Worst case analysis

Stress calculations, fault tree analysis, failure modes analysis, and worst case analysis... 

Worst-case analysis based on the DSC data, namely, the test with the lowest onset temperature, resulted in a graph showing the relationship between initial temperature and time-to-maximum rate under adiabatic conditions. For an initial temperature of 170°C, it would take 2 hours to reach the maximum rate. Venting simulation tests were undertaken on a larger scale to detect safe venting requirements for the separator and for the MNB hold tank. Several vent sizes were tested. It was found that a 10-cm rupture disc with a burst pressure 1 bar above the operating pressure was adequate. 

Hazard assessment worst-case analysis five-year accident history. 

The crudest form of bounding analysis is just interval arithmetic (Moore 1966 Neumaier 1990). In this approach the uncertainty about each quantity is reduced to a pair of numbers, an upper bound and a lower bound, that circumscribe all the possible values of the quantity. In the analysis, these numbers are combined in such a way to obtain sure bounds on the resulting value. Formally, this is equivalent to a worst case analysis (which tries to do the same thing with only 1 extreme value per quantity). The limitations of such analyses are well known. Both interval arithmetic and any simple worst case analysis... 

Probability theory is, of conrse, designed precisely to estimate these chances. Becanse of this, probabilistic assessment is regarded by many as the heir apparent to worst case analysis. However, traditional applications of probability theory also have some severe limitations. As it is used in risk assessments today, probability theory... 

The Monte Carlo analyses are used to observe how device tolerances can affect a design. There are two analyses that can be performed. The Worst Case analysis is used to find the maximum or minimum value of a parameter given device tolerances. Device tolerances are varied to their maximum or minimum limits such that the maximum or minimum of the specified parameter is found. The Monte Carlo analysis is used to find production yield. If the Worst Case analysis shows that not all designs will pass a specific criterion, the Monte Carlo analysis can be used to estimate what percentage will pass. The Monte Carlo analysis varies device parameters within the specified tolerance. The analysis randomly picks a value for each device that has tolerance and simulates the circuit using the random values. A specified output can be observed. 

We must also set up the Worst Case analysis. Click the LEFT mouse button on Carlo/Worst Case button. This will enable the analysis and display its settings ... 

The results of the Worst Case analysis are saved in the output file. Select PSpice and then View Output File from the Capture menu bar. The results are given at the bottom of the output file. 

The simulation says that the maximum value is. 5188, which is less than the expected value. Remember that for the resistor with the 5% Gaussian distribution, the standard deviation was 1.25%, and the absolute limits on the distribution were 4o = 5%. In the Worst Case analysis, a device with a Gaussian distribution is varied by only 3cr. Had we calculated the maximum value with a 3.75% resistor variation, we would have come up with a maximum gain of 0.51875, which agrees with the PSpice result. To obtain the worst case limits, I prefer to use the uniform distribution. Type CTRL-F4 to close the output file and display the schematic. 

Change both resistors to R5pcnt and then run PSpice. The results will again be stored in the output file. At the end of the output file you will see the results of the Worst Case analysis ... 

The Monte Carlo analysis is used to answer the question, What percentage of my circuits will achieve or exceed my specifications Usually you would run a Worst Case analysis to see if all of the circuits pass the specifications. If they all pass, there is no need to run the Monte Carlo analysis. If they do not all pass, the Monte Carlo analysis is used to estimate what percentage of the circuits will pass. 

The dialog box is set up to simulate the circuit at Vcc = 15 V. This was already specified in the circuit and appears to be redundant. It must be specified because the Worst Case analysis must run in conjunction with an AC Sweep, a DC Sweep, or a Transient Analysis. Since we are interested in the DC collector current we must set up a DC Sweep. 

When biasing a BJT, we are also interested in the collector to emitter voltage, V g The minimum or maximum value of Vq can also be easily found using the Worst Case analysis. We can use the same setup that was used to find the collector current. All we have to do is modify the Monte CarlO/WorSt Case settings. Fill in the dialog boxes as shown below ... 

Next we need to set up the Worst Case analysis. Fill in the Monte CarloA/Vorst Case dialog boxes as shown... 

To find the minimum and maximum of a quantity, you will have to run the Worst Case analysis four times. To find the maximum of the quantity, you will have to run die simulation once with the jMAX model and once with the jMIN model. To find the minimum of the quantity, you will also have to run the simulation once with the jMAX model and once with the jMIN model. If you happen to know which of the two models will give you the maximum or minimum of the quantity you are looking for, you may be able to reduce the number of simulations. 

The Worst Case analysis determines the absolute maximum or minimum value of a parameter for given component tolerances. 

If the Worst Case analysis determines that not all circuits will pass a specified performance parameter, the Monte Carlo analysis may be used to estimate what percentage of the circuits will pass. 

The uniform distribution is the easiest to use for the Worst Case analysis since this distribution specifies the upper and lower limits of a component s tolerance. 

The Performance Analysis can be used together with the Monte Carlo analysis to display a histogram. The histogram will display properties such as minimum and maximum values of an output versus random variations. The Performance Analysis can find the minimum and maximum values of quantities not available with the Worst Case analysis, such as bandwidth and rise time. 

Section 6.7 presents the Generalized Outer Approximation GOA approach. After a brief discussion on the problem formulation, the primal and master subproblem formulations are developed, and the GOA algorithm is stated in section 6.7.4. In Section 6.7.5, the worst case analysis of GOA is discussed, while in section 6.7.6 the Generalized Outer Approximation with exact Penalty GOA/EP and its finite convergence are discussed. 

The maximum value for 62 3 is obtained for CA equal to zero, thus < 2 3 is largest for very low effectiveness factors and in the center of the catalyst pellet. Substituting CA = 0 for a worst case analysis gives... 

Average-case analysis The analysis of Lemma 3 is a worst-case analysis and there are instances which achieve actually require 2r — 1 sets. However, it is a bit pessimistic in the sense that it ignores the fact that a chain of nodes of outdegree 1 in ST R,) may consist only of the end point, in which case no subset is generated. This corresponds to the case where vi = Vi or Vr = vj in Step 2. Suppose that the revoked set 7Z is selected at random Ifom all subsets of cardinality r of Af, then what is the expected number of subsets generated The question is how many outdegree 1 chains are empty (i.e. contain only one point). We can bound it from above as follows consider any chain for which it is known that there are k members beneath it. Then the probability that the chain is not empty is at most For any 1 < k < r there can be at... 

In order to determine critical control parameters and their unit operations, constraint analysis techniques followed by fractional factorial designs (Table 4) are used to challenge the tentative control limits (so-called worst-case analysis) established for the process at this intermediate stage. Time and effort spent to qualify the process at the lOX stage often simplifies the work that follows during stages III and IV. 

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