Steady state availability probability

Availability and reliability are different metrics. Reliability is always a function of failure rates and operating time interval. Availability is a function of failure rates and repair rates. While instantaneous availability will vary during the operating time interval, this is due to changes in failure probabilities and repair situations. Availability is often calculated as an average over a long operating time interval. This is referred to as "steady state availability."... 

Steady State Availability— Traditionally, reliability engineers have assumed a constant repair rate. When this is done, probability models can be solved... 

Figure 4-6 shows a Markov probability model of a single component with a single failure mode. This model can be solved for steady state availability and steady state unavailability. 

Given the failure rate of a component and an operational time interval (mission time), one can calculate the reliability of that component. If the component is repairable and the restore rate is estimated, tiie steady state availability of the component can be calculated. If the failure rates, proof test interval, proof test coverage, and component lifetime are known, one can calculate the average probability of fatiure. 

Pq/ Pi, and P2 = steady-state probabilities of the vehicle/transit system being in states 0,1, and 2, respectively The vehicle/transit system steady-state availability is given by... 

The availability of a phase space probability distribution for the steady state means that it is possible to develop a Monte Carlo algorithm for the computer simulation of nonequilibrium systems. The Monte Carlo algorithm that has been developed and applied to heat flow [5] is outlined in this section, following a brief description of the system geometry and atomic potential. 

Since the duration of the non-steady state can be shown (4) to be inversely related to kt1/2 and R 1/2, a high value of kt is unfavorable because it reduces both the time available for measurement and the rate to be measured. For this reason cumene, having a low kt, is the obvious choice for demonstrating the method. Cyclohexene and Tetralin, on the other hand, probably represent the limit of what can be measured their relatively high kt is partially offset by high values of kp [RH], which increase the velocities, hence also the accuracy obtainable at a given Rt The method proved ineffective with fluorene, which must be measured in solution (e.g., 1.8M in chlorobenzene which reduces its kp [RH] by a factor of 4 relative to Tetralin), sec-butylbenzene and cyclohexylbenzene, which probably combine a relatively low kp with considerably higher kt than for cumene (I). 

The complex interplay of basic and acidic sites in the deamination and disproportionationn of amines is the probable cause of the stop-effect which has been observed in the reaction of triethylamine on alumina [155] and, more recently, of other amines [149], When the steady state on the catalyst surface in a flow reactor is rapidly changed by substituting the amine feed for a nitrogen stream, a rapid temporary increase in olefin production is observed. This phenomenon has been explained as the result of the increased availability of basic centres which were previously blocked by adsorbed molecules [149,155]. 

Enzyme kinetics are normally determined under steady-state, initial-rate conditions, which place several constraints on the incubation conditions. First, the amount of substrate should greatly exceed the enzyme concentration, and the consumption of substrate should be held to a minimum. Generally, the amount of substrate consumed should be held to less than 10%. This constraint ensures that accurate substrate concentration data are available for the kinetic analyses and minimizes the probability that product inhibition of the reaction will occur. This constraint can be problematic when the Km of the reaction is low, since the amount of product (10% of a low substrate concentration) may be below that needed for accurate product quantitation. One method to increase the substrate amount available is to use larger incubation volumes. For example, a 10-mL incubation has 10 times more substrate available than a 1-mL incubation. Another method is to increase the sensitivity of the assay, e.g., using mass spectral or radioisotope assays. When more than 10% of the substrate is consumed, the substrate concentration can be corrected via the integrated form of the rate equation (Dr. James Gillette, personal communication) ... 

The permeability trends found in this study for the 1000 pm thick membranes under flowing 1000 ppm H2S/H2 were compared to transient permeability results reported previously . Nearly identical trends in permeability were found for the three Pd-Cu alloys by these two measurement methods reinforcing the suggested correlation between the alloy crystal structure and H2S tolerance. The results of these steady-state permeability experiments indicated that when the Pd-Cu alloys had an fee structure, H2S had little impact on flux but when the structure was bcc, H2S had a moderate to severe impact. However, both of these methods had limitations that probably impacted the results. The transient or batch method was limited by finite H2S availability, competition for the available H2S by other metal surfaces, relatively short test durations and a limited data set. The steady-state 1000 pm thick membrane method was potentially limited by membrane thickness which could have... 

Although these data leave much to be desired, they are probably the best indication available of what normal and pathological ranges are likely to be. The data suggest that the appropriate range of variation to mimic steady-state kinetic behavior in vivo is typically an order of magnitude or less, and that kinetic behavior exhibited in vitro, when concentration variables are varied over more extreme... 

Many ingenious methods have been introduced to study protein adsorption. If the kinetics of the adsorption process are important, the ellipsometric method introduced by Rothen (3) is probably the best. In this method protein adsorption can be studied ijn situ from a solution. The method has been used to study the kinetics of both the adsorption of protein in single layers and in double layers that can occur in the immune-reaction. When protein such as bovine serum albumin (BSA) was adsorbed from a dilute solution onto a surface, after a delay of a few seconds, steady-state diffusion controlled the adsorption process and, consequently, the amount bound to the surface increased linearly with time. However, as the surface became covered, adsorption slowed down, because it was now limited by the number of available sites on the surface. The final layer of BSA was roughly 2 nanometer thick. 

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