Residual lifetime

In some simple cases an additive approach can be successful. The service life is divided into stages, for example moderate exposure for one year, severe exposure for one month and low exposure for five years. The predicted degradation effects for the three periods can be summed and the condition of the product at the end, and hence residual lifetime, estimated. If it is assumed that degradation is proportional to the time of exposure and that the damage from different exposure conditions can be cumulatively added then the so called Miner s rule could be used ... 

Figure 12.23. Photon counting streak camera measurement of the fluorescence decay of DODCI (I0 fi Afl in water, (a) counts (b) weighted residues. Lifetime = 0.66 0.01 ns, (From Ref. 95.) Note the similarities with single-photon timing data, e.g., sec Figure 12,14. Reduced/2 = 1.37.

We may now recall the fundamental equations for calculating chemical conversion in the limiting states of Min Mix and Max Mix. The BPT model provides a convenient picture of the two situations (figure 3). If the bundle is arranged in such a way that the particles of same residual lifetime are situated on the same vertical line, then minimal mixedness corresponds to a perfect insulation between tubes and the conversion for a single reaction is written... 

Assuming that the RTD is equal to that of 5 ISTR in series and that Ti=T2=30ms and applying equations (la-d) and (10) the functions G(a), g(a) and K(a) computed above yield the integral expressions I to V so that with equation (9) the Lewis number can be calculated as a function of the residual lifetime. 

Figure 5 Characteristic functions of the residual lifetime X. Comparison of the improved 3EM (a) and the standard 3EM (b).

The time it takes a molecule to pass through a reactor is called its residence time 6. Two properties of 6 are important the time elapsed since the molecule entered the reactor (its age) and the remaining time it will spend in the reactor (its residual lifetime). We are concerned mainly with the sum of these times, which is 6, but it is important to note that micromixing can occur only between molecules that have the same residual lifetime molecules cannot mix at some point in the reactor and then unmix at a later point in order to have different residual lifetimes. A convenient definition of residence-time distribution function is the fraction J ) of the effluent stream that has a residence time less than 0. None of the fluid can have passed through the reactor in zero time, so / = 0 at 0 = 0. Similarly, none of the fluid can remain in the reactor indefinitely, so that Japproaches 1 as 0 approaches infinity. A plot of J 6) vs 0 has the characteristics shown in Fig. 6-2a. 

Some data from plant operation, such as the number of trips or the numbers and values of variations in temperature and power, may be obtained not by the usual methods of surveillance such as monitoring, measuring and testing, but directly from the records of the plant operating history. This Safety Guide does not deal with such items however, it is recognized that the collection and evaluation of these data are of fundamental importance for the assessment of plant performance and residual lifetime. 

The durability of machines or their components is usually used by companies as an important criterion for strategic decisions having a great influence on the company results. According to the reliability literature, there are two main characteristics that can be used to estimate the best moment to take out a machine from service mean residual lifetime (MRL) and hazard rate (HR) (Reinertsen 1996, Smith 2007). When accurate operational data on the machine history are available, the hazard rate can be estimated and the critical point in the machine s lifetime can be determined. However, operational practice shows that the reliability point of view is only one of the points of view which should be taken into accotmt when the best machine lifetime limit is estimated Bhschke Murthy (2000), (DhUlon 1983). The other premises for such estimations can be described generally as ... 

The authors would like to thank Hans van der Weide at the Delft University of Technology for his helpful comments during the research for this paper. We also thank an anonymous reviewer for pointing out the fact that the recurrence rate t](x) is the reciprocal of the mean residual lifetime ... 

Assessment of reliability and residual lifetime of flexible risers subjected to time-varying corrosive environments... 

Lifetime extension implies analysis of the current state of main systems and components, determination of their residual lifetime, finding the items with expired lifetime and... 

The age a of a fluid (or solid) particle is defined as the time elapsed since it entered the reactor. Its life expectancy or residual lifetime X is the time it has still to spend before leaving the reactor. The residence time t = a + X is the age of the leaving particle in the outlet section. As the reactor contains particles with different histories, all these quantities are distributed. E(tg) is the RTD such that the fraction of leaving flow-rate Q containing particles with a residence time between tg and... 

There are some important assumptions that must be made in constructing the model. Firstly, once the equipment has degraded following one mode, it will follow that mode until it reaches the end of its life. There is hence no connection between the branches. The second assumption is that, the normal condition can last very long with no special characteristics in the measurement. We are interested in the deterioration process, with the purpose of assessing the deterioration level of equipment as well as predict its residual lifetime when it has suffered a problem. For this reason, the initial state can be assumed as a dummy state with no emission of observation. Each branch can therefore be seen as a single model and is assigned an a priori probability... 

Probabilistic methods can be used for the verification of existing structures, or for the assessment of their residual lifetime, when appropriate probabilistic models of the basic variables are known. General guidance for the probabilistic verification of structures including the models of basic variables is given in the JCSS Probabilistic Model Code (2001). 

Since we are in a case of simulated data, it is possible to compare the results obtained from the residual lifetime prognosis using the proposed approach with other classical approaches. The considered approaches are the following ... 

---