Chapter 9 - Part 2

# Chapter 9 Part 2 - Control Charts for Variables Data You plot two control charts for variables data X chart monitors where the x bar process is

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3/10/11 Control Charts for Variables Data You plot two control charts for variables data ∙ X chart: monitors where the process is centered (located) ∙ R chart: monitors the process variation “x bar” chart R stands for “range”

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3/10/11 X Chart You get many small samples Example in section 6 You are in the coffee business and need to monitor the filled weight of coffee cans You obtain 20 samples of 5 cans each How many samples, m The sample size, n Generally, n < 10 m = 20 n = 5
3/10/11 X Chart In section 6, you can see the first 20 oz. This is your target since each can is supposed to weigh 20 oz. A coffee can

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3/10/11 X Chart for Coffee Cans Table 9.2 Summary of sample results Sample 1 2 3 4 5 6 7 8 9 10 X 20.00 19.98 19.88 19.94 20.04 20.06 20.02 19.82 20.02 20.06 R .4 .5 .5 .4 .6 .3 .4 .4 .5 .7 Sample 11 12 13 14 15 16 17 18 19 20 X 19.94 19.86 19.90 20.12 19.92 20.04 20.06 19.98 19.88 20.08 R .4 .3 .2 .5 .5 .4 .3 .5 .6 .4
3/10/11 Procedure for an X Chart 1. Find the average for each sample (X1, X2, ···, Xm) 2. Find the range for each sample (R1, R2, ···, Rm) 3. Average these m values of X Call this X Here, X = 19.98 oz. 4. Average these m values of R Read as “x bar bar” Here, R is . 44 oz.

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3/10/11 Assumed Distribution of Can Weights X = can weig ht Estimate is R/d2 = .44/2.326 =.189 oz Call this µ The estimate of µ is X = 19.98 oz. σ Assumed to be a normal curve in this chapter σ ˆ
3/10/11 X and R Charts Factors for constructing an R chart n d 2 d 3 D 3 D 4 2 1.128 .853 0 3.267 3 1.693 .888 0 2.574 4 2.059 .880 0 2.282 5 2.326 .864 0 2.114 6 2.534 .848 0 2.004 7 2.704 .833 .076 1.924 8 2.847 .820 .136 1.864 9 2.970 .808 .184 1.816 10 1.777 Table 9.3 Use this column to estimate σ Use for constructing R charts

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3/10/11 Assumed Distribution of Can Weights X = can weig ht 20.358 20.54 7 19.413 = .189 oz. σ ˆ Filled can weights are in here
3/10/11 Constructing the X Chart The center line is X The upper control limit is UCL = The lower control limit is LCL = n X σ ˆ 3 + We will ALWAYS use 3 for the UCL and LCL n X ˆ 3 -

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3/10/11 The Coffee Can Example The center line is X = 19.98 oz. The upper control limit is UCL = = 20.23 oz. The lower control limit is LCL = = 19.73 oz. + 5 189 . 3 98 . 19 - 5 189 . 3 98 . 19 Next, plot the 20 values of X
3/10/11 X Chart for Coffee-Can Example 20.23 19.98 19.73 UC L C L LC L | 1 | 10 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 12 | 11 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 Sample number X

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3/10/11 What To Do When a Point is Out of Control Had there been a sample out of control, you need to go look for an assignable cause for this sample If you find it, remove this sample and re-do the chart X and R will change
3/10/11 A Closer Look at the X Chart It is very unlikely for a sample mean to be outside the control limits if the process is in control and on target The chances that a sample mean falls outside the control limits in this situation is the area outside +3 and - 3 under the standard normal curve, illustrated in the next slide

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3/10/11 Finding the Chances of a False Alarm Z 1 2 3 - 1 - 2 - 3 0 The total of these two tails is .0013 + .0013 = .0026 (more accurately, .0027)
3/10/11 Constructing an R Chart The center line is R For the coffee can example, this is .

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## This note was uploaded on 03/09/2011 for the course DSCI 2710 taught by Professor Hossain during the Fall '08 term at North Texas.

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Chapter 9 Part 2 - Control Charts for Variables Data You plot two control charts for variables data X chart monitors where the x bar process is

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