5. PROFILE AND TRENDING ANALYSIS › 5.4 Analytic Technique Tutorial

5.4 Analytic Technique Tutorial

Profile and Trending Analysis analyzes historical series of
observations of data elements contained in the Capacity
Planning database.  Each historical data series is analyzed
to determine two compound growth rates:

o  Long-term Growth Rate:  The compound growth rate which, if
   applied to the first observation n times (where n is the
   number of time intervals between the first and last
   historical observations), yields the final observation in
   the series.

o  Short-term Growth Rate:  The compound growth rate which,
   if applied to the next to last observation n times (where
   n is the number of time intervals between the last two
   historical observations), yields the final observation in
   the series.  This value is defined as the short-term
   growth rate.  These growth rates provide a sense of
   direction for estimating future resource requirements
   (MOR81).

The formula for the compound rate of growth is shown in
Equation 1:

              _                  _
             |     (X(n) -  X(m)) |** (1/(n-m))
         g = | 1 + ______________ |            - 1    (Eqn 1)
             |_         X(m)     _|


     where: X(i) is the i-th observation of user-specified
            variable X.

            g     is the compound rate of growth.

            n     is the number of the last time interval
                  being used for the rate of growth
                  calculations.  (The time intervals are
                  numbered starting with the oldest
                  observations.)

            m     is the number of the previous time interval
                  being used for the calculations.

The formula calculates the j-th root of the percent change
between any two observations of X.  Therefore, if the growth
rate is multiplied by the first observation j times, the
result is equal to the final observation.

You can then develop a forecast on the next k observations
using either the long-term or short-term growth rate.  The
number of intervals to be forecast (k), and which growth rate
should be used for the calculations are specified via control
parameters on the Profile and Trending Analysis control
screen (see Figure 5-4).  The rationale for these selections
is discussed in Section 5.2, Usage Guidelines.

The formula used to calculate the future estimates is shown
in Equation 2:

                X(j+1) = X(j) * (1 + g)               (Eqn 2)

     where:  X(i) is  the  i-th observation of user-specified
                  variable X.

            g     is the compound rate of growth.

            j     is  the   last  known  or   estimated  time
                  interval.

            j+1   is  the  time interval being estimated from
                  the   previous  time   interval  using  the
                  compound rate of growth g.

The formula calculates each new observation by multiplying
the growth rate by the previous observation.  Although the
growth rate for any variable will not remain a constant, this
technique is valuable for determining a sense of direction
for the variables you specify.

The following example illustrates the application of the
compound growth rate methodology.  Typical data for monthly
CPU utilization values are shown below:


                       INTERVAL          CPU
              MONTH     NUMBER       UTILIZATION
             =======   ========      ===========
              JAN 97       1             54.3
              FEB 97       2             56.7
              MAR 97       3             55.8
              APR 97       4             58.0
              MAY 97       5             59.1
              JUN 97       6             60.9

Using Equation 1, The values for the first and last time
intervals (January and June 1997) were substituted to get the
following:

              _                  _
             |     (60.9 -  54.3) |** (1/(6-1))
         g = | 1 + ______________ |            - 1
             |_         54.3     _|


         g = 1.12 ** 0.2 - 1.0 = 1.02 - 1.0 = 0.02

Solving for the short-term rate of growth, you get the
following:

              _                  _
             |     (60.9 -  59.1) |** (1/(6-5))
         g = | 1 + ______________ |            - 1
             |_         59.1     _|


         g = 1.03 ** 1.0 - 1.0 = 1.03 - 1.0 = 0.03


Assuming that you want to estimate the future observation
using the long-term rate of growth, use Equation 2 to
estimate the value for July 1997:


                X(7) = 60.9 * (1 + 0.02) = 62.1

To estimate successive observations based on the previous
estimate and the rate of growth, reapply the equation.