# Volume III - 4.6 Control Charts

Orientation and Training

Food and Drug Administration

**III-04**

**Section 4 - Basic Statistics and Presentation**

10-01-03

1-31-13

A control chart is a graph of test results with limits established in which the test results are expected to fall when the instrument or analytical procedure is in a state of "statistical control." A procedure is under statistical control when results consistently fall within established control limits. There are a variety of uses of control charts other than identifying results that are out of control. A chart will disclose trends and cycles which will allow real time analysis of data and information for deciding corrective action prior to say an entire analytical system goes out of control. The use of control charts is strongly encouraged in regulatory science.

### 4.6.1 Definitions

*Central line*: mean value of earlier determinations, usually a minimum of twenty results*Inner control limit*: the mean value ± 2 standard deviations*Outer control limit*: the mean value ± 3 standard deviation

### 4.6.2 Discussion

Control charts are frequently used for quality control purposes in the laboratory. Control charts serve as a tool that determines if results performed on a routine basis (e.g. quality control samples) are acceptable for the intended purposes of the data.

The mean control chart consists of a horizontal central line and two pairs of horizontal control limits lines. The central line defines the mean value, the inner control limit (mean ± 2 standard deviations), and outer control limit (mean ± 3 standard deviations). Results are plotted on the y-axis against the x-axis variable (e.g. date, batch number).

Results fall within the inner control limits 95% of the time. Results falling outside the inner control limit serve as a warning that the results may be biased. Results falling outside the outer control limit indicate the results are biased and corrective action should be taken.

### 4.6.3 Quality Control Sample Example

The control chart for a laboratory instrument often plots the results of the calibration result (y-axis) against the date (x-axis).

Mean control chart:

- Calculate the mean calibration value
- Calculate ±2 standard deviation, ± 3 standard deviation values
- Draw horizontal lines above and below the mean value at ±2 deviations and the mean value ± 3 standard deviations
- Plot calibration results against the date or batch number
- Define corrective actions if the calibration results fall outside the inner and outer control limits.

### 4.6.4 References

- Pecsok, Shields, Cairns. (1986).
*Modern methods of analysis*(2nd Ed.). New York: John Wiley and Sons. - Steinmeyer, K. P. (1994).
*Mathematics review for health physics technicians*. Hebron, CT: Radiation Safety Associates Publications. (Also 2nd Ed. in 1998.)