A study on inspection schemes in optimal design of control charts for deteriorating processes

The non-uniform inspection scheme obtained by the constant integrated hazard procedure overcomes the uniform scheme economically in optimal design of control charts. The comperative study is generalized in this paper to an optimization problem which looks for the optimal sampling points among all possible sampling schemes. The objective function is simplified here by modelling sequential time intervals as a family of functions of the first sampling interval, which also has been induced by the constant integrated hazard approach. The study demonstrates the model implementation through the economic design of and T²-Hotelling control charts, both under the two widely used process failure mechanisms, that is, Weibull and Chen distributions. A comprehensive numerical investigation illustrates the possibility of existence of sampling schemes which outperform the constant integrated hazard approach and emphasizes the necessity of further investigation into the solution procedure.