I would like to create a model that can increase Availability via preventative maintenance. My current model decreases the availability when I include preventative maintenance. Can you suggest a way to enhance the model so that certain cases of preventative maintenance increase the availability in relation to the no preventative maintenance case?
Consider the formula of Acheived availability ($A_i$): $$A_i = \frac{MTBM}{MTBM + \bar M}$$
With
$$MTBM = \frac{1}{\frac{1}{MTBM_{cm}} + \frac{1}{MTBM_{pm}}}$$
$$ \bar M = \frac{\lambda * \bar M_{CM} + f * \bar M_{PM}}{\lambda + f} $$
$$ \bar M_{PM} =\frac{\sum_j f_j * M_j}{\sum_j f_j} $$
Now for a toy example...
$MTBM_{CM} = MTBF = 12345 $ hours
$\lambda = \frac{1}{MTBM_{CM}} = \frac{1}{12345} = 8.1 *10^{-5}$
$\bar M_{CM} = MTTR = 8$ hours
$MTBM_{PM} = 720 $ hours (Once a month)
$ f = \frac{1}{MTBM_{PM}} = \frac{1}{720} = 1.389 * 10^{-3}$
$\bar M_{PM} = 1 $ hour
Look at the case for no preventative maintenance:
$MTBM = \frac{1}{\frac{1}{MTBM_{cm}} + 0 } = MTBM_{CM} = 12345 $
e.g. set $MTBM_{PM}$ to infinity since it never happens
$\bar M = \frac{8.1 * 10^{-5} * 8 + 0}{8.1 * 10^{-5} + 0} = 8$
$A_i = \frac{12345}{12345 + 8} = 99.935$ %
Now, if I include preventative maintenance, the availability goes down.
$MTBM = \frac{1}{\frac{1}{12345} + \frac{1}{720}} = 680.32 $ hours
$\bar M = \frac{8.1 *10^{-5} * 8 + 1.389 * 10^{-3} * 1}{8.1 *10^{-5} + 1.389 * 10^{-3}} = 1.39 $ hours
$A_i = \frac{680.32}{680.32 + 1.39} = 99.79$ %
Any ideas on how to show preventative maintenance to be worthwhile? For example, a method to increase MTBF based on preventative maintenance?