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 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 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
Country q
(Average )
Canada
0.1912
France
0.1514
Germany
0.1686 UK
0.1749
USA
0.2158