1. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (1) A simple model for drifting buoy life-times, and a method for estimating evolution of a network's size Etienne Charpentier *, Mathieu Belbéoch *, Julien Bourcier ** * JCOMMOPS ** Student, UN. Paul Sabatier, Toulouse JCOMMOPS database contains life-time information –GDP log –Buoy metadata collection scheme –EGOS historical database –Argo Assess drifting buoy life-time using model –Simple exponential model proposed Predict evolution of network size –Using model –Assuming constant deployment rate Use this a management tool

2. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (2) Product reliability Probability density function, f(t) Cumulative distribution function F(t) –Probability that a randomly selected unit will fail by time t –Proportion of population that fails by time t Reliability function –Probability that randomly selected unit survive beyond time t –Proportion of population that survives beyond time t

3. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (3) The Bathtube Curve h(t)=instantaneous failure rate for the survivors at time t h(t)= f(t)/R(t) Early failures can be considered separately Non repairable system; wearout failure period usually not reached Will assume Intrinsic Failure Period only with constant failure rate Exponential model

4. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (4) Example AOML Argos programme #6325 Because of missing information –Only date of last location used to assess age Optimistic approach; are considered alive: Beach platforms still active Buoys picked up still located Platforms removed from GTS still located 452 buoys deployed between 1/1/2002 and 30/6/2004 Average age = 444.9 days Maximum age = 961 days 172 buoys still active

5. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (5)

6. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (6) Survivability Real half life between 465 and 522 days 25% buoys died before 275 days Some buoys still active, life-time unknown: –Optimistic : Active buoys survive forever –Pessimistic: Active buoys die Today

7. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (7) Least square fit, model: R(t) = N(t)/N 0 = e -αt α=0.0012301 Correlation coefficient=0.9965 Model half life = ln(2)/α=563 days Actual failure rate higher than model for units which died after 414 days

8. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (8) Model validation using hind-cast Buoys deployed as in reality Buoys dying according to the model Last deployment

9. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (9) Network size evolution 1.Units deployed at the same time, no further deployments 2.M 0 Units deployed at the same time at time t=-t 0, Constant deployment rate R x between time -t 0 and 0, no further deployment after time t=0 3.Units deployed as in (2) before t=0, new constant deployment rate R x after t=0

10. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (10) Network management example Rx: Deployment rate (units/day) Initial number of buoys: 1000 Target: 1250 in 1 year 1250 in 1 year at rate = 760 units/year Rate to maintain network at target level = 562 units/year 1250 target

11. DBCP-21, Buenos Aires,17-21 October 2005, Life-times (11) Tool available from http://www.jcommops.org