Page 213 - DMGT524_TOTAL_QUALITY_MANAGEMENT

Total Quality Management

Notes
Figure 14.10 (a): Process Accuracy and Precision
Target Target

Accuracy % Accuracy Accuracy % Accuracy
Precision % Precision % Precision % Precision

Figure 14.10 (b): Process Accuracy and Precision

Lower Control Upper Control
x
Limit for bar Limit for bar
x
Distribution of
Distribution of
x bar individual
measurements ( )
x

-3σ -2σ -σ mean +σ +2σ +3σ

Natural variation of
the process

Lower Upper
Spec Spec
Limit Limit

Control Limits are not an Indication of Capability

Those new to SPC often have the misconception that they don’t need to calculate capability
indices. Some even think that they can compare their control limits to the spec limits. This is not
true, because control limits look at the distribution of averages (x-bar; p, np, u, etc.) while
capability indices look at the distribution of individual measurements (x). The distribution of x
for a process will always be more spread out than the distribution of its x-bar values (Figure
14.10 (b)). Therefore, the control limits are often within the specification limits but the plus-and-
minus 3-sigma distribution of individual part dimensions (x) is not.

Note The statistical theory of the “central limit theorem says that the averages, of samples
or subgroups {x-bar} follow more closely a normal distribution. This is why we can easily
construction control charts on process data that are themselves not normally distributed.
But averages-cannot be used for capability calculation/because capability evaluates
individual parts delivered by a process. After all, parts get shipped to customers, not
averages.

208 LOVELY PROFESSIONAL UNIVERSITY