JCOMMOPS database contains life-time information GDP log Buoy metadata collection scheme

1. A simple model for drifting buoy life-times, anda method for estimating evolution of a network's sizeEtienne 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. 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. 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. 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

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. α=0.0012301 Correlation coefficient=0.9965 Least square fit, model: R(t) = N(t)/N0= e-αt Model half life = ln(2)/α=563 days ⇒ Actual failure rate higher than model for units which died after 414 days

8. Model validation using hind-cast • Buoys deployed as in reality • Buoys dying according to the model Last deployment

9. Network size evolution • Units deployed at the same time, no further deployments • M0 Units deployed at the same time at time t=-t0, Constant deployment rate Rx between time -t0 and 0, no further deployment after time t=0 • Units deployed as in (2) before t=0, new constant deployment rate Rx after t=0

10. Network management example Rate to maintain network at target level = 562 units/year • Rx: Deployment rate (units/day) • Initial number of buoys: 1000 • Target: 1250 in 1 year 1250 in 1 year at rate = 760 units/year 1250 target

11. Tool available from http://www.jcommops.org