This example was artificially created to make the point. There is no real construction activity that is truly uniformly distributed, let alone showing two perfectly adjacent and equally sized uniform distributions on successive days. With real data that is not homogeneous, and that may have been collected in several batches, it may be very difficult to make a judgment by looking at an ordered plot of the observations or a scatter diagram. Sometimes the engineer, due to an understanding of what is being observed, will group the data ahead of time. Maio et al. 2000, for example, group truck travel times into several categories according to haul distance and weight before fitting distributions to each. However, often, the engineer will not know if the data are homogeneous. In these cases, the Kruskal-Wallis hypothesis test for homogeneity Law and Kelton 2000 can be used to determine if two or more separately collected sets of data can be treated as homogenous and combined to determine a single distribution. If separately collected data sets are not homogenous, then this is an indication that the conditions under which at least one of the
data sets was collected differs from the others. If this happens, different conditional distributions should be determined for each set. Furthermore, the different conditions need to be understood and modeled. The artificial example used earlier, for example, can be modeled by some process that at the start of each day samples from a distribution to indicate good weather or bad weather and for simplicity we are assuming here that weather is discrete and can only be either good or bad. The time for the loading activity can then be specified as conditional on the weather e.g., Uniform1,2 given that weather is good, Uniform2,3 given that weather is bad.
This example was artificially created to make the point. There is no real construction activity that is truly uniformly distributed, let alone showing two perfectly adjacent and equally sized uniform distributions on successive days. With real data that is not homogeneous, and that may have been collected in several batches, it may be very difficult to make a judgment by looking at an ordered plot of the observations or a scatter diagram. Sometimes the engineer, due to an understanding of what is being observed, will group the data ahead of time. Maio et al. 2000, for example, group truck travel times into several categories according to haul distance and weight before fitting distributions to each. However, often, the engineer will not know if the data are homogeneous. In these cases, the Kruskal-Wallis hypothesis test for homogeneity Law and Kelton 2000 can be used to determine if two or more separately collected sets of data can be treated as homogenous and combined to determine a single distribution. If separately collected data sets are not homogenous, then this is an indication that the conditions under which at least one of thedata sets was collected differs from the others. If this happens, different conditional distributions should be determined for each set. Furthermore, the different conditions need to be understood and modeled. The artificial example used earlier, for example, can be modeled by some process that at the start of each day samples from a distribution to indicate good weather or bad weather and for simplicity we are assuming here that weather is discrete and can only be either good or bad. The time for the loading activity can then be specified as conditional on the weather e.g., Uniform1,2 given that weather is good, Uniform2,3 given that weather is bad.
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