This article focuses on the classification and estimation problems for several normal populations with the equality restriction on means, and the variances are ordered. First, we introduce new estimators for the common mean parameter that outperform existing estimators in terms of Pitman nearness criterion and stochastic domination when the variances are ordered. Secondly, we propose several plug-in type classification rules using these improved estimators. To compare the performance of the rules, we numerically calculate the expected probability of correct classification (EPC). The proposed classification rule performs better than existing ones in terms of EPC values. Finally, we apply these rules to a real-life dataset to assess their accuracy.