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

Transcription

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 1

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 2

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 3

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 1. Income 2. Longevity 3. 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 4

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 5

6 What is Life Quality Index? LQI = cg q e 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 is an ordinal utility function that quantifies the utility of income derived over the potential lifetime of an individual in the society 6

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 7

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 8

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 100% 4% Probability 80% 60% 40% 20% Survival Function Hazard Rate PDF 3% 2% 1% 0% 0% Age (year) Age (year) 9

10 An Example A person of age 50 year is pondering about the lifequality LQI has two components: life time and income 4% 3% Remaining Lifetime Distribution PDF 2% 1% 0% Age (year) 10

11 Survival Curve: Age 50 onwards At age 50, mean remaining lifetime = 29.9 years 100% Probability 80% 60% 40% Survival function Hazard Rate 20% 0% Age (year) 11

12 Utility of Income Average social income or GDP/person in Canada is g = $30,000 /year q Utility of Income = U( g) = g per year 100% 80% Survival Function Probability 60% 40% 20% 0% Income g Age (year) 12

13 Example: LQI Calculation The LQI is the utility derived from income over the remaining lifetime LQI = integration of utility over the remaining lifetime 110 Sx ( ) q LQI (50) = U ( g) dx = g e(50) St () 50 e(50) = remaining LE at age 50 = 29.9 years 0.2 LQI (50) = (30,000) (29.9) = 235 utils 13

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 14

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 dl L = q dg g + de e 0 (per person) 15

16 LQI Invariance and WTP Willingness to Pay (WTP) to preserve the life-quality is estimated from dl = 0 LQI (g, e) LQI (g-dg, e+de) ( dg ) = g q de e ($/person/year) It is also a measure of society s capacity to commit resources for risk reduction 16

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? 17

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 18

19 Understanding the Effect of Hazard: Change in Life Expectancy 100% 80% Survival function Probability 60% 40% 20% Increase in Hazard 0% Age (year) 19

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 g de 30, ( dg) = = = 4,876 $/year/person qe(50) For how long, this payment will continue? 20

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, year = 146,020 $/person Interpretation: Two scenarios are LQI equivalent 35,000 Income ($/year) 30,000 25,000 20,000 15,000 10,000 5,000 g = 30 k, remaining e = g = 25.1 k, remaining e = Mean Age (years) 21

22 Cost per Life Year What is the cost per year that can be invested for saving one life-year per person? dg de = Total life-quality benefit of saving one life-year /person dg de / e 4, = q g = = 5,009 $/year/lifeyear saved 30, = 150,000 $/lifeyear This value is independent of the age of the person A key task is to quantify de correctly and consistently 22

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

24 Societal vs. Individual Perspective Take a closer look at LQI cost rate (dg) dg = g q g q de e = = de e life $/lifeyear = $/year/lifeyear saved saved year saved/year 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 24

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 25

26 LQI Calibration - Results Country Canada France Germany UK USA q (Average )