A Warning Zone Method for the Multiperiod Cost Variance Investigation Problem
提出一种预警区方法，帮助管理者在多期过程中根据成本差异推断过程状态并决定是否调查，相比最优贝叶斯方法更简单，且能捕获大部分成本节约。
ABSTRACT This paper develops a warning zone approach to make variance investigation decisions for a multiperiod process. The assumed cost generation process varies between an in‐control and out‐of‐control state. These states cannot be directly observed, but must be inferred from the reported cost variances. Using the warning zone method of inference, the manager investigates the process whenever an upper threshold is exceeded or a lower threshold is exceeded for two consecutive periods. A four‐state Markov chain models the resulting decision process. Steady state probabilities are derived for this chain and are used to obtain explicit formulas for the effectiveness and efficiency of the decision process. These formulas permit computation of the cost savings attainable by the warning zone method. Compared to other decision rules, the warning zone method is much simpler than the theoretically optimal Bayesian revision method, but uses more information than the Markovian control limit method. Numerical comparison of results shows that the warning zone method usually captures most of the available cost savings, even in cases where the Markovian control limit method does not perform well.