Statistical Quality Control Charts
For Wastewater Evaluation
JOHN M. FAIRALL, Chief
Engineering and Sciences Staff
Effluent Guidelines Division
Office of Water Planning Standards
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
INTRODUCTION
Random selection of a subset of samples from a large population provides the common
basis for statistical evaluation of sample data. When evaluating several grab samples of
water from a well-mixed tank, the value sought is the true value for the contents of the tank
as estimated by the average value of the subset. Samples of wastewater collected from
discharging industrial wastes are collected in sequence and not from a single large well-
mixed volume. The control chart method excels most methods for presenting data from
sequential sampling (1).
For the purpose of evaluating wastewater, a control chart for individuals using moving
ranges of two observations with no standard given is recommended and presented as an
example.
DEVELOPMENT OF CONTROL CHART
A control chart for individual values is prepared from the first 20 to 30 values. Table I
lists 22 values for COD. The moving range, R, the difference in successive values of X or
COD, is computed and listed as shown in Table I. The average value of X and R are
computed. The upper control limit for X, UCLX; lower control limit for X, LCLX;and the
upper control limit for R, UCLR, are computed as shown in Table I. The constants, 2.66
and 3.27, are based on setting the control limits at about three standard deviations from the
average values (1), as plotted in Figure 1.
All values within the control limits are interpreted as emanating from a constant cause
system, which consists of production, control, treatment, sample collection, flow
measurement, and the chemical analysis. Remove the values of X which fall outside UCLX
and LCLX or cause values of R to exceed UCLR, and calculate new limits, thus discarding
the high value of 123.3 as shown on the 21st.
X
= 61.1
UCLX
= 86.0
LCLX
= 36.2
R
=   9.35
UCLR
= 44.1
Dashed lines in Figure 1 depict these revised limits. With the establishment of new
limits, additional elimination of values may be required (2).
If these control limits will not protect the receiving stream, or meet the applicable
effluent limitations, the system must be reviewed and an attempt made to reduce the
variation and narrow the control limits or reduce the average discharges from the system by
improved wastewater management.
As stated previously, all values within the control limits are interpreted as being from a
constant cause system. The chance variations about the mean or average line, sometimes
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