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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Xbar and s chart ： ウィキペディア英語版 Xbar and s chart | varupperlimit = $B\_4\; \backslash bar\; S$ | varlowerlimit = $B\_3\; \backslash bar\; S$ | varstatistic = $\backslash bar\; s\_i\; =\; \backslash sqrt\; \backslash frac\; -\; \backslash bar\; x\_i\; \backslash right\; )^2\; \}$ | meanchart = Xbar chart for a paired xbar and s chart.svg | meancenter = $\backslash bar\; x\; =\; \backslash frac\; ^n\; x\_\}$ | meanlimits = $\backslash bar\; x\; \backslash pm\; A\_3\; \backslash bar\; s$ | meanstatistic = $\backslash bar\; x\_i\; =\; \backslash frac\; \}$ }} In statistical quality control, the $\backslash bar\; x$ and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process. The chart is advantageous in the following situations: #The sample size is relatively large (say, n > 10—$\backslash bar\; x$ and R charts are typically used for smaller sample sizes) #The sample size is variable #Computers can be used to ease the burden of calculation The "chart" actually consists of a pair of charts: One to monitor the process standard deviation and another to monitor the process mean, as is done with the $\backslash bar\; x$ and R and individuals control charts. The $\backslash bar\; x$ and s chart plots the mean value for the quality characteristic across all units in the sample, $\backslash bar\; x\_i$, plus the standard deviation of the quality characteristic across all units in the sample as follows: :$s\; =\; \backslash sqrt^2\}\}$. The normal distribution is the basis for the charts and requires the following assumptions: *The quality characteristic to be monitored is adequately modeled by a normally-distributed random variable *The parameters μ and σ for the random variable are the same for each unit and each unit is independent of its predecessors or successors *The inspection procedure is same for each sample and is carried out consistently from sample to sample The control limits for this chart type are: *$B\_3\; \backslash bar\; s$ (lower) and $B\_4\; \backslash bar\; s$ (upper) for monitoring the process variability *$\backslash bar\; x\; \backslash pm\; A\_3\; \backslash bar\; s$ for monitoring the process mean :where $\backslash bar\; x$ and $\backslash bar\; s\; =\; \backslash frac$ are the estimates of the long-term process mean and range established during control-chart setup and A3, B3, and B4 are sample size-specific anti-biasing constants. The anti-biasing constants are typically found in the appendices of textbooks on statistical process control. As with the $\backslash bar\; x$ and R and individuals control charts, the $\backslash bar\; x$ chart is only valid if the within-sample variability is constant. Thus, the s chart is examined before the $\backslash bar\; x$ chart; if the s chart indicates the sample variability is in statistical control, then the $\backslash bar\; x$ chart is examined to determine if the sample mean is also in statistical control. If on the other hand, the sample variability is ''not'' in statistical control, then the entire process is judged to be not in statistical control regardless of what the $\backslash bar\; x$ chart indicates. When samples collected from the process are of unequal sizes (arising from a mistake in collecting them, for example), there are two approaches: ==See also== *$\backslash bar\; x$ and R chart *Shewhart individuals control chart 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Xbar and s chart」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.