  Shock tube experiments, paired with precision laser diagnostics, are ideal
venues to provide kinetics data critically needed for the development,
validation and optimization of modern combustion kinetics models. However, to
design sensitive, accurate, feasible and information-rich experiments that may
yield such data often requires sophisticated planning. This study presents a
mathematical framework and quantitative approach to guide such experimental
design, namely a method to pin-point the optimal conditions for specific
experimentation under realistic constraints of the shock tubes and diagnostic
tools involved. For demonstration purpose, the current work is focused on a key
type of shock tube kinetic experiments -- direct determination of fundamental
reaction rate constants. Specifically, this study utilizes a Bayesian approach
to maximize the prior-posterior gain in Shannon information of the rate
constants to be inferred from the intended experiment. Example application of
this method to the experimental determination of the CH$_3$OH + H (k$_1$) and
CH$_2$O + H (k$_2$) rate constants is demonstrated in shock tube/laser
absorption studies of the CH$_3$OH pyrolysis system, yielding new recommended
rate constant expressions (over 1287 K - 1537 K) as: k$_1$ = $ 2.50 \times 10^6
(T/K)^{2.35} exp(-2975 K /T) \, cm^3mol^{-1}s^{-1} \pm 11.4\%$ and k$_2$ =
$7.06 \times 10^7 (T/K)^{1.9} exp(-1380 K/T) \, cm^3mol^{-1}s^{-1} \pm 9.7 \%$.
Potential extension to other types of kinetic studies, e.g. prediction of
combustion benchmarks such as ignition delay times and species yields, and
global uncertainty minimization of generic reaction models, are also briefly
discussed.
