ABSTRACTAlthough models of the multiperiod cost variance investigation decision problem have been extensively analyzed, their implementation is hindered by the manager's lack of knowledge of parameter values essential to determining the optimal investigation strategy. This paper develops a minimax approach to determine a reasonable investigation strategy, even without knowledge of certain parameters. Specifically, the Dittman‐Prakash Markovian variance investigation model is modified to allow specification of a suitable strategy when neither the probability of staying in the in‐control state nor the expected cost for the out‐of‐control state is known. An objective function based on controllable costs is derived and a solution technique for the resulting minimax problem is developed. Numerical results indicate that the inherently robust minimax approach captures most of the cost savings available from methods that place greater input demands on the