Abstract


Within the production and manufacturing environment, statistical process control (SPC) is a widely used tool to maintain quality of the manufactured products. Within the SPC, the control charts have been the object of numerous investigations, all aimed to increase the effectiveness of them. This is because the classical Shewhart X¯ and Shewhart S control charts, although they are widely used; they have the disadvantage of its limited effectiveness in detecting small or moderate changes in the mean and the standard deviation of the process respectively.

To try to mitigate this difficulty, several authors have proposed many alternatives for the above control charts. Among the most outstanding ones that one can find are the control charts with run rules, EWMA and CUSUM control charts, variable sample sizes and variable sampling interval control charts, synthetic control charts, etc.

In the actual doctoral thesis two new control charts are being studied, characterized and optimized. The first one is the X¯-RL2 control chart that combines the Shewhart X¯ control chart with a RL2 control chart. The second one is the S-RL2 control Chart that combines the Shewhart S control chart with a RL2 control chart. With these newly developed control charts the power of the classical X¯ and S control charts (proposed by Dr. Walter Shewhart for certain sample sizes and magnitudes of change established design) can be enhanced. Likewise, the X¯ -RL2 and the S-RL2 control charts showed a better performance in comparison with the synthetic control charts for certain parameters design.

In addition, the effectiveness of X¯ -RL2 control charts is compared with the effectiveness of control charts with run rules, CUSUM and EWMA control charts. Correspondingly, the performance of the S-RL2 control chart is compared to CUSUM S and EWMA S control charts, with beneficial results in some cases.
 
All comparisons were performed on the zero-state scenario using the ARL measure (Average Run Length), The ARL is defined as the average of points on a control chart until a one point plots out of control. Computer simulations were performed to verify the results.