerance for risk, questionnaires from relevant studies were adopted.

The questionnaire is based predominantly on the requirements of the Risk Management Standard AS/NZS 4360.1999 issued by Standards Australia.

The questionnaire has been reviewed by Price-Waterhouse Coopers and a range of other agencies to determine its clarity and usability.

The questionnaire is divided into the following segments:
  1. 1.

    Organizational culture.

  2. 2.

    Risk management policy.

  3. 3.

    Risk identification.

  4. 4.

    Risk analysis, evaluation, treatment, and monitoring.

First, the terms used in the questionnaire are defined in Table 1.
Table 1

Terms used in the questionnaire



Business continuity plan

A document that defines the organization’s approach to dealing with a break in business continuity (because of an outage, that is, an adverse business interruption event has occurred) and the steps the organization should take to ensure uninterrupted availability of all key business resources to support essential or critical business functions and activities

Governing board

A governing board is a board (committee) that has been established by law and directs and controls an organization

Government trading enterprise (Accorsi et al. 1999)

The Government Trading Enterprise Sector is largely self-funded from user charges and have a commercial charter but may receive funding from the budget for social programs (non-commercial activities), that is, community service obligations (CSOs)


The chance of something occurring that will, should the event occur, have an impact on the achievement of organizational objectives

It is measured in terms of the likelihood of something happening and its consequences. Risks can be negative (that is having an adverse impact such as loss or harm) or positive (that is a gain or advantage)

Reputation risk

The risk of damage to the organization’s credibility and reputation.

Risk alliance

The risk associated with working with partnering organizations

Opportunity risk

The risk of lost opportunities

Compliance risk

The risk of failing to meet government standards/laws and regulations

Risk analysis

Determining the level of risk following consideration of the sources, consequences, and likelihood of risks

Risk criteria

Measures/standards set by the organization to rank risks and decide whether they are acceptable

Risk evaluation

Comparing the level of risk with the risk criteria and deciding whether the risks are acceptable or unacceptable

Risk financing

The methods applied to fund risk treatment and the financial consequences of risk

Risk identification

The examination of all sources of risk facing the organization from any activity, function, or process undertaken

Risk management

A systematic and logical process of identifying, analyzing, evaluating, treating, monitoring, and communicating risks associated with any activity, function, or process in a way that will enable an organization to minimize losses and maximize opportunities

Risk management champion

A senior executive manager or similar person (or team) who supports the effective development, implementation, and review of the risk management framework within the organization

Risk management framework

Management polices, procedures, and practices applied by the organization to the task of identifying, analyzing, evaluating, treating, monitoring, and communicating risks

Risk management plan

A document that sets out the:


 strategic context and objectives for risk management


 risks identified/analyzed/assessed/prioritized as having critical impacts on the organization


 plan to manage strategically important risks

Risk management policy

A document that defines the organization’s strategy and provides guidance for managing risks faced

Risk treatment

The selection and implementation of appropriate options for dealing with identified risk


Those individuals, groups, institutions, etc. (either internal or external to the organization) who are or perceive themselves to be affected by a decision or activity

2.2 Questionnaire data

The questionnaires were distributed to executive officers in Taiwan. The total of 98 samples collected are from 25 banks, 31 electronics manufacturers, and 42 small and medium enterprises. After testing data, company manager tolerance for risk factors is discussed.

3 Analysis and discussion

3.1 Risk preference

All questions were designed to correlate a higher numerical score with increased risk management actions. From the questionnaire data, 98 samples are classified into 3 groups. The samples, having average scores higher than 3.3, are defined as the high-risk management actions group. Medium- and low-risk management actions groups are also listed in the following Table 2.
Table 2

Degree of risk management action


Average score

Number of samples

High-risk management action

Higher than 3.3


Medium risk management action



Low-risk management action

Below 2.5


The average risk emphasizing level has 3 ranges, 2–2.5, 2.5–3.1, and 3.1–5. If they take more risk management actions, their score was higher. Attitudes toward risk management should correlate with scores. However, the data indicate that for the range of 3.1–5, the company managers applied risk management processes and developed related plans. This might be because the company has already greatly emphasized risk management.

3.2 Risk preference factors

There are 4 risk preference factors defined in the questionnaire.
  1. (A)

    The overall organizational risk culture.

  2. (B)

    Risk management policy.

  3. (C)

    Risk identification.

  4. (D)

    Risk analysis, evaluation, treatment, and monitoring.


These are correlated with individual risk preference. They are represented by X1, X2, X3, and X4, respectively.

We seek to understand the relationship between these 4 risk preference factors. Their correlation matrixes under different risk preference are shown in Table 3.
Table 3

Correlation matrixes under different risk preference


X 1

X 2

X 3

X 4

High-risk management


 X 1



 X 2




 X 3





 X 4





Medium risk management


 X 1



 X 2




 X 3





 X 4





Low-risk management


 X 1



 X 2




 X 3





 X 4





This demonstrates that the 4 risk preference factors have low correlation in each group. In the ANOVA sheet, the 4 factors do not show significant difference among the whole sample.

4 Discussions

  1. (a)

    The four risk preference factors are not highly correlated by different risk preferences.

  2. (b)

    The four risk preference factors almost have the same impact on company manager’s tolerance for risk.

  3. (c)

    Organizational risk culture does not necessarily have the most impact on the company manager’s tolerance for risk.

  4. (d)

    Decisions regarding risk are often multidimensional, where the preferences of the decision maker depend on several attributes. For example, an individual might be concerned about both his/her level of wealth and the condition of her health. If we can find the data describing his/her health, the impact of these data on tolerance for risk might be more significant than the above four risk preference factors.

  5. (e)

    The data are from small and medium enterprise managers. However, data describing their actual commercial volumes are unavailable and deemed significant.

  6. (f)

    All participants discussed and concluded that there are fifteen factors that influence natural disaster risk management: risk sensitiveness (RS), data accuracy (DA), centralized and collaborative emergency planning (CACEP), new risk control technology introduction (NRCTI), training and testing (TAT), process integration (PI), disaster contingency recovery plan (DCRP), physical risk assessment (PRA), building retrofitting improvement (BRI), cost minimization (COM), shareholder satisfaction (SS), building code performance (BOP), minimizing uncertainty (MU), use of financial tools (UOFT), and minimizing resistance to change (MRTC).


5 Optimal strategy evaluation

Maximizing expected benefit while minimizing cost and risk taken is the goal of optimal strategies of risk control (Prater et al. 2001). Disentangling the effects of factors maximizing benefit and factors minimizing cost and risk taken is the essence of the strategy-optimization problem because it results in a trade-off among benefit, cost, and risk. The strategy should reduce losses caused by events beyond human risk control, but it should also provide an acceptable cost and endurable risk. Often, these are conflicting goals. Moreover, it is not easy to define acceptable cost and endurable risk, because budgets are limited and vary.

For most organizations, having no risk control may increase savings, but it creates a higher likelihood of a catastrophic loss—not a good strategy. Taking high risks normally produces only modest savings and could prove to be ruinous in the event of catastrophe.

There are two bundles of models to evaluate strategies of risk control actions: deterministic analysis models and stochastic analysis models.

Deterministic analysis models, sometimes referred to as constrained maximization, use a static set of input variables. The former uses a deterministic model to answer typical optimization questions.

The latter use variables that are selected randomly from probability distributions, sometimes referred to as scenario optimization or maximum-likelihood optimization. They can quantify some functions of the variables, such as expected policyholder deficit and return on capital.

5.1 Deterministic analysis models

In the natural disaster risk control problem, the model is solved for the optimal deterministic contract. An optimal strategy consists of the action a risk-averse person should take and the auxiliary schedule that consists of cost as a function of risk reduction. The term “deterministic” refers to an assumed property of the strategy, namely that no randomization is allowed in the risk control strategy. What we mean precisely by randomization is described in the next section.

5.2 The approach

Our goal is to find one of the best feasible strategies that satisfy a given criterion. We can do this by solving a constrained maximization program. The program consists of an objective function and a set of constraints. The objective function ranks alternative contracts according to some criterion. The constraints describe the set of contracts that are feasible. In this problem, the constrained maximization program represents the problem facing a risk-averse person trying to determine the best feasible contracts to fit his requests.

In the following sections, the concept of the evaluation of economic effects of natural disaster risk control projects is classified by the three items: benefit, cost, and cost-benefit ratio.

5.3 Basic cost-benefit analysis

Cost-benefit analysis has been utilized across broad academic fields for many years. Cost-benefit analysis may be seen as an alternative to economic surplus analysis. In fact, it uses the concept of economic surplus. Cost-benefit analysis originates from project analysis and evaluation where the effects emanate from a project.

As with economic surplus, research benefits are measured as changes in consumer or producer surplus; and when discounted over time, internal rates of return, net present value, and cost-benefit ratio are calculated. The potential advantage of cost-benefit analysis is that no information on price elasticity is required, since by definition, demand and supply functions are either vertical or horizontal. Paucity of data and modeling requirements have established cost-benefit analysis as the standard method for calculating economic gains from research. The disadvantages are that price effects and price spillover effects are ignored as well as the distributional consequences of the economic gains among regions, countries, or social groups.

In our case, we attempt to determine how to calculate the direct damage cost (i.e., price of structure and equipment, and their loss due to damage) and the indirect damage arising from the disruption of businesses and cost for emergency repairs. The benefits of natural disaster risk control projects are calculated by measuring the reduction of the expected damage.

For the method to determine the optimal strategy for contemporary risk control, the historical record of natural disasters was used as data source. Only decreases in damage costs caused by natural disaster are considered to be the benefit of a risk control measure.

The total costs of damage due to natural disasters were calculated as the sum of direct damage costs and indirect damage costs. The direct damage costs were calculated by multiplying the total amount of general properties in the disaster area by the damage ratio. With respect to indirect damage costs, only the losses due to the disruption of businesses were calculated based on assumptions that depended on the character of the business and the value of damage to general properties.

In addition, the data used for calculating these values were derived from natural disaster simulations for various events having different occurrence probabilities, scales, and magnitudes; and decrease in the annual damage costs was treated as the expected benefit. Damage reduction was compared with the costs necessary for improvement to calculate the benefit-cost ratio in the following case.

5.4 Objective function

In basic cost-benefit analysis, the objective functions are minimum cost and maximum benefit. It is written:
$$ \begin{array}{*{20}c} {\text{MAX}} \hfill & {{\text{BENEFIT}}({\text{A}}) + {\text{BENEFIT}}({\text{B}}) + {\text{BENEFIT}}({\text{C}}) + {\text{BENEFIT}}({\text{D}}) \cdots } \hfill \\ {\text{MIN}} \hfill & {{\text{COST}}({\text{A}}) + {\text{COST}}({\text{B}}) + {\text{COST}}({\text{C}}) + {\text{COST}}({\text{D}}) \cdots } \hfill \\ \end{array} $$
where COST(A) is the cost of risk control action A, and BENEFIT(B) is expected damage reduction by risk control action B.
The following are two examples:
  1. 1.

    \( \begin{array}{*{20}c} {\text{MAX}} \hfill & {1.5\sqrt {\text{A}} + 0.5\sqrt {\text{B}} } \hfill \\ {{\text{s}} . {\text{t}} .} \hfill & {0 < {\text{A}} + {\text{B}} = 100} \hfill \\ {} \hfill & {0 < {\text{A}},\quad 0 < {\text{B}}} \hfill \\ \end{array} \)

1.5√A + 0.5√B is expected damage reduction of risk control actions A and B, while variables A and B represent the cost of actions A and B, respectively. The expected damage reduction of risk control is assumed and depending on actions A and B with the concave root function. In this case, A plus B equals 100, that is, the limited budget of the action-taker.
  1. 2.

    \( \begin{array}{*{20}c} {\text{MAX}} \hfill & {(1.5\sqrt {\text{A}} + 0.5\sqrt {\text{B}} )/({\text{A}} + {\text{B}})} \hfill \\ {{\text{s}} . {\text{t}} .} \hfill & {0 < {\text{A}} + {\text{B}} < 100} \hfill \\ {} \hfill & {0 < {\text{A}},\quad 0 < {\text{B}}} \hfill \\ \end{array} \)


(1.5√A + 0.5√B)/(A + B) is expected benefit-cost ratio of risk control actions A and B. In this case, the sum of A plus B is smaller than 100, that is, the maximum budget of the action-taker. The meaning and result of this example, which seeks to determine the maximum benefit-cost ratio, are different from the aforementioned example.

Cost-benefit analysis derives its rationale from welfare analysis. Cost-benefit analysis is a widely used evaluation method used for decisions respecting investments in developing projects. It is the primary investment analytical method and is based on the concept of discounted cash flows taking into account the temporal aspects of costs and benefits of an investment. The main difference between cost benefit and economic surplus is the way in which the benefits from research investments are derived. Cost-benefit analysis emphasizes the research-induced efficiency effect on yield increase and cost reduction at constant market prices, thus, potential market effects due to the changing supply schedule are unaccounted.

The economic surplus approach uses a market framework to derive research benefits, the outcome of which causes a rightward shift in the supply schedule. The economic gains are then calculated as the surplus accruing to producers and consumers, which results from changes in the price and quantity of the commodity. By comparing the aggregate research benefits over time of cost-benefit analysis and economic surplus with the cost of a research alternative, one can calculate summary measures such as the net present value, internal rate of return, and the cost-benefit ratio to compare and rank a set of different research projects. Both methods have been applied to agriculture in ex-post and ex-ante studies to calculate the economic returns from research investments.

6 Conclusion

There are at least two variations of the risk-cost-benefit trade-off. First, if there are alternative ways to provide the desired benefits and each alternative has an acceptable cost, then the alternative with the least risk should be chosen. This approach minimizes risk subject to the constraint of providing the basic benefits at an acceptable cost.

In the second approach, resources can be applied to a project for the purpose of further reducing risk to the point where the marginal cost of reducing the risk just equals the value of the marginal reduction in risk. Once this type of optimal design has been achieved, the residual risk may be defined as the acceptable level of risk in the sense that it would be economically inefficient to pursue further reductions in risk. This argument is most effective when risks and the costs of reducing them can be reasonably categorized in monetary terms.



The authors would like to thank the National Science Council of the Republic of China, Taiwan, for their financial support of this research under Contract Nos. NSC 100-2221-E-022-013-MY2 and NSC 100-2628-E-022-002-MY2.


  1. Accorsi R, Zio E, Apostolakis GE (1999) Developing utility functions for environmental decision-making. Prog Nucl Energy 34(4):387–411CrossRefGoogle Scholar
  2. Chen CW (2004) Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems. Mathematics and Computers in Simulation 66:523–537Google Scholar
  3. Chen CW (2006) Stability conditions of fuzzy systems and its application to structural and mechanical systems. Advances in Engineering Software 37:624–629Google Scholar
  4. Chen CY (2010) Fuzzy control for an oceanic structure: A case study in time-delay TLP system. Journal of Vibration and Control 16:147–160Google Scholar
  5. Chen CY (2012a) Assessment of the major hazard potential of interfacial solitary waves moving over a trapezoidal obstacle on a horizontal plateau. Natural Hazards, 62(3):841–852Google Scholar
  6. Chen CY (2012b) Disaster prevention and reduction for exploring teachers’ technology acceptance using a virtual reality system and partial least squares techniques. Natural Hazards 62(3):1217–1231Google Scholar
  7. Chen TH, Chen CW (2010) Application of data mining to the spatial heterogeneity of foreclosed mortgages. Expert Syst Appl 37(2):993–997CrossRefGoogle Scholar
  8. El-Gayar OF, Fritz BD (2010) A web-based multi-perspective decision support system for information security planning. Decis Support Syst 50:43–54CrossRefGoogle Scholar
  9. Hoecht A, Trott P (2006) Innovation risks of strategic outsourcing. Technovation 26:672–681CrossRefGoogle Scholar
  10. Hsiao FH, Chen CW, Liang YW, Xu SD and Chiang WL (2005a) T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays. IEEE Trans Circuits Syst I Regul Pap 52:1883–1893Google Scholar
  11. Hsiao FH, Hwang, JD, Chen CW and Tsai ZR (2005b) Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control. IEEE Trans Fuzzy Syst 13:152–163Google Scholar
  12. Hsu WK (2011) An integrated flood risk assessment model for property insurance industry in Taiwan. Nat Hazards 58(3):1295–1309Google Scholar
  13. Hsu WK (2012) Risk and uncertainty analysis in the planning stages of a risk decision-making process. Nat Hazards 61(3):1355–1365Google Scholar
  14. Kumar S, Budin EM (2006) Prevention and management of product recalls in the processed food industry: a case study based on an exporter’s perspective. Technovation 26:739–750CrossRefGoogle Scholar
  15. Lauras M, Marques G, Gourc D (2010) Towards a multi-dimensional project performance measurement system. Decis Support Syst 48:342–353CrossRefGoogle Scholar
  16. Lin JW (2012a) Kalman filter decision systems for debris flow hazard assessment. Nat Hazards 60(3):1255–1266Google Scholar
  17. Lin JW (2012b) Modeling and assessment of bridge structure for seismic hazard prevention. Nat Hazards 61(3):1115–1126Google Scholar
  18. Lin JW (2012c) Potential hazard analysis and risk assessment of debris flow by fuzzy modeling. Nat Hazards. doi: 10.1007/s11069-012-0236-z
  19. Lin ML (2011) Using GIS-based spatial geocomputation from remotely sensed data for drought risk-sensitive assessment. International Journal of Innovative Computing, Information and Control 7(2): 657-668Google Scholar
  20. Lin JW, Chen CW, Peng CY (2012) Kalman filter decision systems for debris flow hazard assessment. Nat Hazards 60(3):1255–1266CrossRefGoogle Scholar
  21. Power DJ, Sohal AS, Rahman S (2001) Critical success factors in agile natural disaster risk management: an empirical study. Int J Phys Distrib Logist 31(4):247–265CrossRefGoogle Scholar
  22. Prater E, Biehl M, Smith MA (2001) International natural disaster risk control tradeoffs between flexibility and uncertainty. Int J Oper Prod Manag 21(5/6):823–839CrossRefGoogle Scholar
  23. Raviv A (1979) The design of an optimal insurance policy. Am Econ Rev 69:84–96Google Scholar
  24. Shih BY (2012) Using Lego NXT to explore scientific literacy in disaster prevention and rescue systems. Nat Hazards. doi: 10.1007/s11069-012-0233-2
  25. Tsai CH (2010) An earthquake disaster management mechanism based on risk assessment information for the tourism industry—a case study from the island of Taiwan. Tour Manag 31(4):470–481Google Scholar
  26. Tsai CH (2011a) Development of a mechanism for typhoon and flood risk assessment and disaster management in the hotel industry—a case study of the Hualien area. Scandinavian J Hosp Tour 11(3):324–341Google Scholar
  27. Tsai CH (2011b) The establishment of a rapid natural disaster risk assessment model for the tourism industry. Tour Manag 32(1):158–171Google Scholar
  28. Tseng CP (2011) A new viewpoint on risk control decision models for natural disasters. Nat Hazards 59(3):1715–1733Google Scholar
  29. Tseng CP (2012) Default risk-based probabilistic decision model for risk management and control. Nat Hazards. doi: 10.1007/s11069-012-0183-8.
  30. Tseng CP, Chen CW (2012) Natural disaster management mechanisms for probabilistic earthquake loss. Nat Hazards 60(3):1055–1063CrossRefGoogle Scholar
  31. Tseng CP, Chen CW and Liu FR (2012) Risk control allocation model for pressure vessels and piping project. J Vib Control 18(3):385–394Google Scholar
  32. Wang JT, Lin W, Huang YH (2010) A performance-oriented risk management framework for innovative R&D projects. Technovation 30:601–611CrossRefGoogle Scholar
  33. Yang HC (2012) Potential hazard analysis from the viewpoint of flow measurement in large open-channel junctions. Nat Hazards 61(2):803–813Google Scholar
  34. Yi CS, Lee JH, Shim MP (2010) GIS-based distributed technique for assessing economic loss from flood damage: pre-feasibility study for the Anyang Stream Basin in Korea. Nat Hazards 55(2):251–272Google Scholar
  35. Yusuf YY, Gunasekaran A, Adeleye EO, Sivayoganathan K (2004) Agile natural disaster risk capabilities: determinants of competitive objectives. Eur J Oper Res 159:379–392CrossRefGoogle Scholar
  36. Zhou HJ, Wang JA, Wan JH et al (2010) Resilience to natural hazards: a geographic perspective. Nat Hazards 53(1):21–41CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Cheng-Wu Chen
    • 1
  • Kevin Fong-Rey Liu
    • 2
  • Chun-Pin Tseng
    • 3
  • Wen-Ko Hsu
    • 4
  • Wei-Ling Chiang
    • 5
  1. 1.Institute of Maritime Information and TechnologyNational Kaohsiung Marine UniversityKaohsiungTaiwan
  2. 2.Department of SafetyHealth and Environmental Engineering, Ming Chi University of TechnologyNew Taipei CityTaiwan, ROC
  3. 3.Chung Shan Institute of Science and TechnologyArmaments BureauTaoyuanTaiwan
  4. 4.Research Center for Hazard Mitigation and PreventionNational Central University TaoyuanTaiwan
  5. 5.Department of Civil EngineeringNational Central UniversityTaoyuanTaiwan, ROC

Personalised recommendations