16.322 Stochastic Estimation and Control, Fall 2004 Prof. VanderⅤelde R,()=0.99 e(m)=0.99 0.99 =00 To achieve 99% reliability, the mTTf of a component must be at 100 times the mission lifetime Now suppose the system contains 1000 components of equal t 1011000 10010 105t 200,000 years. This is why we do not conduct high reliability, high6e For a planetary mission where t)=2 years, the component MTTf mu component count missions without redundancy Linearized Error Propagation Example: Orbiting spacecraft Orbiting spacecraft carrying lander Given an initial state: 5=56 Page 4 of 616.322 Stochastic Estimation and Control, Fall 2004 Prof. Vander Velde R t( l) = 0.99 s ⎛ ⎞ tl −⎜ ⎟ ⎜ ⎟ tms e ⎝ ⎠ = 0.99 tl 1 − = 0.99 tms tl = 0.01 tms t = 100t m l s To achieve 99% reliability, the MTTF of a component must be at 100 times the mission lifetime. Now suppose the system contains 1000 components of equal t . mc 1000 1 1 = ∑ = 1000 tms i=1 tmi tmi 1 t = tmc = 100t m l s 1000 t = 105 t m l c For a planetary mission where tl = 2 years, the component MTTF must be 200,000 years. This is why we do not conduct high reliability, high component count missions without redundancy. Linearized Error Propagation Example: Orbiting spacecraft Orbiting spacecraft carrying lander ⎡r Given an initial state: xˆ0 = 0 ⎤ ⎢ ⎥ ⎣v0 ⎦6 1× Page 4 of 6