General Reliability Function

This function can be obtained by using Equation 3.6. Thus, we get 

By integrating both sides of Equation 3.8 over the time interval [0, t], we obtain 

Evaluating the right-hand side of Equation 3.9 and then rearranging it yields 

Equation 3.11 is the general reliability function. This equation can be used to obtain the reliability function of an item/system when its times to failure follow any time-continuous probability distribution (e.g., exponential, Rayleigh, Weibull). 

Assume that the hazard rate of an oil and gas industry system is expressed by Equation 3.1. Obtain an expression for the oil and gas industry system reliability function by using Equation 3.11. 

Assume that the times to failure of a transportation system are exponentially distributed and that the constant failure rate is 0.007 failures per hour. Calculate the transportation system s reliability for a 4-hour mission. 

By substituting the given data values into Equation (3.11), we get 

---

This is one reason why in general reliable function predictions cannot be inferred from structural models and mere significance of structural similarity at the level of folds. The current state-of-the-art of understanding structure-function relationships requires additional evidence to make such predictions. This, however, could be available via additional experimental measurements (e.g. expression data) or knowledge on biochemical and protein interaction networks. 

Einally, acmal detection of the analyte has to be done by choosing a cost-effective and reliable method. In general, the functional groups of many of the PPCPs can render their extraction from water and measurement with GC and HPLC difficult. Eurthermore, the environmental matrices such as soil and sediments also impose significant interference in the analysis of these compounds. To that effect, no single method or piece of equipment can measure all the compounds of concern. Individual laboratories typically have to optimize the methods. 

Similarly, a generally reliable representation of an outer surface V(r), i.e., Fs(r), can be obtained by some semiempirical methods [56-59] and by density functional... 

The next example regards the determination of Li+ and Na+ ions affinity for glycine and cytosine. Because our aim is also that to establish what functional can have general reliability for all kind of systems, we have used, in this case, the PWP/TZVP combination. On the other hand this choice is easily justified by the similar MIA values of Table 11. 

In 2005, the Davies group discovered that the generally reliable catalyst Rh2(DOSP)4 failed to induce high levels of chiral control when benzyl silyl ether derivatives 37 were employed as reaction components. Fortunately, Hashimoto s Rh2(iS-PTTL)4 catalyst showed a superb performance, delivering C—H bond functionalization products 38 in prominent levels of diastereo-and enantioselectivity (up to >95% de and 98% ee) (Scheme 1.11). 

Unlike most materials simulation methods that are based on classical potentials, the main advantages of Ab initio methods, which is based on first principles density functional theory (without any adjustable parameters), are the generality, reliability, and accuracy of these methods. They... 

In our present work, V(r) is in most instances determined from an ih initio STO-5G SCF molecular orbital wave function, using the GAUSSIAN programs [18-20], with all integrals in equation (1) evaluated rigorously. It has been shown that electrostatic potentials obtained even from SCF wave functions that are not near Hartree-Fock quality are generally reliable [33,44-49]. Many alternative procedures for computing V(r) have been discussed and analyzed in depth elsewhere [35,36,50]. 

Knowledge of the load placed on batteries in the course of the discharge phase will generally not suffice even in capacitive operation for the development of a reliable, functional power concept. The intervals between applications dictated by the sequence control system, which forms the basis for the plan of charging, have a decisive influence, particularly in the case of cyclic operation. Furthermore, attention must be paid to further basic application parameters. The more data known on the application of the batteries, the more reliable it is to specify the power concept. 

---