Control chart for exponential individual samples with adaptive sampling interval method based on economic statistical design: an extension of costa and Rahim’s model

In this paper, an economic statistical design for individual samples of quality characteristics which have Exponential distributions presented with variable sampling method. To do this, first the Exponential distribution is transformed to a Normal distribution Using Nelson's approximation, then using Costa and Rahim’s economic model, an economic statistical design is obtained for the transformed data. The transition probability matrix and the economic and statistical parameters are formulated. Optimal design parameters (sampling interval, warning and control limits) are determined using Artificial Bee Colony algorithm and a sensitivity study is done for various values of the model parameters. Based on the results, the mentioned method in compared with the fixed ratio sampling method is more effective when a moderate shift occurs. A simulated example is given also to illustrate the proposed design.