Monitoring the Log-normal Process using Bootstrap X̄-R Control Charts  
Author Lee-Ing Tong

 
Co-Author(s) Chao-Ching Hung; Kai-Wei Su; Yu-Chiun Wang

 
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.

 
Keywords Bootstrap Sampling, Bootstrap Confidence Intervals, Control Charts, Log-normal Distribution
   
    Article #:  22035
 
Proceedings of the 22nd ISSAT International Conference on Reliability and Quality in Design
August 4-6, 2016 - Los Angeles, California, U.S.A.