Six Sigma and Beyond: Statistical Process Control, Volume IV

The np control chart is made for nonconforming (defective) parts and offers the same advantages and disadvantages as the p chart does. The np chart is especially easy and simple to make because the number of defective parts is plotted directly on the control chart. Because the proportion of nonconforming parts is not calculated, this control chart requires less time to make than does the p chart.

STEPS FOR CONSTRUCTING AN NP CHART

The steps for constructing an np chart are nearly identical to those of the p chart. Several differences are listed below.

1. Establish a Sampling Plan for the Control Chart

1. Determine an appropriate sample size (n). The sample size used to construct an np chart must be constant. The sample size must also be large enough so that a typical sample subgroup contains nonconforming (defective) parts.

2. Determine a sampling frequency. Collect sample subgroups often enough to provide diagnostic information. People must identify special causes of variation and search for the cause of the unexpected variation.

3. Record the process data on the control chart. Record the number of defective parts ( np ), sample size ( n ), time, shift, and date for each subgroup on an attribute control chart form. Maintain a process log as a record of all major changes to the process (e.g., changes in machinery, material, methods , or personnel).

2. Calculate the Process Center Line

Calculate the mean number of parts defective (npbar) using the following:

npbar = & pound ; np · k = ( np ₁ + np ₂ + ‹ + np _k ) · k

where

3. Calculate the Standard Deviation ( ƒ _np ) for the Number of Parts Defective

Calculate the standard deviation for proportions as

where

Figure 9.8 shows the sequence of operations needed to calculate the standard deviation for proportions with the Sharp series of calculators .

Figure 9.8: The sequence of operations needed to calculate the standard deviation for proportions.

4. Calculate Control Limits (UCL and LCL)

The upper control limit (UCL) and the lower control limit (LCL) are boundaries of common variation. They are calculated as three standard deviations above and below the process center line.

where

A negative control limit may be calculated for the LCL when the average number of defectives (npbar) is low or the sample size ( n ) is small. Under these conditions, the lower control limit does not exist.

5. Determine the Vertical Scale for the NP Chart

Determine the vertical scale for control charts only after calculating the process center lines and the control limits.

6. Plot the Number of Defectives on the Control Chart

Plot the np value for each sample on the chart. Place each plotted point directly above the data and time sequence information included in the data table. The plotted points may be connected with a solid line as an aid to the analysis of patterns and trends in the data. Proofread the plotted points before analyzing the control chart.

7. Draw the Process Center Line and Control Limits on the Chart

Draw the npbar line as a solid horizontal line. A control limit is usually drawn as a dashed, bold, horizontal line. Date and label all lines.

8. Analyze the NP Chart for Process Control

Use the five criteria for process control to evaluate the np chart. Identify and note all out-of-control conditions and factors which contribute to instability. In the process log, note the time, shift, date, material lot number, material vendor, process parameters, and production personnel included in the manufacturing operation during the out-of-control period.

• Are there one or more point(s) beyond the control limits?

• Are there runs of seven (7) or more points?

• Are there trends of seven (7) or more points?

• Are there cycles of points?

• Is there unusual variation (the 1/3 or 2/3 rule)?

If all of the plotted data on the np chart are within the control limits and randomly distributed around the center line, the defective rate for the process is stable and predictable. The process is in control. Unless the process is in control, ongoing control limits cannot be calculated, process capability cannot be studied, and experimental studies cannot be generalized to longer and larger production runs.

9. Identify and Eliminate the Special Causes of Variation

How people react to control chart signals is the most critical part of the SPC program. To identify and eliminate special variation, people must analyze the manufacturing operations and the resources used. In addition to the control chart, fishbone diagrams, Pareto charts, process flow charts, and controlled experiments may be needed to identify and resolve factors which create instability in the process. It is very important to react promptly to eliminate and prevent special causes of variation. A production department's reaction to out-of-control conditions indicates its commitment to understanding and controlling the manufacturing process. The control chart provides signals to help production departments maintain good quality.

10. Extend the Control Limits for Ongoing Process Control

When the data from the process (at least 25 subgroups) are consistently within the control limits and in control, the control limits may be extended to future samples of data. Production operators and supervisors should closely monitor the charts and act promptly to correct special causes of variation. If the process is improved or if extreme sources of variation are eliminated, the process center line and control limits may no longer be appropriate. The changes made to the process may make it necessary to recalculate the process center lines and control limits. When a production department continually improves its operations, control charts require frequent recalculation. The improvement activities are recorded on np charts as downward trends and/or runs below npbar. These out-of-control conditions verify that the process has been improved.