A self-starting statistical control chart methodology for data exhibiting linear trend

Quality goods and services are highly valued by today’s consumer and companies that do not meet their quality expectations will suffer financially and lose customer loyalty. Therefore, it is in the best interest of the company to ensure that as many of their goods are of satisfactory quality as possible. The meaning of quality goods and services is well known but how do we ensure a process has the ability to consistently output a quality product. The answer lies in monitoring the process based on its statistical measures and quality control charts help us do just that.

Quality control charts help us define quality both mathematically and visually by charting a quantity of interest such as the mean value of a quality characteristic of the process. We estimate the mean and standard deviation of such a quality characteristic by collecting a sufficient amount of data from the process when it is said to be in-control. After gathering these estimates we have a baseline for which we can compare our future process observations against. We can then make a determination of the state of the process based on the number of standard deviations an observation lies from our in-control state. If we determine the process has deviated significantly from its in-control state, the engineer can take corrective action to resolve the quality issues.

Unfortunately, the time and effort taken to get enough observations up front to properly estimate the in-control parameters can prove to be difficult and costly. So the charting technique we propose has a self-starting property in which charting can begin at the start of a production run which helps to reduce the cost and time commitment taken to estimate the in-control process parameters. In addition, traditional control charts have another limitation in that they are limited to the case in which the quality characteristic of interest has a stable mean. However, in many processes such as a degradation or deterioration process this mean is not stable and is instead approximated with a linear trend. Traditional control charts would signal immediately because they are designed for stable means, so we propose three methods that will effectively monitor deviations from a linear trend. Lastly, another problem we have encountered with traditional self-starting charts is that our in-control parameter estimates can be contaminated with out of control observations. Therefore, we introduce a delay parameter to our statistic that minimizes the in-control state contamination. In order to monitor the performance of such a process it is our desire to develop a chart that can detect in-control and out of control linear trend which we accomplished by applying linear regression results to a self-starting control chart statistic.