By E. F. Codd, Robert L. Ashenhurst
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Extra resources for Cellular Automata
15) For a design with/i = 1 this time t* < EXlC = EXlF; for 2 < a < 4 the ratio 0-63 < (t*/EXlF) < 0-73. Thus the fatigue sensitivity criterion fx = 1 produces a time to first failure which differs only slightly from the time at which the failure risks are equal. This time t* ~ 2 / 3 EXlF can thus be considered as a fair estimate of safe life. 16) = XlCIX1F is itself a random variable. It has been assumed so far that the expectation Efx is closely enough approximated by the ratio of the expectations of XlC and XlF.
M. S. , Tech. Rep. 1966. 2. J. EUGENE, Proc. 4th Congress Internat. Council Aeronaut. Sciences [edited by R. R. Dexter], Spartan Books—MacMillan, 1965, 679-698. ] 3. A. M. FREUDENTHAL and M. SHINOZUKA, Structural Reliability, J. Wiley and Sons, New York, 1967. 4. A. M. FREUDENTHAL and E. J. GUMBEL, Advances in Applied Mechanics, Academic Press, New York, 4, 116-156 (1956). ] Reliability Analysis Based on Time to the First Failure 43 5. A. M. FREUDENTHAL and E. J. GUMBEL,/. Am. statist. , 49, No.
17). 30) where EX2 is given by Eqn. 19). The expected value of the interval (X2 - X,) according to Eqn. 31) EX = pv + v(l - P) r ( l + l/«) Because of Eqn. 32) while — ^ 3 ^ § o Vx — Fig. 2a. 2 ^ / / ^ j o o l 1000 Z/>" Vx — Fig. 2b. O / II A / y / j^/ 1000 Vy — 2 Fig. 2c. Ratio Var Xi/(EX) versus coefficient of variation Vx for Log-Normal distribution 26 ALFRED M. 1 ^ / - ^ * Fig. 2d. Ratio Var (X2-Xi)/(EX)2 versus coefficient of variation Vx for Log-Normal distribution The ratios EXJEX, E(X2-X1)IEX, Var XJiEX)2 and Var (X2~X1)I(EX)2 evaluated on the basis of Eqn.
Cellular Automata by E. F. Codd, Robert L. Ashenhurst