Application of the Life-Quality Index to Infrastructure Maintenance Decision Optimization

1. Application of the Life-Quality Index to Infrastructure Maintenance Decision Optimization Professor Mahesh Pandey Institute of Risk Research and Department of Civil Engineering University of Waterloo, Waterloo CANADA

2. Introduction • Rehabilitation and renewal of aging infrastructure involve large financial investments • In Canada, refurbishment of electrical generation and transmission infrastructure requires over 40 billion $ investment in next 15 years • Such investments are intended to sustain high quality of life in the society • LQI is useful in quantifying the benefits of improved safety and economic progress • LQI can be used to optimize rehabilitation strategies

3. Objectives • Illustrate the LQI method of assessing the benefits and costs in the context of an infrastructure improvement program • Illustrate the key issues and concepts used in quantifying the LQI variables • Present some new ideas about societal capaity to commit resources

4. Life Quality - Overview • United Nations Development Program – Human Development Index – measure of quality of life • Main determinants of the life quality at societal level are • Income • Longevity • Education • Engineering advancements have resulted in large improvements in longevity and prosperity • Engineering risk management programs & regulations are also responsible for maintaining and improving the quality of life

5. Life Quality – Infrastructure Maintenance • The impact on life quality of risk reduction achieved through any engineering project should be quantified to guide the decision maker • This also enables a strategic optimization of risk management at societal level • Infrastructure maintenance decisions also fall into this category • Rehabilitation of roads, bridges, dams, dikes, power plants, water distribution system costs large sum of money • Decisions to improve infrastructure are often delayed due to inadequate information about their life-quality benefits • The proposed LQI method intends to fill this gap

6. What is Life Quality Index? • LQI is an ordinal utility function that quantifies the utility of income derived over the potential lifetime of an individual in the society g = Social income/person ($/year) gross domestic product /person/year e = Life expectancy per person q = Calibrated constant (< 1) money is an imperfect substitute for lifetime (q~ 0.2)

7. LQI • g = GDP/year = productive capacity of society/person • q = annual work time/year/person it depends on labour productivity • e = life time, a measure of living conditions • In this context, LQI also relates to society’s productive capacity to generate resources

8. LQI Research • Derivation of LQI from macro-economic theory and demographic data about longevity • Development of net benefit criterion based on LQI invariance principle • Calibration of LQI from economic data (q 0.2) • Applications • Conceptual developments for further applications of LQI to infrastructure maintenance problems

9. Human Lifetime Distribution • Lifetime is an uncertain variable • Mean lifetime = area under the survival curve • In Canada (2001), mean lifetime at birth or life expectancy = 77.5 years

10. An Example • A person of age 50 year is pondering about the life- quality • LQI has two components: life time and income

11. Survival Curve: Age 50 onwards • At age 50, mean remaining lifetime = 29.9 years

12. Utility of Income • Average social income or GDP/person in Canada is g = $30,000 /year • Utility of Income = per year

13. Example: LQI Calculation • The LQI is the utility derived from income over the remaining lifetime • LQI = integration of utility over the remaining lifetime • e(50) = remaining LE at age 50 = 29.9 years

14. LQI & Risk Management • Actual value of LQI is of little interest in engineering risk management • The main interest is in the evaluation of a change in the LQI when facing with a new risk • This evaluation allows us to determine • Individual willingness to pay for safety (WTP) • Societal Capacity to Commit Resources

15. Net Benefit Criterion • The impact of a hazard • Increased mortality – change in life expectancy (dE) • Monetary costs – change in social income (dG) • Net-benefit criterion in terms of change in LQI being positive (per person)

16. LQI Invariance and WTP • Willingness to Pay (WTP) to preserve the life-quality is estimated from dL = 0 • It is also a measure of society’s capacity to commit resources for risk reduction LQI (g, e) LQI (g-dg, e+de)

17. LQI Application: Illustration • Unabated air pollution increases the mortality risk particularly to people at age 50 and beyond • The mortality rate increases with age, and some data are available to estimate this age dependent mortality • Proposal: install equipment that would control air pollution from coal power plants for next 40 years • Question: what is the suitable investment to avert the pollution risk?

18. Other Potential Applications • Other similar contexts in which LQI can be applied are • Increasing dike heights or strengthening dams and structures • Renewal of old transportation systems (roads, bridges, pipelines) • Refurbishment of nuclear power plants

19. Understanding the Effect of Hazard: Change in Life Expectancy

20. Quantify Willingness to Pay • The impact of a new risk over a 40 year is estimated by modifying the hazard rates from age 50- 90 in the national lifetable • The loss of life expectancy = de(50) = 0.97 year • The willingness pay from net benefit criterion • For how long, this payment will continue?

21. Individual Willingness to Pay • The payment will continue over the mean remaining life of the person (i.e. 29.94 years) • Total life-quality benefit derived from this project = • 4,87629.94 year = 146,020 $/person • Interpretation: Two scenarios are LQI equivalent

22. Cost per Life Year • What is the cost per year that can be invested for saving one life-year per person? • Total life-quality benefit of saving one life-year /person • This value is independent of the age of the person • A key task is to quantify de correctly and consistently

23. LQI Method: Summary Infrastructure Maintenance Project Probability of Failure over Time without Maintenance Cost of Maintenance Program (C $) Mortality rates LQI-based Benefit (L $) Direct Monetary Benefit (B $) Net Benefit (L + B - C)

24. Societal vs. Individual Perspective • Take a closer look at LQI cost rate (dg) • Societal capacity to commit resources to this project over 40 year = 40×(dg = 4876) = 195,000 $/person • Calculations are normalized as per person and per life year

25. Summary • In LQI method, we compute the impact of mortality risk reduction in monetary terms = it is the benefit accruing from risk reduction • It is a cornerstone of LQI analysis • LQI provides a basis to assess the societal capacity to commit resoucres • This method allows to explore alternate strategies that would maximize the benefit to society

26. LQI Calibration - Results