Performance criteria for control charts
Open Access
- Author:
- Wang, Wei
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 21, 2013
- Committee Members:
- Dennis Kon Jin Lin, Dissertation Advisor/Co-Advisor
Dennis Kon Jin Lin, Committee Chair/Co-Chair
Le Bao, Committee Member
Murali Haran, Committee Member
Russell Richard Barton, Special Member - Keywords:
- Average Run Length
Continuous Ranked Probability Score
Functional data
Goodness-of-fit
Paired Comparison. - Abstract:
- % Place abstract below. Within the manufacturing process, Statistical Process Control (SPC) is a powerful collection of problem-solving tools useful in both achieving process stability and improving capability through the reduction of variability. SPC is applied in order to monitor and control a process so that the process can make as much conforming product as possible with a minimum of waste. Arguably, control charts are the most successful tool in SPC procedure. If control chart analysis indicate a stable process, then data from that process can be used to predict the performance of the process in the future. If the monitored process is found to be not in control, analysis of the chart can help determine the sources of variation. Identifying sources of variation will reduce degraded process performance. Increased demand for control charts has led to more effective use of statistical methodologies, thus improving the quality of a product or a process. Researchers have made great efforts in the advancement of control charts. However, when two or more control charts monitor the same manufacturing process, comparing the control charts becomes a key issue. The performance of control charts is typically evaluated by run length distributions. The run length distribution of a control chart is the probability distribution of run length, which is the number of samples that need to be taken before the chart signals the change in the process. Difficulties exist in the comparison of control charts when using run length distribution as a criterion. For example, it is hard to determine whether a distribution is better than another graphically. Therefore, Average Run Length (ARL), which is the mean of run length distribution, has been accepted instead. However, using the first moment to summarize the entire distribution seems questionable. In this thesis, we first address whether or not traditionally used ARL can be considered a sufficient criterion. Research results indicate that using the average to present the entire run length distribution is not only less informative, but can also be misleading. Second, we investigate meaningful methods for comparing control charts. Continuous Ranked Probability Score (CRPS) is proposed here as a single-number criterion for the performance of control charts. CRPS is applicable when the run length distributions of two compared control charts are independent. The newly proposed score captures the distance from the distribution to zero. As it is shown in this thesis, CRPS could be considered as an ideal measurement when comparing the performance of control charts. The newly proposed score involves straight forward computation and is easily interpreted. When comparing the performance of control charts, dependency between the control charts is often overlooked. We have developed a procedure to solve this issue. Paired comparison is proposed in order to directly calculate the probability of which control chart detects the change earlier. The proposed method no longer treats the run length distribution independently, as it is taking the joint run length distribution into consideration. Paired comparison would increase statistical power due to the reduction of potential confounding errors. The proposed procedure is also easy to understand and simple to generalize to any control charts comparison, while taking the dependency into consideration. Examining SPC applications over the past decades, there has been a great demand for a profile control charts. Here the quality of a process or a product is described and summarized by a profile between a response variable and one or more explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. However, the goodness-of-fit for the functional profiles (i.e., how well the model fits the profiles) has not been given proper attention. The project in this thesis intends to explore a method to monitor the goodness-of-fit for profile control charts before using the chart to monitor other features of interest. In summary, we believe this thesis has solved the issue of how to compare the control charts for different cases. We anticipate that the proposed methods will be useful and meaningful for SPC applications, so that in the future there will be powerful performance criteria available for comparing control charts. We hope that this work will contribute to the development of quality improvement in the field of manufacturing.