Principles of Food Sanitation

p Charts

Thepchart, one of the more useful attrib-
ute control charts, is used for determining
the unacceptable (p) fraction. It is defined as
the number of unacceptable items divided by
the total number of items inspected. For
example, if a producer examines five samples
per hour (for an 8-hour shift) from the pro-
duction line and finds a total of eight unac-
ceptable units, p would be calculated as
follows:

Total number of unacceptable = 9

Total number of inspected = 5(8) = 40

p total number inspected.

number of unacceptable

40

= ==^8020

Sometimes this value is represented as per-
centage unacceptable. In this example, percent-
age defective would be:

0.20×100 = 20%

An attribute control chart can be con-
structed from a sampling schedule by obtain-
ing an average fraction unacceptable (p) value
from a data set and using the formula p±3d,
or the desired control limits. Because attribute
testing follows a binomial distribution, the
standard deviation would be calculated:
tt(),
n
d=^1 -

where nis the number of items in a sample.
Control limits would be obtained by:

UCL=+t 3 d

LCL=t- 3 d

When these data are plotted and no points
are outside of the control limits, it can be
assumed that the process is in a state of sta-
tistical control, and any variation can be
attributed to natural occurrences.

np Charts

npcharts can be used to determine the
number of unacceptable instead of the frac-

tion defective, and the sampling lots are con-

stant. The formula for the number of unac-

ceptable (np) is:

number of unacceptable (np) = n×p,

where nis the sample size and pis the unac-

ceptable fraction defective. If one value is

known, the other can be easily calculated. For

example, if a sample lot of 50 is known to be

2% unacceptable, the number of unaccept-

able should be:

np= 50 ×0.02 = 1

The calculation for determining the con-

trol limits would be the same as for the p

chart, except that the standard deviation

would be:

d=-np() 1 p

c Charts

These charts are used when the concern is

the number of defects per unit of product.

They are not as frequently incorporated as

thepandnpcharts but can be effective if

applied correctly. Assume that a manufac-

turer examines 10 lots and discovers 320

defects. The equations for the average (c) and

standard deviation required for a cchart is:

c==^3201032

d== =c 32 5 66.

The control limits would be:

UCL=+ = +c 3 c 32 3 566(. )= 4897.

LCL=- = -c 3 c 32 3 566(. )= 1503.

u Charts

Sometimes, a constant lot size may not be

attainable when examining for defects per

unit area. The uchart is used to test for sta-

tistical control. By establishing a common

unit in terms of a basic lot size, one can

determine equivalent inspection sample lot

Quality Assurance for Sanitation 137