Comparison of optimised composite control charts: improved statistical process control for the manufacturing industry

MacNaughton, David (2008) Comparison of optimised composite control charts: improved statistical process control for the manufacturing industry. Masters (Research) thesis, James Cook University.

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Abstract

Selecting and configuring control charts can be a difficult task. Literature has not provided evidence as to which type of composite control chart is best among composite moving average (CMA), composite exponentially weighted moving average (CEWMA) and composite cumulative sum (CCUSUM). Optimising three-component composite control charts was considered very difficult, if not impossible, to achieve. Additionally, a traditional method for comparing control charts across a domain of step shift sizes called the average ratio of average time to signal (ARATS), can lead to inconsistent conclusions. Thus, there have been insufficient methods and data published for an informed selection from composite control chart types and configurations.

This study is the first to optimise and compare two and three-component composite control charts. Distribution parameters were assumed to be unknown and were estimated from 200 observations. Software was created to automatically configure composite control charts to achieve specifications for the in-control average time to signal (ICATS) and the contribution of each of the components to false alarms, or loadings. Detection time profiles were simulated for full factorial experiments of control chart parameters using averages of at least 1,000,000 chart runs per simulation.

New performance and comparison measure were invented to complete the research. A new performance measure Mean Relative Loss (MRL) was defined and used for optimising control chart configurations. MRL compares the average time to signal (ATS) profile across a step shift domain to the profile of a reference CUSUM control chart. Average Difference Relative to the Average (ADRA) was defined to overcome the problem noted with ARATS.

Three-component CCUSUM bettered three-component CEWMA (ADRA = 5.0%) which in turn performed better than three-component CMA. Three-component CEWMA performed better than two-component CEWMA (ADRA = 5.2%). Thus it can be seen that the type of component and the number of components selected has a significant effect on performance.

This study shows how much the statistical performance of various types of optimised composite control charts can differ. Results from this study will better inform statistical quality control professionals when selecting a control chart type. The methods developed here have the further advantage of being adaptable to different assumptions and parameters. A final implication of the study is that composite control charts may now be optimised and thus fairly compared against other categories of control charts which are typically optimised in literature.

Item ID: 31904
Item Type: Thesis (Masters (Research))
Keywords: CUSUM; cumulative sum; exponentially weighted moving average; EWMA; moving average; quality control charts; statistical process control
Date Deposited: 30 Apr 2014 02:27
FoR Codes: 01 MATHEMATICAL SCIENCES > 0104 Statistics > 010406 Stochastic Analysis and Modelling @ 50%
15 COMMERCE, MANAGEMENT, TOURISM AND SERVICES > 1503 Business and Management > 150313 Quality Management @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 50%
97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 50%
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