Optimal allocation under partial ordering of lifetimes of components

1993 ◽  
Vol 25 (04) ◽  
pp. 914-925 ◽  
Author(s):  
Emad El-Neweihi ◽  
Jayaram Sethuraman
Keyword(s):  
Optimal Allocation ◽  
Reliability Theory ◽  
Partial Ordering ◽  
Threshold Models ◽  
Minimal Repair ◽  
Stochastic Orderings ◽  
Redundancy Allocation ◽  
Arrangement Increasing ◽  
Increasing Functions

Assembly of systems to maximize reliability when certain components of the systems can be bolstered in different ways is an important theme in reliability theory. This is done under assumptions of various stochastic orderings among the lifetimes of the components and the spares used to bolster them. The powerful techniques of Schur and arrangement increasing functions are used in this paper to pinpoint optimal allocation results in different settings involving active and standby redundancy allocation, minimal repair and shock-threshold models.

Optimal allocation under partial ordering of lifetimes of components

1993 ◽  
Vol 25 (4) ◽  
pp. 914-925 ◽  
Author(s):  
Emad El-Neweihi ◽  
Jayaram Sethuraman
Keyword(s):  
Optimal Allocation ◽  
Reliability Theory ◽  
Partial Ordering ◽  
Threshold Models ◽  
Minimal Repair ◽  
Stochastic Orderings ◽  
Redundancy Allocation ◽  
Arrangement Increasing ◽  
Increasing Functions

Assembly of systems to maximize reliability when certain components of the systems can be bolstered in different ways is an important theme in reliability theory. This is done under assumptions of various stochastic orderings among the lifetimes of the components and the spares used to bolster them. The powerful techniques of Schur and arrangement increasing functions are used in this paper to pinpoint optimal allocation results in different settings involving active and standby redundancy allocation, minimal repair and shock-threshold models.

A Stochastic Comparison for Arrangement Increasing Functions

1994 ◽  
Vol 3 (3) ◽  
pp. 345-348 ◽  
Author(s):  
Abba M. Krieger ◽  
Paul R. Rosenbaum
Keyword(s):  
Distributive Lattice ◽  
Partial Order ◽  
Random Permutation ◽  
The Other ◽  
Stochastic Comparison ◽  
Finite Distributive Lattice ◽  
Set Of Permutations ◽  
Arrangement Increasing ◽  
Increasing Functions ◽  
Increasing Function

Let h(·) be an arrangement increasing function, let X have an arrangement increasing density, and let XE be a random permutation of the coordinates of X. We prove E{h(XE)} ≤ E{h(X)}. This comparison is delicate in that similar results are sometimes true and sometimes false. In a finite distributive lattice, a similar comparison follows from Holley's inequality, but the set of permutations with the arrangement order is not a lattice. On the other hand, the set of permutations is a lattice, though not a distributive lattice, if it is endowed with a different partial order, but in this case the comparison does not hold.

Extinction in the Pigeon after Continuous Reinforcement: Effect of Number of Reinforced Responses

1971 ◽  
Vol 28 (1) ◽  
pp. 331-338 ◽  
Author(s):  
Laurel Furumoto
Keyword(s):  
Animal Studies ◽  
Food Pellet ◽  
Key Peck ◽  
Continuous Reinforcement ◽  
Gm Food ◽  
Free Operant ◽  
Time To Extinction ◽  
Monotonically Increasing Function ◽  
Increasing Functions ◽  
Increasing Function

Number of responses and time to extinction were measured after 3, 10, 1000, 3000, 5000, and 10,000 reinforced key-peck responses during conditioning. Each response was reinforced with a 045-gm. food pellet. The number of responses in extinction was a monotonically increasing function which became asymptotic beyond 1000 reinforced responses. Number of reinforced responses during conditioning significantly affected the number of responses in extinction ( p < .001) but not the time to extinction. The results support the findings of previous free-operant bar-press studies with rats. Free-operant animal studies of extinction after continuous reinforcement have consistently produced monotonically increasing functions and have typically employed relatively small amounts of reinforcement. Amount of reward may be an important parameter determining the shape of the extinction function in the free-operant studies.

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