Unformatted text preview: cs Technical
standards
Problem concerning
dispersion
Problem solution
through dispersion
reduction Technical
standards Technical
standards
Problem concerning outliers
Problem solution though the
prevention ofoutliers Discussion
This text briefly introduces some of the key concepts related to the dispersion of data. You
will find much more detail in Unit 11 – Statistical Methods. In the meantime, discuss how
these concepts could be used to recognize abnormalities in your work processes. This text
does not have an action plan. A Roadmap to Quality 21 Unit 9  Problem solving 0587581_unit 9.qxd 09/09/2005 11:54 Page 22 9.8 Control charts
Introduction
1. Control charts are a key tool in interpreting data. They can distinguish between
dispersions caused by accidental factors and dispersions caused by abnormal factors,
and can show whether the process is in a stable condition or not. A control chart
consists of a central line (CL) and upper and lower control limits (UCL and LCL). UCLs
and LCLs are based on calculated values.
2. When characteristic values that indicate process conditions are plotted as data points on
the control chart, and all the points fall within the upper and lower control limits, or
there is no bias in the way the points are distributed (i.e. they are not distributed in any
particular way), the process is said to be “under control”. When the plotted points fall
outside the control limits or there is a bias in the way the points are distributed, the
process is “out of control”. In other words, an abnormality has emerged in the process.
You should then investigate the causes of the abnormality and take countermeasures.
(Texts 11.4.1 to 11.4.5 in Unit 11, Statistical Methods, provide more detailed guidelines
on using control charts.)
3. The following criteria indicate when the process is out of control:
a. When one or more plotted points fall outside the control lines.
b. When the points indicate a bias. This can be:
i. When seven or more points form a chain above or below the central line.
ii. When a large number of points are on one side of the central line, e.g. 10 out of
11 consecutive points.
iii. When five or more consecutive points form an upward or downward line.
iv. Other cases which show periodicity.
4. Data may include variables or discrete values or both. Variables include measured
values such as length (meter) and weight (kilogram). These are continuous values (i.e.
they are uncountables – you cannot count them). Discrete values are noncontinuous
values such as the number of defective units and flaws within a sheet (i.e. they are
countable). Types of control chart
5. There are several kinds of control chart:
a. –R control charts (average and range).
x
These are used in the management of variable data. – and R represent a subgroup
x
– control charts are used for
average and subgroup range respectively. The x
monitoring changes in the subgroup average (variation among subgroups), while
the R control charts are used for managing dispersions within a subgroup (variation
within a sub group). These two charts are paired for use. Unit 9  Problem solving 22 A Roadmap to Quality 0587581_unit 9.qxd 09/09/2005 11:54 Page 23 b. “p” control charts and “pn” control charts:
These manage processes in which the characteristic values of discrete values are
considered. “pn” control charts are used when the number of samples (n) is constant
and the number of defective units (pn) is considered. When the number of samples
(n) is not constant, in other words when the ratio of defects (p) is considered, “p”
control charts are used.
c. “c” control charts (defects per unit) or “u” control charts (standard defects per unit)
may be used depending on the characteristics of measured values.
Figure 9.8a Flow chart for selection of control chart types Selection of control charts Does the
data indicate the
number of defective
units? –xR Control
x–
charts –Rs Control
x
charts pn Control
charts Is the group size
constant?
Not constant –R Control charts
x
–R Control charts
x Is the group
size constant?
Not constant Can the data be
compiled and
grouped? Constant Does the central
line (CL) take –?
x Discrete values n=2 Grouping impossible Does the
group (n) contain two
or more members? Grouping possible n≥2 Is the data
variable? Constant Variables c Control
charts p Control
charts u Control
charts How to draw control charts 6. These directions are for –R control charts, the type that is most frequently used.
x
Step 1. Gather data
In principle, more than 100 pieces of data should be collected. This data must be relatively
new, nearly identical to what future processes are expected to produce in terms of
technology, and accompanied by a clear history.
Step 2. Classify the data
Classify the data into subgroups and arrange it by measuring times or lots. The number of
data items that one subgroup contains is known as the subgroup size. It is represented by
the letter “n”. Usually, “n...
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 Spring '12
 anamika
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