| Summary: | 碩士 === 國立交通大學 === 工業工程與管理系所 === 102 === The control limits of a traditional X-bar control chart are derived under the assumption that the process data follow a normal distribution. However, the Type I and Type II errors may have a higher chance to occur in using the X-bar chart to monitor the process when data follow a non-normal distribution. In the past, there are studies utilized non-parametric bootstrap methods to construct control limits based on non-normal distributions. These studies have applied the Percentile Bootstrap (PB) confidence interval in constructing the X-bar control limits. However, they did not verify the effectiveness of bootstrap control chart in monitoring the process mean of non-normal distributions. This study utilizes two non-parametric bootstrap confidence intervals (i.e., PB, Bias-Corrected and Accelerated Percentile Bootstrap (BCa)) in constructing the X-bar control limits and the effectiveness was verified using the sensitivity analysis based on Lognormal distribution. Although some studies indicated that BCa confidence interval performs better than the other three bootstrap confidence intervals, the simulation results of this study indicated that when control limits are constructed using non-parametric bootstrap method, PB confidence intervals performs better than BCa. PB confidence interval does not grant the best detecting ability in terms of type I and type II errors, but as a whole, it outperforms the traditional X-bar control chart in monitoring data that follow a Lognormal distribution.
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