International Society of Science and Applied Technologies |
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Monitoring the Log-normal Process using Bootstrap X̄-R Control Charts | ||||
Author | Lee-Ing Tong
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Co-Author(s) | Chao-Ching Hung; Kai-Wei Su; Yu-Chiun Wang
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Abstract | The control chart is one of the most frequently utilized tools of statistical process control (SPC) in industry to monitor the process variation. The control limits of Shewhart x̄-R control charts are derived under the assumption that the process data are independently and normally distributed. The false alarm may be increased for x̄-R charts when the process data follow a nonnormal distribution (e.g., log-normal distribution). The objective of this study is to utilize the non-parametric bootstrap sampling method and two popular bootstrap confidence intervals (i.e., percentile bootstrap (PB) and bias-corrected and accelerated (BCa)) to construct the x̄-R charts for the log-normal distribution. The sensitivity analysis is conducted to verify the effectiveness of the proposed method. The simulation results indicates that for n = 2 to 5, the control limits of the bootstrap x̄-R charts constructed by PB method performs generally better than that of BCa method and Shewhart x̄-R charts in terms of average run length (ARL) for the log-normal distribution.
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Keywords | Bootstrap Sampling, Bootstrap Confidence Intervals, Control Charts, Log-normal Distribution | |||
Article #: 22035 |
August 4-6, 2016 - Los Angeles, California, U.S.A. |