Some asymptotic results for optimal stopping based on capture times

1976 ◽  
Vol 13 (4) ◽  
pp. 741-750
Author(s):  
Robert L. Wardrop
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Linear Time ◽  
Random Time ◽  
Time Cost ◽  
Asymptotic Results ◽  
Expected Payoff

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Zi; where Z1, Z2, …, Zn are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.

Some asymptotic results for optimal stopping based on capture times

1976 ◽  
Vol 13 (04) ◽  
pp. 741-750
Author(s):  
Robert L. Wardrop
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Optimal Stopping ◽  
Optimal Strategy ◽  
Linear Time ◽  
Random Time ◽  
Time Cost ◽  
Asymptotic Results ◽  
Expected Payoff

A region contains n prey labeled 1, 2, …, n. Prey i is captured at the random time Z i; where Z 1, Z 2, …, Z n are i.i.d. with distribution function F. The statistician must decide when to stop searching, with the goal of maximizing the number of prey captured minus a linear time cost, c. The optimal strategy and its expected payoff are studied asymptotically as n, c →∞, for F a beta or Weibull distribution.

Optimal and adaptive stopping based on capture times

1974 ◽  
Vol 11 (2) ◽  
pp. 294-301 ◽  
Author(s):  
Norman Starr
Keyword(s):  
Optimal Stopping ◽  
Linear Time ◽  
Stopping Time ◽  
Statistical Procedure ◽  
Time Cost ◽  
Expected Payoff ◽  
Optimal Stopping Time

Independent exponential capture times are assumed for each of N prey. The payoff is the number of prey caught less a linear time cost. The optimal stopping time and value are obtained. When N is known an adaptive statistical procedure is proposed for which the expected payoff differs from the value by at most one-half plus a term which tends to zero (of order N–α, a < 1) as N → ∞.

Optimal and adaptive stopping based on capture times

1974 ◽  
Vol 11 (02) ◽  
pp. 294-301 ◽  
Author(s):  
Norman Starr
Keyword(s):  
Optimal Stopping ◽  
Linear Time ◽  
Stopping Time ◽  
Statistical Procedure ◽  
Time Cost ◽  
Expected Payoff ◽  
Optimal Stopping Time

Independent exponential capture times are assumed for each of N prey. The payoff is the number of prey caught less a linear time cost. The optimal stopping time and value are obtained. When N is known an adaptive statistical procedure is proposed for which the expected payoff differs from the value by at most one-half plus a term which tends to zero (of order N –α, a &lt; 1) as N → ∞.

Influence of Overheating Degree on Material Reliability of A390.0 Alloy

2012 ◽  
Vol 191 ◽  
pp. 23-28 ◽  
Author(s):  
Jaroslaw Piątkowski
Keyword(s):  
Tensile Strength ◽  
Distribution Function ◽  
Weibull Distribution ◽  
Fatigue Testing ◽  
Testing Machine ◽  
Time To Failure ◽  
The Impact ◽  
Failure Evaluation ◽  
Graphic Interpretation ◽  
Gravity Cast

The object of the studies was A390.0 alloy (AlSi17Cu5Mg), similar to A3XX.X series, gravity cast into sand and metal moulds. This alloy is mainly used for cast pistons operating in I.C. engines, for cylinder blocks and housings of compressors, and for pumps and brakes. The A390.0 alloy was poured at temperatures 880 and 980°C, holding the melt for 30 minutes and casting from the temperature of 780°C. The assessment of the impact of the degree of overheating was to analysis the tensile strength. Studies were carried out on a normal-running fatigue testing machine, which was the mechanically driven resonant pulsator. For the needs of quantitative reliability evaluation and the time-to-failure evaluation, the procedures used in survival analysis, adapted to the analysis of failure-free operation with two-parametric Weibull distributions, were applied. Having determined the boundary value σ0 for Weibull distribution, the value of „m” modulus was computed along with other coefficients of material reliability, proposed formerly by the authors. Basing on the obtained results, a model of Weibull distribution function was developed for the tensile strength with respective graphic interpretation.

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