何正斌 博士 國立屏東科技大學工業管理研究所 教授 組抽樣原則 何正斌 博士 國立屏東科技大學工業管理研究所 教授

組抽樣基本原則 組抽樣原則決定Rbar Xbar管制界限與Rbar有關 Rule of Thumb 不對的分組 短時間且同批 連續抽 Vs 隨機抽 不對的分組 同件多個不同尺寸 根據量測的順序而非製造的順序 Subgroups are required in order to use X-bar & R or X-bar & S charts. There must be a reasonable, rational basis for sub grouping data. The within subgroup variation (R-bar or S) is used to calculate the control limits of the X-bar chart. There must be a reasonable expectation that the within-group variation has some predictive value on the group-to-group variation. The following example shows the effect of subgroup selection on the data analysis.

範例 某塑膠射出廠利用模具生產汽車尾燈，其產品之尺寸是重要的品質參數，模具上有4個槽，所以射出一次可以產生4個尾燈。該廠決定使用Xbar-R管制圖來管制產品尺寸，工程師以下列方式搜集資料，每兩小時至現場一次，每次連續搜集5個循環(A,B,C,D,及E),每循環在模具的上每個槽(S1,S2,S3,S4)均會生產1個尾燈，一天8小時共搜集4個sample，一共搜集5天20個samples。 工程師每兩小時(Sample i) 所搜集尾燈資料如下

分組原則 每兩小時20個尾燈為1組 每兩小時每循環4個尾燈為1組 每兩小時每槽可得5個尾燈為1組 Describe verbally what each of the sub grouping strategies is attempting to evaluate. Is this reasonable? Why or why not? 每兩小時每槽可得5個尾燈為1組

每兩小時20個尾燈為1組 Rbar由每組20個data決定 最大=10.6 In an X-bar chart, there are two types of variation: between subgroup and within subgroup variation. Each chart allocates the variation into one of the groups or the other. The question is always to ask which variation should be allocated and where. In this example, each of the three scenarios (and there are more) allocates the variation in different ways.

每兩小時每循環4個尾燈為1組 Rbar由每組4個data決定 次之=7.88 In an X-bar chart, there are two types of variation: between subgroup and within subgroup variation. Each chart allocates the variation into one of the groups or the other. The question is always to ask which variation should be allocated and where. In this example, each of the three scenarios (and there are more) allocates the variation in different ways.

每兩小時每槽可得5個尾燈為1組 Rbar由5個data決定 最小=3.312 In an X-bar chart, there are two types of variation: between subgroup and within subgroup variation. Each chart allocates the variation into one of the groups or the other. The question is always to ask which variation should be allocated and where. In this example, each of the three scenarios (and there are more) allocates the variation in different ways.

重新排序-slot, sample, cycle Estimate Parameters by Groups In…Slot Subgroup Size=5

Graphical Analysis Boxplot Graph/Boxplot Q3 Median Q1 outlier