Unformatted text preview: Source: Heizer and Render (2006) 4QA3 F12 A. Gandomi 14 27 Number of defects 24 21 18 15 12 9 6 3 2 4QA3 F12 4 6 8 10 Sample number A. Gandomi 12 14 16 15 ● Common (Normal) Causes o Variation inherent in a process o Can be eliminated only through improvements in the system ● Special (Abnormal) Causes o Variation due to identi3iable factors o Can be modi3ied through operator or management action 4QA3 F12 A. Gandomi 16 Normal Abnormal e.g., old machinery e.g., wrong material Small (>3σ, < 3σ) noticeable (<3σ, >3σ) Due to common causes Due to special causes Process in control Process out of control Individuals Chart of Training Expenses
Last 2 Years 110000 Ave = 97700
95000 Impurities
(milligrams) Expense ($$) 105000 100000 90000 LCL = 88000
Jun
Jul
Aug
Sep
Oct
Nov
Dec Jan
Feb
Mar
Apr
May Jun
Jul
Aug
Sep
Oct
Nov
Dec UCL = 39.8 40
30 X = 19.8 20
10
0 85000 Jan
Feb
Mar
Apr
May Individuals Chart of Impurities
5/1 – 6/23 50 UCL = 107400 1 3 5 7 9 11 13 15 17 19 21 23 25 L CL = none Sample # Month 4QA3 F12 A. Gandomi 17 ● Relies on properties of the normal distribution. The Central Limit Theorem justi3ies the assumption that the average of measurements within a subgroup follows a normal distribution. Mean = 11
Std. Dev. = 1 8 9 10 11 12 13 14
Mean = 12
Std. Dev. = 2 6 7 8 9 10 11 12 13 14 15 16 17 18 Mean = 7
Std. Dev. = 0.5 4QA3 F12 6 7 8 9 A. Gandomi 18 ● Control charts are based on the following property of the normal distribution: o The likelihood that an observation falls within two standard deviations of the mean (that is, µ±2σ) is about 0.95 and within three standard deviations of the mean (µ±...
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 Spring '14
 Normal subgroup, W. Edwards Deming, A., UCL, LCL, Gandomi

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