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首页> 外文期刊>Quality and Reliability Engineering International >Optimal Designs of the Variable Sample Size (X)over-bar Chart Based on Median Run Length and Expected Median Run Length
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Optimal Designs of the Variable Sample Size (X)over-bar Chart Based on Median Run Length and Expected Median Run Length

机译：基于中位数游程长度和预期中位数游程长度的可变样本大小（X）条形图的优化设计

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摘要

The variable sample size (VSS) (X) over bar chart, devoted to the detection of moderate mean shifts, has been widely investigated under the context of the average run-length criterion. Because the shape of the run-length distribution alters with the magnitude of the mean shifts, the average run length is a confusing measure, and the use of percentiles of the run-length distribution is considered as more intuitive. This paper develops two optimal designs of the VSS (X) over bar chart, by minimizing (i) the median run length and (ii) the expected median run length for both deterministic and unknown shift sizes, respectively. The 5th and 95th percentiles are also provided in order to measure the variation in the run-length distribution. Two VSS schemes are considered in this paper, that is, when the (i) small sample size (n(S)) or (ii) large sample size (n(L)) is predefined for the first subgroup (n(1)). The Markov chain approach is adopted to evaluate the performance of these two VSS schemes. The comparative study reveals that improvements in the detection speed are found for these two VSS schemes without increasing the in-control average sample size. For moderate to large mean shifts, the optimal VSS (X) over bar chart with n(1)=n(L) significantly outperforms the optimal EWMA (X) over bar chart, while the former is comparable to the latter when n(1)=n(S). Copyright (C) 2016 John Wiley & Sons, Ltd.
机译：条形图上的可变样本大小（VSS）（X）专门用于检测中等均值漂移，已在平均游程标准的背景下进行了广泛研究。因为游程长度分布的形状随平均偏移的大小而变化，所以平均游程长度是一个令人困惑的度量，并且游程长度分布的百分位数的使用被认为更直观。本文通过最小化（i）确定行程和未知行程大小的中位行程长度和（ii）预期中位行程长度，开发了条形图上的VSS（X）的两种最佳设计。还提供了第5个和第95个百分位，以测量游程长度分布的变化。本文考虑了两种VSS方案，即为第一个子组（n（1））预定义了（i）小样本量（n（S））或（ii）大样本量（n（L））时）。采用马尔可夫链方法评估这两种VSS方案的性能。对比研究表明，这两种VSS方案的检测速度得到了提高，而没有增加对照中的平均样本量。对于中等到较大的均值漂移，当n（1）= n（L）时，条形图上的最佳VSS（X）明显优于条形图上的最佳EWMA（X），而当n（1）时，前者与后者相当）= n（S）。版权所有（C）2016 John Wiley＆Sons，Ltd.

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