Decision dependent stochastic processes

• A new Bayesian inferencing method for decision dependency in a stochastic process.
• Real world examples provided using preventive and corrective maintenance in a nuclear power plant.
• A stochastic optimization problem is solved using the decision dependent probability distribution inferences.

Managers, typically, are unaware of the significant impact their decisions could have on the random mechanism driving a data generating process. Here, a new parametric Bayesian technique is introduced that would allow managers to obtain an estimate of the impact of their decisions on the stochastic process driving the data; this, in turn, should enhance a company’s overall decision-making capabilities. This general approach to modeling decision-dependency is carried out via an efficient Markov chain Monte Carlo method. A simulated example, and a real-life example, using historical maintenance and failure time data from a system at the South Texas Project Nuclear Operating Company, exemplifies the paper’s theoretical contributions. Conclusive evidence of decision dependence in the failure time distribution is reported, which in turn points to an optimal maintenance policy that results in potentially large financial savings to the Texas-based company.