Page 240 - Mechanical Engineers' Handbook (Volume 2)

6 Data Display and Reporting 229

2 h at 15:00, the starting point on a trend line would be 13:00 and the ending point would
be 15:00. Ten minutes later the starting point on the trend line would be 13:10 and the
ending point would be 15:10.
For relational data, there is often a desired time frame as described above (to restrict
the size of the data to be searched) and some selection criteria based on characteristics of
the data itself or of related data, including events. For example, one may wish to find those
manufactured units for the past month that were for product X and see how many had quality
defects. As described above under third-party data acquisition systems, there are techniques
for selecting data from process history databases that approach (but do not equal) relational
capability.

Representation of Historical Data
The primary difference between current data and historical data is that there are multiple
data points, normally with an order defined by the time they were acquired (for process
history data) and/or by their relationship to other variables and events (for relational data).
Once the time frame and relationships are selected, the data must have some method of
representation on a display.
Historical data have a number of potential representation techniques. Multiple data val-
ues can be combined into a single number such as average, standard deviation, mode, max-
imum, minimum, range, variance, and so on. These can then be represented by techniques
for individual data elements as described above. The equations in Section 4.4 are examples
of summary statistics formulas.
The simplest form to represent historical data is the list. Create a column for each
variable of interest. If they are all collected at the same time (the ‘‘records’’ described above),
then each time data were collected can be used as the first value on the left in each row.
The data for each variable of interest can be placed on the row corresponding to its time
stamp, similar to that for files shown in Table 4.
Where data were collected with different time stamps, a new row can be created when-
ever a new value is obtained and values only placed in the column–row combinations where
there is a corresponding time stamp between the row’s time stamp and the time stamp of
the variable in question. While useful, the problem with this is that there are now holes in
the data. This list is very useful when viewing a trend line or graphical tool to validate
numbers, to verify time stamps, and diagnose problems with collection.
Often, one desires to view the relationships between data and time or other variables.
Trend plots typically are used to show the relationship between variables and time. The X
axis is typically represents the time range and the Y axis represents the value of the desired
variable. The range of data on the Y axis can vary depending on how one wishes to view
the data. The maximum and minimum of the data can be used to set the top and bottom of
the range of the Y axis, respectively. This can have two undesired effects. It may make small
movements in data appear to be very large when the range is small. In cases where there
are spikes in the data where a value is disproportionately high or low, representing the Y
axis based on the maximum and minimum could make it difficult to view normal variation
in the data. One has to understand the potential use of the data to choose the Y-axis scale
appropriately.
When more than one variable is shown on a trend chart, the selection of scale of the Y
axis becomes more complex. If all the variables are representative of the same domain, such
as all temperatures, then perhaps the same Y axis can be used for all of them. Often, however,
the viewer is attempting to compare relative variations in data, sort of a poor man’s corre-
lation analysis. In this case it may be useful to have multiple Y axes and select the range of