worksheet computes and displays the n-step transition
matrix. The Start button sets the matrix to equal
the transition matrix defined on the Matrix worksheet.
button, provides subsequent transition matrices.
The example below shows the transition matrix for the first
three months of the light bulb case. The 1-step
matrix is the transition matrix given in the original model.
The 2-step matrix is the square of the 1-step matrix. The
k+1 step matrix is produced by multiplying
the k-step transition
matrix by the 1-step transition matrix. The information
is colored green because it is computed by a VBA algorithm.
To illustrate the meaning
of the matrix contents, consider the 3-step matrix. An
entry in row i column j gives the probability
of a transition from state i to state j in
three steps. For example, the
row for 2-mo. gives the probability distribution for
the age of the bulb at some location, given that the
bulb was 2 months old at the location at the beginning
of a three month period.