c Control Charts
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This month's e-zine introduces the c control chart. On occasion, there is a customer complaint. Sometimes someone gets injured on the job. Sometimes the warehouse does not have an item that is supposed to be in stock. These situations require examining counting type attributes data. Each count (customer complaint, injury, or stock out) is considered a defect. The c chart is one technique to use for examining variation in counting type attributes data over time.
c charts are used to look at variation in counting type attributes data. They are used to determine the variation in the number of defects in a constant subgroup size. Subgroup size usually refers to the area being examined. For example, a c chart can be used to monitor the number of injuries in a plant. In this case, the plant is the subgroup. Since the plant doesn't change size very often, it is a subgroup of constant size.
To use the c chart, the opportunities for defects to occur in the subgroup must be very large, but the number that actually occurs must be small. For example, the opportunity for injuries to occur in a plant is very large, but the number that actually occurs is small.
Operational definitions (March 2004 e-zine available on website) must be used to determine what constitutes a defect. A subgroup can contain different types of defects. For example, a customer complaint can occur for a number of different reasons. If this is the case, operational definitions must exist for each defect.
The figure above is an example of a c chart. In this example, the variation in the number of OSHA recordable injuries in a plant is being monitored. The subgroup size in this case is the plant. The operational definition for an injury is any injury that is OSHA recordable. The opportunity for defects to occur is very large since there are many opportunities for injuries to occur. However, the number of defects (injuries) that actually occur is small. A c chart is appropriate under these conditions. The time frame was selected as one month.
The number of injuries each month is plotted for a two-year period. For example, there were 2 injuries (c = 2) in January 2002 and 4 injuries (c =4) in February 2002. The overall average and control limits have also been calculated and plotted.
The figure is in statistical control. What does it mean when the c chart is in statistical control? It means that there are only common causes of variation present (see January 2004 e-zine on variation, available on the web-site). It also means that the number of injuries will remain consistent in the near future. The average number per month will be around 2. Some months it may be as high as 6, others as low as 0.
Since the process is in control, the system must be changed to decrease the number of injuries. This is management's responsibility. However, the people closest to the job will usually have great ideas about what needs to be done to improve the process. They usually do not have the authority to make the required changes. Attempting to decrease the number of injuries by encouraging the workforce to be more careful will not work. The process must be changed. Examine the reasons why injuries occur. A Pareto diagram (June 2004 e-zine available on the website) can be used for this. Look for ways to prevent injuries from occurring in the first place.
The steps in constructing a c chart are given below. The equations you need are shown to the right.
1. Gather the data
a. Select the subgroup size. The subgroup size is the area where defects have the opportunity to occur. It must be constant from subgroup to subgroup. The opportunity for defects to occur must be large. The number of defects that actually occur must be small.
b. Select the frequency with which the data will be collected. Data should be collected in the order in which they are generated.
c. Select the number of subgroups (k) to be collected before control limits will be calculated (at least twenty).
d. Count the number of defects (c) in each subgroup. Ensure that operational definitions of a defect are complete.
e. Record the data.
2. Plot the data.
a. Select the scales for the control chart.
b. Plot the values of c for each subgroup on the control chart. c. Connect consecutive points with straight lines.
3. Calculate the process average.
a. Calculate the process average number of defects ( cbar):
b. Draw the process average number of defects on the control chart as a solid line and label.
4. Calculate the control limits.
a. Calculate the control limits for the c chart. The upper control limit is given by UCLc. The lower control limit is given by LCLc.
b. Draw the control limits on the control chart as dashed lines and label.
5. Interpret the chart for statistical control.
a. The following tests for statistical control as a minimum should be used (see April 2004 e-zine available on the web site). If any of these conditions are present, the process is out of statistical control due to the presence of a special cause of variation.
· Points beyond the control limits
· Seven points in a row trending up or trending down
· Seven points in a row above or below the average
One of the great features of our software, SPC for Excel, is that it runs as a Microsoft Excel add-in. Entering data, navigating around the workbook, etc. are necessary skills to use Excel. So, we have included some tips to help you with Excel.
1. Changing column headers to show numbers instead of letters
Choose Tools > Options and select the General tab.
Check the box for 'R1C1 reference style'
2. Quickly copying a range of cells to another location.
Select the range of cells by dragging your mouse over it.
Point your mouse to the border of the range.
Hold the Ctrl key while dragging it to a new location.
When you release the mouse button, you will see the same range of cells in the new location.
3. Change the colors of sheet tabs
You can change the sheet tab colors (in Excel 2002 and later).
Right-click on a sheet tab, and choose Tab Color
When the sheet is selected, the color will show in a thin strip at the bottom of the sheet tab. The full tab is colored for non-selected sheets.
4. My data ends in row 50 but the scroll bars go to row 200. Why?
To go to the cell which is currently the "Last Cell" in the worksheet, hold the Ctrl key, and press the End key. If the Last Cell is outside the range of cells that is actually being used, you can reset the used range, so the scroll bar works correctly. To manually reset the used range:
Select the last cell that contains data in the worksheet
To delete any unused rows:
Move down one row from the last cell with data.
Hold the Ctrl and Shift keys, and press the Down Arrow key
Right-click in the selected cells, and, from the shortcut menu, choose Delete
Select Entire Row, click OK.
To delete any unused columns:
Move right one column from the last cell with data.
Hold the Ctrl and Shift keys, and press the Right Arrow key
Right-click in the selected cells, and, from the shortcut menu, choose Delete
Select Entire Column, click OK.
5. Locking the title row so you can view it at all times.
Assuming title row is 1, select cell A2, then choose Window, then Freeze Panes.
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