Читать книгу Reliability Analysis, Safety Assessment and Optimization - Enrico Zio - Страница 15
ОглавлениеNotations
Notations: Part I
| t | time point |
| nf(t) | number of failed items |
| ns(t) | number of the survived items |
| n0 | sample size |
| T | random variable of the failure time |
| F(t) | cdf of failure time |
| f(t) | pdf of failure time |
| R(t) | reliability at time t |
| h(t) | hazard function at time t |
| H(t) | cumulative hazard function at time t |
| Q^(t) | estimate of the unreliability |
| R^(t) | estimate of the reliability |
| D(t) | component or system demand at time t |
| G(t) | performance function at time t |
| MTTF | mean time to failure |
| X | random variable |
| a | crack length |
| N | load cycle |
| Q | total volume of wear debris produced |
| Rs(t) | reliability of the system at time t |
| (⋅) | unreliability function of the system |
| C | cost |
| x | decision variable |
| g(x) | inequality constraints |
| h(x) | equality constraints |
| f(x) | criterion function |
| D=(V, A) | directed graph |
| d(⋅) | length of the shortest path |
Notations: Part II
| t | time point |
| S | state set |
| M | perfect state |
| x=(x1,…,xn) | component state vector |
| X=(X1,…,Xn) | state of all components |
| ϕ(⋅) | structure function of the system |
| gi | performance level of component i |
| λkji | transition rate of component i from state k to state j |
| Qkji(t) | kernel of the SMP analogous to λkji of the CTMC |
| Tni | time of the n-th transition of component i |
| Gni | performance of component i at the n-th transition |
| θjki(t) | probability that the process of component i starts from state j at time t |
| AφW(t) | availability with a minimum on performance of total φ at time t |
| ui(z) | universal generating function of component i |
| pij=Pr(Xi=j) | probability of component i being at state j |
| p(t) | state probability vector |
| λij(t) | transition rate from state i to state j at time t in Markov process |
| Λ | transition rate matrix |
| Π(⋅) | possibility function |
| N(⋅) | necessity function |
| Bel(⋅) | belief function |
| Pl(⋅) | plausibility function |
| F−1(⋅) | inverse function |
| E(⋅) | expectation equation |
| ⊗ | UGF composition operator |
| Π(⋅) | possibility function |
| N(⋅) | necessity function |
| Bel(⋅) | belief function |
| Pl(⋅) | plausibility function |
| F−1(⋅) | inverse function |
| E(⋅) | expectation equation |
| S(⋅) | system safety function |
| Risk(⋅) | system risk function |
| C(⋅) | cost function |
Notation: Part III
| ri | reliability of subsystem i |
| x=(x1,…,xn)T | decision variable vector |
| c=(c1,…,cn)T | coefficients of the objective function |
| b=(b1,…,bm)T | right-hand side values of the inequality constraints |
| z=(z1,z2,…,zM) | objective vector |
| xl*, l=1,2,…,L | set of optimal solutions |
| w=(w1,w2,…,wM) | weighting vector |
| x* | global optimal solution |
| R(⋅) | system reliability function |
| A(⋅) | system availability function |
| M(⋅) | system maintainability function |
| S(⋅) | system safety function |
| C(⋅) | cost function |
| Risk(⋅) | system risk function |
| RN | N-dimensional solution space |
| fi | i-th objective functions |
| gj | j-th equality constraints |
| hk | k-th inequality constraints |
| ω | random event |
| ξ=(q(ω)T, h(ω)T, T(ω)T) | second-stage problem parameters |
| W | recourse matrix |
| y(ω) | second-stage or corrective actions |
| Q(x) | expected recourse function |
| U | uncertainty set |
| u | uncertainty parameters |
| ζ | perturbation vector |
| Z | perturbation set |
| xu* | optimal solution under the uncertainty parameter u |
