Research On The Statistical-economic Design Of VSSI-T~2Control Chart

Control chart is important to statistical process quality control and its mainfunction is to give an alarm to the factors and make sure the process to be in control,so the manufacturing quality of the products can be ensured. As the development ofthe technology, the variety of the costomer’s demand and more than one factoraffecting the product quality, the multi-variable quality control charts are more andmore important. The standards of evaluating the control charts are usually statisticalcharacteristic and economic characteristic. And the researches of statisticalcharacteristic are more than economic characteristic, which consider the cost ofquality control and the income of correcting the assignable cause and then make surethe least cost or the most profit.This article aims to traditional multi-variable control chart, which isn’t sensitiveenough to abnormal factors of the process of production. Based on sampling strategyof VSSI (Variable from the size and interval, VSSI for short), the economic designand the statistical-economic design are studied and the models are established. Theapplication of the models is verified through the example of vehicle welding.The main researches of this article are the following.（1） VSSI-T~2statistical performance is studied and compared with MEWMA.Markov chain method is applied to calculate Average Time to Signal (ATS for short),which is statistical evaluation index of VSSI-T~2control chart. Then at the samecondition of expected sample interval and sample number, the statistical performanceof VSSI-T~2and MEWMA control chart is compared. The results show that thestatistical properties are affected by the markov distance.（2） VSSI-T~2economic performance is studied. Quality loss function isestablished through parameter combination of sampling interval, sampling sizeandcontrol limits, and then particle swarm algorithm is used to solve the optimaleconomic model. Compared with the traditional T~2control chart, VSSI-T~2alwayshas a better economy and improved its corresponding statistical property as well.Lastly, the estimated delta, hourly income of in-control state and hourly income ofout-of-control state are studied and the result shows that the applicability of theeconomy model is good.（3） The economic-statistical design of VSSI-T~2is studied. Its statistical constraint is set according to statistical items of fixed sampling strategy. Besides, theinitial vector is changed according to actual production situation. To solve this model,penalty function is introduced to particle swarm algorithm. The results show thatcompared with the economic design, the number of false alarm reduces greatly whichmakes the production process smoother. Lastly, the estimated delta, hourly income ofin-control state and hourly income of out-of-control state are studied. The resultshows that the applicability of the model is stronger.