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Chapter 6

Chapter 6. Control Chart Example. Is there special cause variation present? Does it look normal?. When do I make a change to the process?. Is the process in control?. Is there a pattern?. Is measurement variation having a big effect?. Remember Walter Shewhart ?

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Chapter 6

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  1. Chapter 6

  2. Control Chart Example Is there special cause variation present? Does it look normal? When do I make a change to the process? Is the process in control? Is there a pattern? Is measurement variation having a big effect? Remember Walter Shewhart? He is credited with the control chart. We will refer to these as the Shewhart Methods.

  3. Why chart? • We need to have an accurate, efficient way to determine how well the process is running • Control charts give you the ability to look at groups of data from processes and conclude how well it is performing • It lets an individual easily identify patterns, trends, cycles, points out of control, etc.

  4. Gas Price Example …from a long, long time ago.

  5. Example • Look at the data in the table on the previous page (2 min) and make a decision on the data: • In what 2 months did the highest gas price occur and at what price? • In what 2 months did the lowest gas price occur and at what price? • What is the range of the gas prices? • In what 2 consecutive months did the largest change in gas prices occur? • Is there a trend in the data?

  6. The graphic way

  7. Variables vs. Attributes Data • Variables Data - Numerical measurements made at the interval or ratio level- quantitative data, • ohms, voltage, diameter, subdivisions of the measurement scale are conceptually meaningful, e.x., 1.6478 volts • Attribute data is data that takes on fixed values • counts, good or bad, on or off, right or wrong, values without intervals What are the advantages and disadvantages of each of these?

  8. Median, Range 9 o Average, Range t 2 = n e r o m r o 0 1 = n Average, sigma s n t o n - n o r m a n n l d a t a = 1 e m Run chart s e n e o r l r m u b a l s a d i a a r t a e a IX control chart M V A t t d e x r i f C n i np control chart b o u u s n e c t e s i p n t s v a n t r i i e u s p control chart n o u C r o d e x i f n C c chart o u n t o c c u r e n c e s n v a r i e s u chart Control Chart Decision Tree Variable: Provides the most information Median, Range 9 9 Average, Range Average, Range o o t t 2 2 = = n n e e r r o o m m r r o o 0 0 1 1 = = n n Average, sigma Average, sigma s s n n o o n n - - n n o o t t r r m m n n a a l l d d a a = = t t a a n n 1 1 e e m m Run chart Run chart s s n n o o e e e e r r r r m m l l a a u u b b l l d d s s a a a a t t i i a a a a r r e e a a IX control chart IX control chart M M V V A A t t t t d d r r e e C C x x i i i i f f n n np np control chart control chart b b o o u u u u t t n n s s e e t t e e s c c s s s e e i i p p n n v v t t a a s s r r i i n n e e t t s s i i p control chart p control chart u u n n o o u u C C r r o o d d e e x x i i f f n n C C o o c chart c chart u u n n t t o o c c c c u u r r e e n n c c e e s s n n v v a a r r i i e e s s u chart u chart Attribute: Needs a lot of data Control chart – The basic tool of SPC

  9. When do I get the data? You always need to take random samples. • At random times ~or~ • At regular intervals • Time based • Quantity based • Use “Rational Subgroups” • Small variation within groups • Large variation between groups (sources of variation that occur over time)

  10. How much data do I need? • There is a very statistical way to calculate this, but we’re not going to go there • Let’s remember the assumptions: normal, homogeneous, need rational subgroups • Typical Shewhart Methods will state: • rational subgroups of 4, 5, or 6 if you have a lot of data recorded periodically, or • 100% for small sample sets • Based on process capability

  11. What is a run chart? • A very simple technique used to analyze the process when other charting techniques are not applicable • Data is usually compared to a target value How am I doing?

  12. Run chart • Used to get a graphical view of the data • Does not have control limits

  13. Control chart control limits • Warning indicators • Drawn on the chart at +3 (UCL) and -3 (LCL) from the average • These limits define the boundaries which the measured subgroup of your process must fall into Process

  14. Control limits • Another term for control limits are Natural Process Limits (NPL) • These limits will indicate or signal you if your process is operating in a state of statistical control, or if it is out of control

  15. Statistical control • Shows if the inherent variability of a process is being caused by normal causes of variation, as opposed to assignable or non-normal causes

  16. How distributions relate to control charts • A control chart is simply a distribution of values, turned 90 degrees on its side...

  17. …and stretched out over time. This gives the advantage of seeing when an event occurs. It is highly recommended to use a histogram and control chart together. How distributions relate to control charts

  18. 11 step procedure for control charts • Select a process measurement • Stabilize process and decrease obvious variability • Check the gages (10:1, GRR) • Make a sample plan • Setup the charts and process log • Setup the histogram • Take the samples and chart the points • Calculate the control limits and analyze for control • Calculate the capability and analyze for capability • Monitor the process • Continuous Improvement

  19. How to calculate control limits • As we discussed before, control limits are usually set at 3 from the mean For the range control chart: For the average control chart:

  20. Class exercise • Exercise on pg 594/602 • 1-4 • Review Chapter 10 • Finish 5-7

  21. Pg 595

  22. Histogram for exercise

  23. Target Value Lower Limit Upper Limit Process Capability • Helps determine what the process can produce under normal, stable conditions • Helps set realistic goals for improvement by showing what to expect from the process • Main indices used to define process capability: Cp, CR, and Cpk, PPM, slevel • Make sure that our +/- 3sdistribution (99.73% of data) falls within the tolerance zone

  24. What happens when “Shift happens”? • Because we are using all of our tolerance, we’re forced to keep the process exactly centered • If the process shifts at all, nonconforming parts will be produced Lower Specification Limit Upper Specification Limit Target

  25. Getting started • Using 75% or less of a tolerance will allow processes to shift slightly without producing any defects • The goal is to improve your process in order to use the least amount of tolerance possible • Reduce the opportunity to produce defects • Reduce the cost of the process

  26. Potential Process Capability Index (Cp) • Defines the width of the process distribution • Cp is calculated by dividing the tolerance zone width by the width of the ±3σ distribution • This Cp number (or index) tells how many times the distribution will fit into the tolerance zone * * Which standard deviation do I use?

  27. What it looks like... • If a process uses 100% of a tolerance zone , the Cp value would be 1.0 • If a process uses 1/2 of the tolerance zone , the Cp value would be 2.0 • If a process uses 200% of the tolerance zone , the Cp value would be 0.5

  28. Capability Ratio (CR=PCR) • Process capability as a percentage of tolerance • The inverse of the calculations for Cp • Divide the width of the ±3σ distribution by the width of the tolerance zone * * Which standard deviation do I use?

  29. Calculating CR • If a processes Cp = 1.0 the CR = 100% • If a processes Cp = 2.0 the CR = 50% • If a processes Cp = .5 the CR = 200% neat

  30. Actual Process Capability (Cpk) • Takes into account not only the spread of the distribution, but also the location of it as well • Calculating Cpk: * Cpk = Cp - a “Penalty” for off-center distributions! * Which standard deviation do I use?

  31. What it looks like... • If a process uses 100% of a tolerance zone, Cp = 1.0 • If the distribution is not centered, the Cpk <1.0 Cpk = 1.0 Cpk <1.0

  32. Target LSL USL Target LSL USL Cpk = 2.0 Cpk <2.0 What it looks like (cont.) • If a process uses 1/2 of the tolerance zone, the Cpk = 2.0 • If the process is not centered, the Cpk value would be <2.0 this stuff is so awesome

  33. MEAN - LSL Cpk = 3s USL - MEAN Cpk = USL - LSL Cp = 3s 6s PROCESS CAPABILITY “Cp”, “CR” & “Cpk” Low Speed Limit High Speed Limit MEAN 1s 65 70 75 * * * 6 s Min CR = USL - LSL

  34. Where do I improved? • Shape – control chart • Stabilize proces • Am I in control? 2. Spread – Cp Reduce variation Cp>1.33? 3. Location – Cpk Center process Cpk>1.33?

  35. USL = 1.505 LSL = 1.500 s = .00045 CR = Cp = USL = .507 LSL = .506 s = .00006 CR = Cp = USL = 2800 PPH LSL = 2700 PPH Xbar = 2750 PPH s = 12.5PPH CR = Cp = Cpk = USL = 750 Mhz LSL = 735 Mhz Xbar = 740 Mhz s = 1.333Mhz CR = Cp = Cpk = USL = 1.503 LSL = 1.500 Xbar = 1.501 s = .00045 CR = Cp = Cpk = USL = .251 LSL = .250 Xbar = .250 s = .00015 CR = Cp = Cpk = Capability Indices exercise

  36. Sigma Level (Zst value) • The number of standard deviations that would fit between the average value of the process and the closest tolerance limit • Very important in order to understand the amount of waste that is occurring Low Specification Limit High Specification Limit MEAN 65 70 75 s level = Cpk * 3 s capability = Cp * 3 6s level

  37. Parts Per Million a.k.a. PPM • It’s difficult to understand the exact degree of improvement as the process gets better by capability measures • The PPM method considers the total amount of nonconforming parts produced by a process for its measure

  38. Calculating PPM • PPM is the percentage of non-conforming parts multiplied by 1,000,000 • Example: A process produces 7% bad parts • PPM = (%bad) x 1,000,000 = .07 x 1,000,000 = 70,000 = 70,000 parts per million • Commitment to achieve 6 Sigma processes, which is a defect level of 3.4 PPM

  39. Class exercise • Continue exercise on pg 594/602 • 8

  40. What is Six Sigma? • Metric based on standard deviation • Vision • Benchmark • Philosophy • Methodology • Aggressive (Stretch) Goals 6s What does 3s or 6s feel like?

  41. Number of Defects by Sigma Level • 6s = 3.4 defects per million • 5s = 233 defects per million • 4s = 6,210 defects per million • 3s = 66,807 defects per million *Based on a possible 1.5s shift See Table 6.5 on pg. 255 slevel = Cpk * 3

  42. Summary • Remember! • Cp...... Larger is better • CR...... Smaller is better • Cpk.... Larger is better • PPM…Smaller is better • slevel…Larger is better Cp, CR, Cpk, s level, PPM, etc. are indices you can use to determine how well your process is performing

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