控制图典型错误应用一例

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有公司在画控制图时,对进度偏差率画了XMR控制图。原始数据如下:

度量日期
开发进度偏差率
05-14
-2%
05-19
0%
05-21
-1%
05-22
-2%
05-23
-2%
05-26
-4%
05-27
-5%
05-28
-8%
05-29
-11%
05-30
-12%
06-02
-14%
06-03
-15%
06-04
-21%
06-05
-27%
06-06
-9%
06-10
-9%
06-11
-6%
06-12
-4%
06-13
-4%
06-16
0%
06-17
-5%
06-18
-5%
06-19
-5%
06-20
-7%
06-23
-6%
06-24
-5%
06-25
-4%
06-26
-4%
06-27
-3%
06-30
-2%
07-01
-2%
07-02
-1%
07-03
-1%
07-04
-1%


XMR图为:








其实上述对控制图的应用是错误的,因为违背了采样的基本前提,即样本的独立性,前后2个采用点应该是独立的,不是相关的2个点。对于上述的原始数据可以对自相关的分析如下:


前一天
前一天的进度偏差率
后一天
后一天的进度偏差率
05-14
-2.00%
05-19
0.00%
05-19
0.00%
05-21
-0.50%
05-21
-0.50%
05-22
-1.90%
05-22
-1.90%
05-23
-2.40%
05-23
-2.40%
05-26
-3.50%
05-26
-3.50%
05-27
-4.90%
05-27
-4.90%
05-28
-8.10%
05-28
-8.10%
05-29
-11.20%
05-29
-11.20%
05-30
-11.80%
05-30
-11.80%
06-02
-13.60%
06-02
-13.60%
06-03
-15.00%
06-03
-15.00%
06-04
-21.00%
06-04
-21.00%
06-05
-27.00%
06-05
-27.00%
06-06
-9.00%
06-06
-9.00%
06-10
-9.00%
06-10
-9.00%
06-11
-6.00%
06-11
-6.00%
06-12
-4.00%
06-12
-4.00%
06-13
-4.00%
06-13
-4.00%
06-16
-0.20%
06-16
-0.20%
06-17
-5.00%
06-17
-5.00%
06-18
-5.00%
06-18
-5.00%
06-19
-4.90%
06-19
-4.90%
06-20
-6.60%
06-20
-6.60%
06-23
-5.80%
06-23
-5.80%
06-24
-4.70%
06-24
-4.70%
06-25
-3.80%
06-25
-3.80%
06-26
-4.20%
06-26
-4.20%
06-27
-3.10%
06-27
-3.10%
06-30
-2.30%
06-30
-2.30%
07-01
-1.50%
07-01
-1.50%
07-02
-1.20%
07-02
-1.20%
07-03
-1.20%
07-03
-1.20%
07-04
-1.30%


对前后2天的进度偏差率散点图为:





显然前后2天的进度偏差率是相关的。

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