Integration of production quantity and control chart design in automotive manufacturing

Joint determination of control limit and production quantity is modeled in p-chart.Sample average approximation is used to solve stochastic programming model.Magnitude of shift on defect rate increases the production quantity and cost.Process variance insignificantly affect control limit.Special cause occurrences significantly affect total cost. This study presents a two-stage stochastic programming model for the determination of control limits in p-charts when a production process produces above a certain quantity. Consideration of production quantity needed along with control limit determination is important for the following competing two reasons: (1) Wider control limits make it difficult to detect the changes in the process, therefore producing excessive number of cars with paint defects. (2) Narrower control limits, on the other hand, increase the number of unnecessary interventions even if there is no deterioration in the process so that inspection costs increase. In both cases, quantity produced reduces due to defective products and unnecessary interventions. Therefore, it is important to design a control chart for proportion of defects that takes production quantity requirements into account. We consider the problem in an automotive manufacturing setting in which the cars are inspected for paint defects after paint operations.We formulate the problem as a two-stage stochastic programming model. In the first stage, control limit parameter k is decided for the p-chart and in the second stage, production quantity is determined that minimizes total quality-related and production costs. We solve the model by sample average approximation algorithm (SAA). In a numerical study, we investigate the effect of various factors on control limit parameter k and the total cost. Our numerical study shows that (i) an increase on the mean defect rate increases both the total cost and the total production quantity, (ii) effect of an increasing process variance to the control limit parameter k is significantly small, (iii) frequency of special cause occurrences affects the total cost significantly and (iv) all the experiments show that the commonly used 3 ź control limits in practice are wider than required.