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 Sigma 18-50mm f/3.5-5.6 DC Lens f/Sony Minolta+ KIT NEW US $127.97 
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 Sigma AF 18-50 /3.5-5.6 DC Lens for Pentax SLR NEW US $100.00
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 Sigma AF 18-50 mm f/3.5-5.6 DC f/Sony & Minolta SLR NEW US $100.00
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 Sigma AF 18-50mm f/3.5-5.6 DC Lens for Pentax + KIT NEW US $127.97
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 UV PROTECTION FILTER FOR SIGMA 18-50mm f/3.5 70-300mm US $9.60
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 SIGMA 18-50 mm aperture flex cable US $8.98
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 Sigma 18-50mm F2.8 EX DC For Pentax US $319.99
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 72mm Hi Res Close Up Set Sigma 17-70mm 18-50mm 2.8 new US $21.99
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 SIGMA 18-50mm F2.8 -4.5 DC OS F Canon 450D 500D 350D US $239.00
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 SIGMA 18-50mm F2.8 -4.5 DC OS F Canon XS XSI XT XTI TI US $239.00
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 SIGMA 18-50mm f/2.8-4.5 DC OS HSM Lens f/ Pentax 861109 US $199.00
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 New Sigma SD15 + 18-50mm lens US $749.90
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 Sigma 18-50mm F/2.8 EX DC Macro Lens For Nikon US $315.00
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 Minty Nikon D90 w/ Sigma DC 18-50 f/2.8-4.5 optical stabilized lens W/ EXTRAS!! US $725.00
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 SIGMA 18-50mm 2.8 OS HSM Nikon D50 D60 D70 D70s D80 D90 US $239.89
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 SIGMA 18-50mm 2.8 OS HSM Lens KIT Nikon D300 D300S D200 US $269.95
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 SIGMA 18-50mm f/2.8-4.5 OS HSM Lens KIT Nikon D40 D40X US $269.95
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 SIGMA 18-50mm f/2.8 OS fr Nikon D3000 D3100 D5000 D7000 US $239.89
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 SIGMA 18-50mm f/2.8 DC OS HSM fr Nikon SLR Camera 18-50 US $269.95
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 Nikon D80 with Tamron 70-300mm Sigma 18-50mm metal Case, US $600.00
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 Canon EOS 10D 6.3 MP Digital SLR Camera - w/Sigma 18-50 lens & Charger US $123.00
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 Nikon D7000 Digital SLR Camera Body 3 Lens Package + Sigma 18-50mm BRAND NEW US $2,099.99
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 Nikon D7000 Digital SLR Body 3 Lens Package Sigma 18-50mm + Accessories US $2,149.99
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 Sigma 18-50mm f/2.8 EX DC MACRO NIKON - RARE VERSION US $419.00
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 SIGMA 18-50mm 18-50 LENS KIT F Canon T1I 40D 50D XS XT US $189.99
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 SIGMA 18-50mm 2.8 OS for Nikon D40 D40X D60 D80 D90 D70 US $239.99
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 SIGMA 18-50mm F2.8 -4.5 DC OS F Canon 50D 40D 30D 20D US $239.99
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 SIGMA 18-50mm F2.8 -4.5 DC OS IS F Canon T2I T1I XSI XS US $239.00
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 NIKON SIGMA 18-50mm f2.8 EX DC macro lens US $11.61
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 Sigma 18-50mm f/2.8-4.5 DC OS HSM Zoom For PENTAX AF D-SLRs Free World Shipping US $249.95
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 SIGMA 18-50mm DC OS HSM F/ Nikon DSLR 18-50 D90 D80 D70 New - Free World Ship US $249.95
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 Sigma 18-50mm 2.8 EX DC macro HSM lens for Nikon SLR US $399.99
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 SIGMA 18-50mm f/2.8-4.5 DC OS HSM Lens for SIGMA 861110 US $199.00
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 SIGMA 18-50mm 2.8 -4.5 DC OS F Canon XS XSI XT XTI TI US $239.99
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 Sigma Wide Angle 18-50mm f/2.8 EX DC MACRO Lens For Pentax Cameras: K7 K20D K5 US $358.99
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 Sigma 18-50mm F2.8-4.5 DC OS For Canon AF Optical Stabilizer SLD Glass US $79.99
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 SIGMA 18-50mm f/2.8 DC OS HSM Lens KIT fr Nikon D90 D80 US $269.95
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 Sigma 18-50mm f/2.8 EX DC Macro Lens for Canon DSLR US $329.99
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 Sigma 630-02 bayonet mount lens hood shade for 18-50mm f/3.5-5.6 US $12.00
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 Lens Band STOP ZOOM CREEP for Sigma 18-50mm in Black US $4.99
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 Sigma 18-50 F3.5-5.6 for minolta AF D US $144.99
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 Sigma Nikon 18-50mm F2.8 AF DC EX SLD Lens US $.01
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 SIGMA LH 630-02 for 18-50 F3.5-5.6 DC Lenses US $11.99
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 Sigma 18-50 F2.8-4.5 DC OS HSM Zoom Lens for Nikon w/ 3 Piece Filters + Case US $199.00
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 Genuine Lens Hood Shade LH630-01 For Sigma AF 18-50mm f/3.5-5.6 DC Japan New OEM US $11.99
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 Front Lens Sleeve/Cover/Bag/Case/Pouch Protector for Sigma 18-50&Tamron 28-75 US $4.50
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 New 0.5x Super Wide Angle w/ Macro +10 Lens For Sigma 18-50mm Fits 67mm Lens US $56.51
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 67mm Universal Replacement Lens Cap for Sigma 18-50mm F2.8-4.5 DC OS HSM US $1.99
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 67mm Universal Multi-Layer UV Filter for Sigma 18-50mm F2.8-4.5 DC OS HSM US $3.89
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 Sigma 18-50mm F2.8-4.5 DC OS HSM for Pentax SLR NEW US $199.00
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 Sigma 18-50mm F2.8-4.5 DC OS HSM for Nikon SLR NEW US $199.00
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 SIGMA 18-50mm F2.8 -4.5 DC OS F Nikon D90 D80 D60 D300 US $219.99
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 Lens Band STOP ZOOM CREEP for Sigma 18-50mm in Red US $4.99
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 SIGMA LH 630-01 for 18-50mm f3.5-5.6 DC, 28-70mm f2.8-4 DG Lenses US $9.99
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 Sigma 18-50mm F/2.8-4.5 OS Lens Pro Kit for Sony/Minolta Free USA Ship 18-50 US $229.95
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 Sigma 18-50mm f/2.8-4.5 DC OS HSM Zoom f/ Sony/Minolta Free World Shipping 18-50 US $249.95
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 SIGMA 18-50mm f/2.8-4.5 DC OS HSM Lens for Nikon 861306 US $199.00
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 Lens CAP for Sigma 18-50mm F2.8-4.5 DC OS HSM US $9.95
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 SIGMA 18-50mm 18-50 LENS KIT F NIKON D50 D70 D80 D300 US $239.99
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 Nikon Sigma 18-50mm f3.5 DC Autofocus Zoom lens for DSLR camera - Nice Mint-! US $130.00
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 SIGMA 18-50mm f/2.8-4.5 DC OS HSM Lens for Canon 861101 US $199.00
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 Sigma 18-50mm F2.8-4.5 DC OS HSM Wide Angle AF Lens for Canon EOS NEW US $199.00
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 67mm 3PC Filter Kit for Sigma 18-50mm F2.8-4.5 DC OS US $34.99
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 Sigma 18-50mm f/2.8 EX DC SLD ELD Aspherical Macro Lens for Sony Digital SLR US $315.99
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 Test Chart for Sigma 18-50mm F2.8-4.5 DC OS HSM Lens US $11.95
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 SIGMA 18-50mm 2.8 -4.5 DC OS For Canon 7D 60D 50D 40D T3I T2I 600D 550D T1I US $239.99
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 SIGMA 18-50mm 2.8 OS F Nikon D80 D90 D300 D300S D3000 D5100 D3100 D5000 D60 VR US $249.99
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 SIGMA 18-50mm F 2.8 DC OS F Sony A390 A580 A550 A230 A35 A33 A77 A55 A330 A350 US $219.99
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 72mm UV Lens Filter For Sigma 18-200mm F/3.5-6.3 DC OS 18-50mm F/2.8 EX DC MACRO US $11.99
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 72mm 3PC Filter Kit for Sigma 18-50mm f/2.8 EX DC Lens US $34.99
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 Rear Lens cap For Nikon sigma 18-50mm 18-55mm 70-300mm 50-200mm 10-20mm 18-200mm US $3.79
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 Sigma 18-50mm f/2.8 for Sony Mount + 67mm UV Filter US $219.99
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 67mm Hi Res Filter KIT For Sigma 18-50mm 2.8 OS 18-50 nikon 18-135mm 18-70mm US $16.99
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 Rear Lens cap Sigma 70-300mm 70-300 18-50mm 18-50 28-70 US $3.99
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 Sigma 18-50mm F2.8-4.5 DC OS HSM For Sigma mount Camera - SD9,SD10,SD14,SD15,SD1 US $149.99
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 UV Protection Filter for Sigma 17-70mm 18-50mm Lens US $13.64
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 SIGMA 18-50mm f/2.8-4.5 DC OS HSM Lens for Sony 861205 US $199.00
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 Sigma 18-50mm f/2.8-4.5 DC OS HSM for CANON Free World Shipping NIB 18-50 US $249.95
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 SIGMA 18-50mm F2.8 -4.5 DC OS F Canon 5D 5DII 1D 1DS US $239.00
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Sigma 18-50
Run Charts
Adding the element of time will help clarify your understanding of the causes of variation in your processes. A run chart is a line graph of data points organized in time sequence and centered on the median data value. The patterns in the run chart can help you find where to look for assignable causes of variation.
What can it do for you?
Histograms or frequency plots can show you the general distribution or variation among a collection of data points representing a process, but one histogram or one frequency plot can not show you trends or help pinpoint unusual events. Sometimes, a normal-looking distribution will hide trends or other unusual data. To spot those trends, the data must be considered in time order. Plotting data on a run chart can help you identify trends and relate them to the time they occurred. This will help you in your search for the special causes that may be adding variation to your process.
Run charts are especially valuable in the measure and analyze phases of Lean Six Sigma methodology.
How do you do it?
1. Select a characteristic from one of your processes. This characteristic could be presenting a problem because excessive variation often drives it outside of specification limits, or it could be a cause of customer complaints.
2. Measure the characteristic over time intervals and record the data. Note the time or the time period that is associated with each data point.
3. Find the median data value. To do this, list the data values in numeric order. Include each data point, even if it is a repeat value. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is halfway between the two values nearest the middle. For example, if the collected data points were: 5, 1, 18, 8, 12, 9, the ordered values would be: 1, 5, 8, 9, 12, and 18. The middlemost values are 8 and 9. The median is the average of those values, or 8.5. (Remember, the numerically-ordered data is only for determining the median. The data must be plotted in time order on the run chart to be of any value.)
4. Set up the scales for your run chart. The vertical scale will be the data values, and the horizontal scale will be the time. Make the horizontal scale about two to three times the distance of the vertical scale.
5. Label the vertical scale so that the values will be centered approximately on the median and so the scale is about 1 ½ to 2 times the range of the collected data.
6. Draw a horizontal line representing the median value.
7. Plot the data points in sequence. Connect each point to the next point in the sequence with a line.
Some special cause variation reveals itself in unusual run-chart patterns. These clues can direct you in your search for causes. Count the number of runs. Runs are sequences of points that stay on one side of, either above or below, the median line. One way of counting the runs is to circle these sequences and tally them. Another way of doing this is to count the number of times the run-line crosses the median, and then add one. Compare the number of runs you count to the accompanying chart.
• Numbers of runs outside the range shown for the number of data points are statistically unusual.
• Too few runs (below the lower limit) generally indicate that something cyclic is systematically shifting the process average.
• Too many runs could point to a problem of consecutive, over-compensating process adjustments or indicate that the data points actually came from two sources with different process averages.
• Look for sequences of ascending or descending values. Seven or more continuously increasing or continuously decreasing points indicates a trend that is shifting the process average. When counting points, ignore any points that repeat the previous value. Repeated values neither add to the length of the run nor break it.
• Search for seven or more consecutive points on the same side of the median line or 10 of 11 points or 12 of 14 or 16 of 20. (Ignore any points that are exactly on the median.) Such a sequence indicates that something has occurred to shift the process average in that direction.
• A sequence of 14 or more data points alternating up and down suggests a variation related to sampling (such as one reading early in the day and one reading toward the end) or that the data is coming from two sources with different process averages (such as from two machines making the same part.) In looking for up-and-down alternation, ignore any points that are exactly the same as the preceding point.
• A sequence of seven or more points with exactly the same value usually should signal you to look for a special cause. While it is possible that your process has improved to the extent that the existing measurement technique is no longer sensitive enough to measure variation, it is usually more probable that a gauge is stuck or broken or that someone is making up the data.
Now what?
Run charts can be very valuable in helping your search for sources of variation. They are easy to plot and easy to interpret. The sampling is uncomplicated, and there are no statistical computations to make. They can also be applied to almost any process or any data.
On the other hand, they are not an instant indicator. They are best used for spotting trends; short shifts in the process cannot always be detected with run charts. In addition, special causes that produce general piece-to-piece variation will not be readily detected on run charts.
Finally, a simple run chart cannot establish the natural capabilities of a process, so it isn't possible to use one to predict what specifications a process can actually meet. To do that, you need to create a control chart, a run chart with statistical control limits.
About the Author
Steven Bonacorsi is a Senior Master Black Belt instructor and coach. Steven Bonacorsi has trained hundreds of Master Black Belts, Black Belts, Green Belts, and Project Sponsors and Executive Leaders in Lean Six Sigma DMAIC and Design for Lean Six Sigma process improvement methodologies.
Author for the Process Excellence Network (PEX Network / IQPC)
Process Excellence Network
Steven Bonacorsi, President of International Standard for Lean Six Sigma(ISLSS)
Certified Lean Six Sigma Master Black Belt
47 Seasons Lane
Londonderry, NH 03053
Phone: +(1) (603) 401-7047
E-mail: http://bit.ly/n4hBwu
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