{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 9 - Part 2 - Control Charts for Variables Data You...

Info icon This preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
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”
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
3/10/11 X Chart In section 6, you can see the first three samples 20 oz. This is your target since each can is supposed to weigh 20 oz. A coffee can
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 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.
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 6
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 3.078 1.777 Table 9.3 Use this column to estimate σ Use for constructing R charts
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/10/11 Assumed Distribution of Can Weights 19.98 X = can weig ht 20.169 20.358 20.54 7 19.791 19.602 19.413 = .189 oz. σ ˆ Filled can weights are in here
Image of page 8
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 σ ˆ 3 -
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 10
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
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 12
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
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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)
Image of page 14
3/10/11 Constructing an R Chart The center line is R For the coffee can example, this is .
Image of page 15

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 16
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern