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Description: Involves the use of statistical signals to identify sources of variation, to maintain or improve performance to a higher quality level, typically through the use of control charts. Process Control Statistical “Quality control by statistical methods is now so extensively applied in all lines of industry, and in all sections of the United States, that everyone who is interested in manufacturing should also have a definite interest in the methods.” - Control Charts, E.S. Smith XI-2

 Statistical control - shows if the inherent variability of a process is being caused by common causes of variation, as opposed to assignable causes. XI-2

Minimize cost by making economical decisions 2. Attain a consistent process or improve a process 3. Identify when a process has changed 4. Allow everyone to contribute to process improvement XI-2

 A control chart is simply a distribution of values, turned 90 degrees on its side... This gives the advantage of seeing when an event occurs. It is highly recommended to use a histogram and control chart together. …and stretched out over time. XI-5

 Warning indicators  a.k.a Natural Process Limits (NPL)  Usually drawn on the chart at +3  (UCL) and -3  (LCL) from the process average.  Defines the process boundaries of your measured subgroups  Signals you if your process is operating in a state of statistical control, or if it is out of control XI-5

Is there special cause variation present? Does it look normal? Is there a pattern? Is the process in control? When do I make a change to the process? Remember Walter Shewhart? He is credited with the control chart. We will refer to these as the Shewhart Methods. Is measurement variation having a big effect? XI-5

Histogram of gas mileage data Control chart based on gas mileage data Same data shown using different tools XI-5

Analyze where SPC should be done. 2. Decrease any obvious variability 3. Verify Gage R&R is acceptable 4. Create sampling plan with rational subgroups 5. Create control chart – allow only common cause variability 6. Run the process and verify control 7. Calculate process capability 8. Monitor process or improve if necessary 9. Pre-control 10. Continue to monitor or improve XI-5

10 You always need to take random samples. 1. At random times 2. At regular intervals ◦ Time based ◦ Quantity based 3. Use “Rational Subgroups” ◦ Small variation within groups ◦ Large variation between groups (sources of variation that occur over time) XI-6

11  Let’s remember the assumptions: normal, homogeneous, need rational subgroups 1.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 2.Based on process capability XI-6

12 t e s M e a s u r e m e n t s C o u n t s Median, Range Average, Range Average, sigma Run chart IX control chart npcontrol chart p control chart c chart u chart n = 2 t o 9 n = 1 0 o r m o r e n = 1 n o n - n o r m a l d a t a n o r m a l d a t a n f i x e d n v a r i e s n f i x e d n v a r i e s C o u n t p i e c e s o r u n i t s C o u n t o c c u r e n c e s V a r i a b l e s A t t r i b u M e a s u r e m e n t s C o u n t s Average, Range Average, sigma Run chart IX control chart npcontrol chart p control chart c chart u chart n = 2 t o 9 n = 1 0 o r m o r e n = 1 n o n - n o r m a l d a t a n o r m a l d a t a n f i x e d n v a r i e s n f i x e d n v a r i e s C o u n t p i e c e s o r u n i t s C o u n t o c c u r e n c e s V a r i a b l e s A t t r i b u t e s Variable: data provides the most information Attribute: Needs a lot of data Control chart – The basic tool of SPC Control chart – The basic tool of SPC XI-10

13 1. Select a process measurement 2. Stabilize process and decrease obvious variability 3. Check the gages (10:1, GRR) 4. Make a sample plan 5. Setup the charts and process log 6. Setup the histogram 7. Take the samples and chart the points 8. Calculate the control limits and analyze for control 9. Calculate the capability and analyze for capability 10. Monitor the process 11. Continuous Improvement XI-11

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15  Pronounced “individual x and moving range”  The most common chart used with limited data  Each point on the chart represents an individual value  Used when subgroup samples need to be 1  Works well with processes that have trends that develop and disappear quickly XI-18

16 1. Select a process measurement 2. Stabilize process and decrease obvious variability 3. Check the gages (10:1, GRR) 4. Make a sample plan 5. Setup the charts and process log 6. Setup the histogram 7. Take the samples and chart the points – at least 10 measurements before calculations 8. Calculate the control limits and analyze for control - histogram 9. Calculate the capability and analyze for capability 10. Monitor the process ( ) 11. Continuous Improvement XI-18

17 For the moving range control chart: For the individual control chart: estimate s by UCL-LCL 6 XI-18

18  The data below was collected as part of a development process  The tolerance is.655 to XI-18

20 1. Select a process measurement 2. Stabilize process and decrease obvious variability 3. Check the gages (10:1, GRR) 4. Make a sample plan 5. Setup the charts and process log 6. Setup the histogram 7. Take the samples and chart the points* 8. Calculate the control limits and analyze for control* 9. Calculate the capability and analyze for capability* 10. Monitor the process 11. Continuous Improvement XI-24

21 7. Chart the points ◦ Sets scales for control chart ◦ Calculate each subgroup’s proportion nonconforming ◦ Plot the proportion nonconforming on the chart 8. Calculate control limits and analyze for control ◦ Plot your control limits You can use these equations – but it’s better to let the computer do it. XI-24

22 9. Calculate the capability and analyze for capability ◦ Capability is based on average defective ◦ Is UCL or LCL within your goal value?  If UCL > USL or LCL < LSL then Cpk<1  If UCL LSL then Cpk>1 XI-24

23 This data represents the number of errors found in purchase orders over a 30 week period. 1. Complete a p chart. 2. What can you tell from the data? 3. Complete a np chart. 4. What can you tell from the data? 5. How are these charts different? XI-24

25 50% -1  -2  -3  +1  +2  +3  0       z value = distance from the center measured in standard deviations Zones A B C C B A XI-32

26  The process creating the data on the control chart is operating under statistical control.  Produces a graphic that will have a high center, and sloping sides.  The points tend to cluster around the center of the chart, show random variation, with only a few points spreading out toward the control limits.  Points look random – good but not too good ◦ Here is an example of a process running in statistical control: XI-32

27  Data that fluctuates excessively and fails to center itself around the centerline is characteristic of assignable or non-normal variation.  Several of these patterns have been classified. ◦ aka “The Western Electric Rules”  The next few pages describe the most common patterns seen in processes.  Not necessarily a bad thing. ◦ Heading in right direction ◦ Result of improvement XI-32

28  A random part located outside of the control limits (1 point outside of zone A)  Occurs for a number of reasons  Any reason requires investigation before continuing to run the job.  Reasons to occur: ◦ An incorrect machine adjustment that is immediately noticed and fixed ◦ Errors in measurement or plotting ◦ A cutting tool that “caught a chip” ◦ May be normal variation XI-32

29  Occurs when the points occur in clusters  Can be done visually  Can be done statistically (2 of 3 points in zone A or beyond – 4 of 5 points in zone B or beyond)  Grouping can be caused by: ◦ Differences in setups ◦ Tools moving ◦ Method problems Grouping XI-32

30  Set of seven or more consecutive points that are all on one side of the center line indicating the center has changed (8 or more points in zone C or beyond, all on one side of the center line)  Usually temporary / sudden  A sudden shift in the level of parts shown on a chart can be good or bad ◦ Good: if the shift is bringing the parts back to split limit ◦ Bad; if the shift is taking the parts away from split limit  Sudden shifts can be caused by: ◦ A change of material, new operator or inspector, an offset change, two or more machines/suppliers on one chart XI-32

31  Defined as consecutive points on a control chart that are steadily increasing or decreasing in value (6 or more consecutive points that either increase or decrease in value – also, 10 out of 11 consecutive points that either increase or decrease in value )  Usually gradual  Trends can be caused by: ◦ Air, coolant, or part temperatures that are steadily increasing or decreasing. ◦ Tool wear that allows a part to steadily increase or decrease in size ◦ A fixture that is constantly wearing, causing the parts to steadily increase or decrease in size. ◦ Operator fatigue XI-32

32  There are no number rules to identify cycles  Cycles are defined as repeated patterns in a process  Cycles can be caused by: ◦ Machines that are continually heating up and cooling down ◦ Air temperatures in the shop that rise to a certain point, then are reduced quickly as cooling systems are activated ◦ Tool wear that allows a part to increase or decrease in size until an offset is made ◦ Seasonal XI-32

33  Can be identified by looking for a majority of parts hugging the center line. (15 or more consecutive points inside zone C)  Will have a "sawtooth" look to it.  Stratification can be caused by: ◦ Gaging concerns (rule of 10s) ◦ Honest reporting? XI-32

34  Can be identified by looking for a majority of parts falling very close to the control limits, with very few in the center of the chart. (5 or more consecutive points outside zone C)  Will have a "sawtooth" look to it.  Typically, this type of situation is actually a combination of two separate distributions within a process, one at high limit, and one at low limit.  Mixtures can be caused by: ◦ Two different gages being used ◦ Output from two or more machines mixed together on the same chart. ◦ Gaging concerns (rule of 10s) ◦ Honest reporting? XI-32

35 Use the right level of control that brings long term stability to the process that you are improving. There will most likely be a tradeoff between the effectiveness, effort and cost of the control technique. Poka-Yoke (Mistake Proofing) Statistical Process Control (SPC) Verbal Instructions (Training, Sounds, etc….) Written Procedures (SOPs, FMEAs, etc….) XI-36

36 Draw a rectangle. Draw a semi- circle along the left edge. Draw another rectangle along the right edge of the rectangle. Draw a trapezoid along the right edge of that rectangle. Draw a rectangle along the right edge of the trapezoid. What is your result? XI-36

Draw the described figure XI-32

38  A Control Plan is simply a plan that documents your process ◦ Intended to make the process robust ◦ Assures that we meet our customer expectations ◦ It contains Key Input and Output Variables ◦ Data comes from process map, fishbone (C-N-X), standard operating procedures, FMEA and error proofing XI-32

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