| The general problem of process design is considered when some of the required data are uncertain. The mean and variance of the output variable of interest is found by using a linear approximation to the process. The output variable is shown to be normally distributed with the calculated mean and variance. The probability of successful process performance, the dependability, is calculated using the known normality of the output variable. The dependability thus calculated was checked by Monte-Carlo simulation. The Monte-Carlo estimate of the process dependability agreed to within 5 percent of the approximate value. The dependability was used as a constraint in the optimization of a simple chemical process. The dependability was included in the objective function in the optimization of the ethylene process. Results show that traditional rule-of-thumb overdesign factors insure proper process performance, but at a higher cost than is required. The use of a stochastic optimization procedure is recommended for all process designs involving uncertain variables. |
