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Economic-Statistical Design of VSSI$\bar{X}$ Control Charts Considering Two Assignable Causes  

Lee, Ho-Joong (Department Industrial & Information Systems Engineering, Soongsil University)
Lim, Tae-Jin (Department Industrial & Information Systems Engineering, Soongsil University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.31, no.1, 2005 , pp. 87-98 More about this Journal
Abstract
This research investigates economic-statistical characteristics of variable sampling size and interval (VSSI)$\bar{X}$charts under two assignable causes. A Markov chain approach is employed in order to calculate average run length (ARL) and average time to signal (ATS). Six transient states are derived by carefully defining the state. A steady state cost rate function is constructed based on Lorenzen and Vance(1986) model. The cost rate function is optimized with respect to six design parameters for designing the VSSI $\bar{X}$ charts. Computational experiments show that the VSSI $\bar{X}$ chart is superior to the Shewhart $\bar{X}$ chart in the economic-statistical sense, even under two assignable causes. A comparative study shows that the cost rate may increase up to almost 30% by overlooking the second cause. Critical input parameters are also derived from a sensitivity study and a few guideline graphs are provided for determining the design parameters.
Keywords
VSSI control chart; two assignable causes; economic-statistical design; ARL; ATS;
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