Research On Statistical Process Control For Small Batch Production With Bayesian Method

The main characteristic in small batch production is the lack of process information, and we cannot use them to control process quality in it because that the traditional statistical techniques of SPC are applicable to the continuous and mass production. In this paper, we does the research on statistical process control based on the Bayesian theory, and proposes the Bayesian control charts and the Bayesian process capability index to solve the problem that the effective quality control model cannot be established because of less samples in the small batch production environment.Generally, the quality characteristics of the products which are made from one production line or under the same production condition with the same standards conform to the normal distribution when the process is in control, and also the prior and posterior information of the products conforms to the normal distribution. Based on the above assumption, we use the Bayesian theory to deduce iterative computational equations for the mean, the range, and the standard deviation from which we calculate the control chart lines, the process capability index and the nonconforming rate. In the empirical part, on the one hand, We use Matlab to compare the difference between the Shewhart method and the Bayesian method. The result shows that the Bayesian control chart lines are closer to the theoretical values than the Shewhart control chart lines with the inspection batches gradually increasing. On the other hand, we use the Bayesian method and the traditional method to calculate the process capability index and nonconforming rate of the small-batch production process of a electronics company. By comparing the standardization of the process capability and nonconforming rate, it shows that with the inspection batches gradually increasing, the process capability index calculated by the traditional method is between 1.33 and 1.67, and the process capability is in good condition;while the process capability index calculated by the Bayesian method is less than 1.33,the process line is warning. Also, the nonconforming rate calculated by the Bayesian method is much bigger than the one calculated by the traditional method. So using the Bayesian method to analyze the process capability can forewarn the production of nonconforming more accurately, and it is more reliable and more effective than traditional SPC.