Worst case

An other worst case for the projection technique used is the ease if corrosion is on both sides of the wall in the double wall penetration. Then by the nature of the double wall penetration it is only possible to determine the integral material loss in the penetrating direction without any possibility to distinguish the side on which the erosion can be found. 

The nominal visibility level VL om was determined from the viewing conditions of indications as decribed in 2.2 (Fig. 1). Assuming that this VL o , is equivalent to the VL with nominal inspection parameters, for the worst case of any inspection parameter the relative reduction R of the visibility of the indications was determined and summarized to the overall visibility level VLmin. Naturally the following data may be varied and/or completed. 

Following the law of error propagation for independant values (root sum square ) in the worst case for the parameters mentioned above, the overall reduction of the visibility level will be Rvl = -0.55, that means VLmin = 0.45 VL om... 

Forward Analysis In this type of analysis, we are interested in the propagation of initial perturbations Sxq along the flow of (1), i.e., in the growth of the perturbations 5x t xo) = (xo -h Sxq) — xq. The condition number K,(t) may be defined as the worst case error propagation factor (cf. textbook [4]), so that, in first order perturbation analysis and with a suitable norm j ... 

In applications, one is often interested in approximating time averages over a time interval [0, T] via associated mean values of a , k = 1. ..Tfr. For T (or r) small enough, the above backward analysis may lead to much better error estimates than the worst case estimates of forward analysis. 

The complexity analysis shows that the load is evenly balanced among processors and therefore we should expect speedup close to P and efficiency close to 100%. There are however few extra terms in the expression of the time complexity (first order terms in TV), that exist because of the need to compute the next available row in the force matrix. These row allocations can be computed ahead of time and this overhead can be minimized. This is done in the next algorithm. Note that, the communication complexity is the worst case for all interconnection topologies, since simple broadcast and gather on distributed memory parallel systems are assumed. 

In the worst case, the backtracking algorithm will form a search tree of depth n, where n is the number of atoms in the query graph. Also, in this case a separate sub-tree search process for each atom of the target graph will be initiated. That is why the linear multiplier m is apphed to Eq. (7). 

The system considered in this example was chosen for convenience, not as either a best or worst case example. Eyring and co-workers have published numerous examples in which the theory (slightly modified) fits experimental data quite well. 

The subsequent step is to identify the various scenarios which could cause loss of control of the hazard and result in an accident. This is perhaps the most difficult step in the procedure. Many accidents have been the result of improper characterization of the accident scenarios. For a reasonably complex chemical process, there might exist dozens, or even hundreds, of scenarios for each hazard. The essential part of the analysis is to select the scenarios which are deemed credible and worst case. 

The ha2ard assessment is to iaclude identification of a worst-case scenario and other more likely scenarios for release of a regulated substance, and analy2e the off-site consequences of such releases. The release and consequence assessment is to iaclude the rate, duration, and quantity of the release, the distances for exposure or damage (usiag atmospheric, called "F" stabiUty and a 1.5-m/s wiad, and most-often-occurriag conditions), populations that could be exposed, and environmental damage that could be expected. 

Comparison of these environmental compartment concentrations with the actual measurements made at a variety of locations show reasonable agreement but indicate that emission estimates are rather high. It is likely that the fault Hes with worst case estimates for losses from outdoor appHcations and the washing of PVC flooring. In addition a large proportion of the phthalates lost by these routes will not enter rivers because they will be removed by wastewater treatment plants. 

The documented occurrence of pesticides in surface water is indicative that mnoff is an important pathway for transport of pesticide away from the site of appHcation. An estimated 160 t of atra2ine, 71 t of sima2ine, 56 t of metolachlor, and 18 t of alachlor enter the Gulf of Mexico from the Mississippi River annually as the result of mnoff (47). Field appHcation of pesticides inevitably leads to pesticide contamination of surface mnoff water unless mnoff does not occur while pesticide residues remain on the surface of the soil. The amount of pesticides transported in a field in mnoff varies from site to site. It is controUed by the timing of mnoff events, pesticide formulation, physical—chemical properties of the pesticide, and properties of the soil surface (48). Under worst-case conditions, 10% or more of the appHed pesticide can leave the edge of the field where it was appHed. 

Pitch Control. Resinous constituents of wood cause problems in paper machines by sticking to the rollers and causing spots or holes in the paper the worst cases cause paper webs to mpture. Costly stoppages, wastages, and quaUty problems because of these resinous substances can be avoided by using Upases (84). 

Determine the worst-case gas mixture combustion charac teris-tics, system pressure, and permissible pressure drop across the arrester, to help select the most appropriate element design. Not only does element design impac t pressure drop, but the rate of blockage due to particle impact, liquid condensation, and chemical reaction (such as monomer polymerization) can make some designs impractical even if in-service and out-of-seivdce arresters are provided in parallel. 

Endurance Burn Under certain cou(itious, a successfully arrested flame may stabilize on the unprotected side of an arrester element. Should this condition not be corrected, the flame will eventually penetrate the arrester as the channels become hot. An endurance burn time can be determined by testing, which specifies that the arrester has withstood a stabilized flame without penetration for a given period. The test should address either the actual or worst-case geometry, since heat transfer to the element will depend on whether the flame stabilizes on the top, bottom, or horizontal face. In general, the endurance burn time identified by test should not be regarded as an accurate measure of the time available to take remedial action, since test conditions will not necessarily approximate the worst possible practical case. Temperature sensors may be incorporated at the arrester to indicate a stabilized flame condition and either alarm or initiate appropriate action, such as valve closure. 

An engineering evaluation should then be made of the worst-case... 

It is important to note that the worst case should be something that is reahstic, not something that is conceivable but extremely unlikely. The Dow Chemical Company has adopted the following philosophy for design scenarios in terms of independent causative effects ... 

For any proposed suppression system design, it is necessary to ascribe with confidence an effective worst-case suppressed maximum explosion overpressure Pred.max- Provided that the suppressed explosion overpressure is less than the process equipment pressure shoclc resistance and provided further that this projected suppression is achieved with a sufficient margin of safety, explosion protection security is assured. These two criteria are mutually independent, but both must be satisfied if a suppression system is to be deployed to provide industrial explosion protection. 

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