Optimization of on-line quality control

A manufacturing firm experiences problems in its process that change the product quality characteristic. When measuring the product quality characteristic and adjusting the process, errors may be made that result in further problems. A process quality control strategy should address these errors.; A procedure has been developed to determine the optimal control limits of the production process when the product quality characteristic is continuous with a sudden shift in its level value. The procedure uses the loss function and Markov theory to derive a long-run expected total cost model or equation of the production process. The optimal control limit is computed by taking the first derivative of the model and setting it to zero. The application of the procedure was illustrated with an example. The procedure has been compared with the traditional x-chart; the comparison shows that this procedure's expected cost per part value is smaller than that of the traditional x-chart.; Another procedure has also been developed for deciding whether the production process is stopped and the adjustment to the process is performed, or if the production process is continued. In this case, the product quality characteristic is also assumed to be continuous with a gradual linear shift in its level value. The procedure uses the least square method for updating some of the parameters. For each batch, the loss function is also used to derive the cost model. Some factors were also considered in deriving the model. The process is stopped and an adjustment is performed if the total expected future cost is bigger than the initial cost in addition to the adjustment cost and the cost due to inspection lag. The application of the procedure is illustrated by performing the process simulation. This procedure has also been compared with the trended x-chart. The comparison also shows that this procedure has a smaller expected cost per part value than the trended x-chart.