Statistical and economic design of regression control chart : a comparative study with Shewhart control chart

Statistical process control is one of the greatest technological developments of twentieth century because it is easy to use, based on sound principles, has significant impact and is flexible. Statistical Process Control (SPC) concepts and methods have become very important in the manufacturing and process industries. Control charts are the simplest type of online statistical process control procedure. There are different types of control charts are available each of which performs best for a particular kind of data. Today, Shewhart charts are most commonly used. However other types of charts such as CUMSUM, EWMA, MA etc are also getting popularized. There is so much work done with respect to these types of charts. The main motivation of this thesis was to do something simple and unique. This thesis work is inspired from work done by B.J. Mandal (1969). In Service and Manufacturing contexts, situations arise in which a manager does not want to use a statistical process control chart that simply tracks a single variable over time. Instead, the manager may wish to monitor the relationship between two key variables and be able to identify unusual changes in the relationship. The goal of this thesis is to combine traditional control chart techniques and regression. Linear regression and control chart theory are combined to yield an effective techniques for controlling two variables at same time. This combination is referred as “Regression Control chart”. The model is developed for Regression control chart and the proposed model is tested with the simulated data. In order to have the more control on the Model, different scenarios are simulated and average behaviour of the chart is found with different scenarios and repeating the procedure in order to get stable result. The Economic design for regression control chart is also proposed. Sensitivity analysis is performed for cost, for Regression control chart with different R2 values, by including large and small error while simulating Y variable. The Regression Control chart proves good in every scenario. With the help of this chart, we can monitor two variables at the same time and thus save money and time for charting another variable separately. This chart can be used for industrial processes where we want to monitor two variables which has some correlation between them.