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274 Part IV: Quality Assurance
Part IV.B.4
time, or both, we do not want to take the measurements. We may prefer to use a
more economical method such as a go/no-go gauge. Therefore, it is important that
we study control charts that are appropriate for quality characteristics that can’t be
measured numerically. Such control charts are called control charts for attributes. In
this section, we study various control charts for attributes for detecting large process
shifts, which usually occur in phase I implementation of SPC.
When a quality characteristic can not be measured numerically we classify
the product as defective or nondefective. In SPC it has become more common to
use the terminology conforming or nonconforming instead of nondefective or defective.
Thus, in this section, we shall continue use of the terminology conforming or
nonconforming. A quality characteristic that classifies any product as conforming
or nonconforming is called an attribute.
For instance, quality characteristics such as the determination that a soft drink
can is not leaking, a stud has regular edges, a rod fits into a slot, a 100-watt light
bulb meets the desired standard, or a steel rivet meets the manufacturer’s quality
specifications are some examples of attributes. Note that the data collected
on a quality characteristic that is an attribute is simply count data. Moreover, the
sample sizes when using control charts for attributes are normally much larger
(usually in the hundreds) than the sample of size four or five that we usually use
in control charts for variables.
In general, variable control charts are more informative and they are very
effective in detecting a defect before even it occurs whereas attribute charts are
used only after the defects have occurred. There are cases, however, when variable
control charts show some limitations. For example, consider a product that is
nonconforming due to any one of 10 quality characteristics that do not conform to
specifications. Clearly, in this case we can not control all 10 quality characteristics
by using one variable control chart, since one variable control chart can control
only one quality characteristic at a time. Thus, in this case, to control all 10 quality
characteristics we would have to use 10 different variable control charts. On the
other hand, however, one attribute control chart can study all the quality characteristics
because a nonconforming unit is nonconforming irrespective of the number
of quality characteristics that do not conform to specifications. Thus, we can
conclude that both variable and attribute control charts have their pros and cons.
In some cases the quality characteristic is such that instead of classifying a
unit as conforming or nonconforming, we record the number of nonconformities
per manufactured unit. For example, the number of holes in a roll of paper, the
number of irregularities per unit area of a spool of cloth, the number of blemishes
on a painted surface, the number of loose ends in a circuit board, the number of
nonconformities per unit length of a cable, the number of nonconformities of all
types in an assembled unit, and so on. In such cases, we use control charts that
fall under the category of control charts for attributes, and such control charts are
used to reduce the number of nonconformities per unit length, area, or volume of
a single manufactured unit, or to reduce the number of nonconformities per manufactured
or assembled unit.
The control charts for attributes are quite similar to the control charts for variables,
that is, the center line and the control limits are set in the same manner as
in the case of control charts for variables. However, it is important to note that the
purposes of using control charts for variables and control charts for attributes are