Question

a) What is a control chart and what is it used for?

b) What are the steps for constructing a Control Chart?

c) Explain the out of control signals?

Answer 1

Types of Control Charts.

• X bar control chart. ...
• Range “R” control chart. ...
• Standard Deviation “S” control chart. ...
• “p” and “np” control charts. ...
• Pre-control Charts.

A)

The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data.

• When controlling ongoing processes by finding and correcting problems as they occur
• When predicting the expected range of outcomes from a process
• When determining whether a process is stable (in statistical control)
• When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process)
• When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process

B)

1. Choose the appropriate control chart for your data.
2. Determine the appropriate time period for collecting and plotting data.
3. Collect data, construct your chart and analyze the data.
4. Look for "out-of-control signals" on the control chart. When one is identified, mark it on the chart and investigate the cause. Document how you investigated, what you learned, the cause and how it was corrected.

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 ( c):

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 publication 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

C)

The control limits of your control chart represent your process variation and help indicate when your process is out of control. Control limits are the horizontal lines above and below the center line that are used to judge whether a process is out of control.

1. 

   Figure 1 Control Chart: Out-of-Control Signals

   • A single point outside the control limits. In Figure 1, point sixteen is above the UCL (upper control limit).
   • Two out of three successive points are on the same side of the centerline and farther than 2 σ from it. In Figure 1, point 4 sends that signal.
   • Four out of five successive points are on the same side of the centerline and farther than 1 σ from it. In Figure 1, point 11 sends that signal.
   • A run of eight in a row are on the same side of the centerline. Or 10 out of 11, 12 out of 14, or 16 out of 20. In Figure 1, point 21 is eighth in a row above the centerline.
   • Obvious consistent or persistent patterns that suggest something unusual about your data and your process.

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