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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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)

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)

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?

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

Understanding the Effect of Hazard: Change in Life Expectancy

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?

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

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

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)

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

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

LQI Calibration - Results Country q (Average ) Canada 0.1912 France 0.1514 Germany 0.1686 UK 0.1749 USA 0.2158