Engineering statistics random variables

For certain types of stochastic or random-variable problems, the sequence of events may be of particular importance. Statistical information about expected values or moments obtained from plant experimental data alone may not be sufficient to describe the process completely. In these cases, computet simulations with known statistical iaputs may be the only satisfactory way of providing the necessary information. These problems ate more likely to arise with discrete manufactuting systems or solids-handling systems rather than the continuous fluid-flow systems usually encountered ia chemical engineering studies. However, there ate numerous situations for such stochastic events or data ia process iadustries (7—10). 

Haugen, E. B. 1982b Modern Statistical Materials Selection - Part 2 Random Variables and Reliability. Materials Engineering, 96, August, 49-51. 

Accurate estimates of the Probability Density Functions (PDFs) of random variables require large amount of data. However, in most engineering cases, the number of samples that can be obtained is ex-tremely limited, sometimes even cannot obtained. So the traditional probabihty statistical method is no longer apphcable. In such circumstances, Bayesian inference method offers a workable solution, and... 

In engineering calculations, it can be important to determine how uncertainties in independent variables (or inputs) lead to even larger uncertainties in dependent variables (or outputs). This analysis is referred to as error analysis. Due to the uncertainties associated with input variables, they are considered to be random variables. The uncertainties can be attributed to imperfect measurements or uncertainties in unmeasured input variables. Error analysis is based on the statistical concepts of means and variances, considered in the previous section. 

Engineers are often faced with the problem of using a set of data to calculate quantities that they hope will describe the behavior of the process from which the data were taken. Because the measured process variable may be subject to random fluctuations as well as to random errors of measurement, the engineers calculated estimate is subject to error, but how much Here is where the method of statistical estimation can help. 

The mean and the standard deviation ofa set of data are statistics of primary importance in all types of science and engineering. The mean is important because it usually provides the best esiimaic of the variable of interest. The standard deviation of the mean is equally important because it provides information about the precision and thus the random error associated with the measurement. 

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