**
**QUALITY IMPROVEMENT TOOLS
BROAD CONTENTS
Seven Basic Tools of Statistical Process Control
38.1 Seven Basic Tools of Statistical Process Control (SPC):**
**
They are as follows:
1. Data Tables
2. Cause-and Effect Analysis
3. Histograms
4. Pareto Analysis
5. Scatter Diagrams
6. Trend Analysis
7. Process Control Charts
**
**
**
**Quality Improvement Tools:
Over the years, statistical methods have become prevalent
throughout business, industry, and
science. With the availability of advanced, automated systems
that collect, tabulate, and analyze
data; the practical application of these quantitative methods
continues to grow. Statistics today
plays a major role in all phases of modern business.
More important than the quantitative methods themselves is their
impact on the basic
philosophy of business. The statistical point of view takes
decision making out of the subjective
autocratic decision-making arena by providing the basis for
objective decisions based on
quantifiable facts.
This change provides some very specific benefits:
- Improved
process information
- Better
communication
- Discussion
based on facts
- Consensus for
action
- Information for
process changes
*
**Statistical Process Control (SPC) *
takes advantage of the natural
characteristics of any process.
All business activities can be described as specific processes
with known tolerances and
measurable variances. The measurement of these variances and the
resulting information
provide the basis for continuous process improvement. The tools
presented here provide both a
graphical and measured representation of process data. The
systematic application of these tools
empowers business people to control products and processes to
become world-class
competitors.
The basic tools of statistical process control are data figures,
Pareto analysis, cause-and-effect
analysis, trend analysis, histograms, scatter diagrams, and
process control charts. These basic
tools provide for the efficient collection of data,
identification of patterns in the data, and
measurement of variability.
282
The following Figure 38.1 shows the relationships among these
seven tools and their use for the
identification and analysis of improvement opportunities. We
will review these tools and
discuss their implementation and applications.
Figure 38.1:
Seven Quality Improvement Tools
**
**38.1.1 Data Tables:
Data tables or data arrays provide a systematic method for
collecting and displaying
data. In most cases, data tables are forms designed for the
purpose of collecting specific
data. These tables are used most frequently where data is
available from automated
media. They provide a consistent, effective, and economical
approach to gathering data,
organizing them for analysis, and displaying them for
preliminary review. Data tables
sometimes take the form of manual check sheets where automated
data are not
necessary or available. Data figures and check sheets should be
designed to minimize
the need for complicated entries. Simple-to-understand,
straightforward tables are a key
to successful data gathering.
Figure 38.2 is an example of an attribute (pass/fail) data
figure for the correctness of
invoices. From this simple check sheet several data points
become apparent. The total
number of defects is 34. The highest number of defects is from
supplier A, and the most
frequent defect is incorrect test documentation. We can subject
this data to further
analysis by using Pareto analysis, control charts, and other
statistical tools.
In this check sheet, the categories represent defects found
during the material receipt
and inspection function. The following defect categories provide
an explanation of the
check sheet:
• *Incorrect
invoices: *The invoice does
not match the purchase order.
• *Incorrect
inventory: *The inventory of
the material does not match the invoice.
• *Damaged
material: *The material
received was damaged and rejected.
• *Incorrect test
documentation: *The required
supplier test certificate was not received
and the material was rejected.
283
**
****Figure 38.2: **
Check Sheet for “Material Receipt and Inspection”
**
**38.1.2 Cause-and -Effect Analysis (C and EA) “Fishbone”:
After identifying a problem, it is necessary to determine its
cause. The cause-and-effect
relationship is at times obscure. A considerable amount of
analysis often is required to
determine the specific cause or causes of the problem.
Cause-and-effect analysis uses diagramming techniques to
identify the relationship
between an effect and its causes. *
Cause-and-effect diagrams are also known
as* *
***
****fishbone diagrams**.
Figure 38.3 demonstrates the basic fishbone diagram. Six steps are
used to perform a cause-and-effect analysis.
**
****Figure 38.3: **
Cause-and-Effect Diagram
**
**
**
**Step 1 – Identify the problem:
This step often involves the use of other statistical process
control tools, such as Pareto
analysis, histograms, and control charts, as well as
brainstorming. The result is a clear,
concise problem statement.
**
**Step 2 – Select interdisciplinary brainstorming team:
Select an interdisciplinary team, based on the technical,
analytical, and management
knowledge required determining the causes of the problem.
**
**Step 3 – Draw problem box and prime arrow:
The problem contains the problem statement being evaluated for
cause and effect. The
prime arrow functions as the foundation for their major
categories.
**
**Step 4 – Specify major categories:
Identify the major categories contributing to the problem stated
in the problem box. The
six basic categories for the primary causes of the problems are
most frequently
284
personnel, method, materials, machinery, measurements, and
environment, as shown in
Figure 38.3. Other categories may be specified, based on the
needs of the analysis.
**
**Step 5 – Identify defect causes:
When you have identified the major causes contributing to the
problem, you can
determine the causes related to each of the major categories.
There are three approaches
to this analysis:
*the random method, the systematic method, and the process analysis* *
*method.
**
****Figure 38.4: **
Random Method
**
****Random method: **
List all six major causes contributing
to the problem at the same time.
Identify the possible causes related to each of the categories,
as shown in Figure 38.4.
**
****Systematic method: **
Focus your analysis on one major
category at a time, in descending
order of importance. Move to the next most important category
only after completing
the most important one. This process is diagrammed in Figure
38.5.
**
****Figure 38.5: **
Systematic Method
**
****Process analysis method: **
Identify each sequential step in the
process and perform
cause-and-effect analysis for each step, one at a time. Figure
38.6 represents this
approach.
**
****Figure 38.6: **
Process Analysis Methods
285
**
**Step 6 – Identify corrective action:
Based on (1) the cause-and-effect analysis of the problem and
(2) the determination of
causes contributing to each major category, identify corrective
action.
The corrective action analysis is performed in the same manner
as the cause-and-effect
analysis. The cause-and-effect diagram is simply reversed so
that the problem box
becomes the corrective action box. Figure 38.7 displays the
method for identifying
corrective action.
**
****Figure 38.7: **
Identify Corrective Action
**
**38.1.3 Histogram-(HG):
A histogram is a graphical representation of data as a frequency
distribution. This tool
is valuable in evaluating both attribute (pass/fail) and
variable (measurement) data.
Histograms offer a quick look at the data at a single point in
time; they do not display
variance or trends over time. A histogram displays how the
cumulative data looks
*
**today*. It is
useful in understanding the relative frequencies (percentages) or frequency
(numbers) of the data and how that data are distributed. Figure
38.8 illustrates a
histogram of the frequency of defects in a manufacturing
process.
**
****Figure 38.8: **
Histogram for Variables
**
**38.1.4 Pareto Analysis (PA):
A Pareto diagram is a special type of histogram that helps us to
identify and prioritize
problem areas. The construction of a Pareto diagram may involve
data collected from
data figures, maintenance data, repair data, parts scrap rates,
or other sources. By
identifying types of nonconformity from any of these data
sources, the Pareto diagram
directs attention to the most frequently occurring element.
286
There are three uses and types of Pareto analysis:
1. The basic Pareto analysis identifies the vital few
contributors that account for most
quality problems in any system.
2. The comparative Pareto analysis focuses on any number of
program options or
actions.
3. The weighted Pareto analysis gives a measure of significance
to factors that may
not appear significant at first— such additional factors as
cost, time, and criticality.
The basic Pareto analysis chart provides an evaluation of the
most frequent occurrences
for any given data set. By applying the Pareto analysis steps to
the material receipt and
inspection process described in Figure 38.9, we can produce the
basic Pareto analysis
demonstrated in Figure 38.10. This basic Pareto analysis
quantifies and graphs the
frequency of occurrence for material receipt and inspection and
further identifies the
most significant, based on frequency.
**
****Figure 38.9: **
Material Receipt and Inspection Frequency of Failures
**
****Figure 38.10: **
Basic Pareto Analysis
A review of this basic Pareto analysis for frequency of
occurrences indicates that
supplier A is experiencing the most rejections with 37 percent
of all the failures.
Pareto analysis diagrams are also used to determine the effect
of corrective action, or to
analyze the difference between two or more processes and
methods. Figure 38.11
287
displays the use of this Pareto method to assess the difference
in defects after corrective
action.
**
****Figure 38.11: **
Comparative Pareto Analysis
**
**38.1.5 Scatter Diagrams:
Another pictorial representation of process control data is the
scatter plot or scatter
diagram. A scatter diagram organizes data using two variables:
an independent variable
and a dependent variable. These data are then recorded on a
simple graph with *X *
and
*Y* *
*
coordinates showing the relationship between the variables.
Figure 38.12 displays the
relationship between two of the data elements from solder
qualification test scores. The
independent variable, experience in months, is listed on the
*X*-axis.
The dependent
variable is the score, which is recorded on the
*Y*-axis.
**
**
**Figure 38.12: **
Solder Certification Test Score
These relationships fall into several categories, as shown in
Figure 38.13 below. In the
first scatter plot there is no correlation— the data points are
widely scattered with no
apparent pattern.
288
**
****Figure 38.13: **
Scatter Plot Correlation
The second scatter plot shows a curvilinear correlation
demonstrated by the U shape
of the graph. The third scatter plot has a negative correlation,
as indicated by the
downward slope. The final scatter plot has a positive
correlation with an upward
slope.
From Figure 38.12 we can see that the scatter plot for solder
certification testing is
somewhat curvilinear. The least and the most experienced
employees scored highest,
whereas those with an intermediate level of experience did
relatively poorly. The next
tool, trend analysis, will help clarify and quantify these
relationships.
**
**38.1.6 Trend Analysis (T/A):
Trend analysis is a statistical method for determining the
equation that best fits the
data in a scatter plot. Trend analysis quantifies the
relationships of the data,
determines the equation, and measures the fit of the equation to
the data. This
method is also known as curve fitting or least squares.
Trend analysis can determine optimal operating conditions by
providing an equation
that describes the relationship between the dependent (output)
and independent
(input) variables. An example is the data set concerning
experience and scores on the
solder certification test (see Figure 38.14).
**
****Figure 38.14: **
Scatter Plot Solder Quality and
Certification Score
The equation of the regression line, or trend line, provides a
clear and understandable
measure of the change caused in the output variable by every
incremental change of the
input or independent variable. Using this principle, we can
predict the effect of changes
in the process.
289
One of the most important contributions that can be made by
trend analysis is
forecasting. Forecasting enables us to predict what is likely to
occur in the future. Based
on the regression line we can forecast what will happen as the
independent variable
attain values beyond the existing data.
**
**38.1.7 Process Control Charts (C/C):
The use of control charts focuses on the prevention of defects,
rather than their
detection and rejection. In business, government, and industry,
economy and
efficiency are always best served by prevention. It costs much
more to produce an
unsatisfactory product or service than it does to produce a
satisfactory one. There are
many costs associated with producing unsatisfactory goods and
services. These costs
are in labor, materials, facilities, and the loss of customers.
The cost of producing a
proper product can be reduced significantly by the application
of statistical process
control charts.
• **Control
Charts and the Normal Distribution:** **
**
The construction, use, and interpretation of control charts is
based on the normal
statistical distribution as indicated in Figure 38.15. The
centerline of the control
chart represents the average or mean of the data ( ). The
*upper and lower control* *
**limits (UCL and LCL)*,
respectively, represent this mean plus and minus three
standard deviations of the data either the lowercase
*s *
or the Greek letter (sigma)
represents the standard deviation for control charts.
The normal distribution and its relationship to control charts
are represented on the
right of the figure. The normal distribution can be described
entirely by its mean
and standard deviation. The normal distribution is a bell-shaped
curve (sometimes
called the Gaussian distribution) that is symmetrical about the
mean, slopes
downward on both sides to infinity, and theoretically has an
infinite range. In the
normal distribution 99.73 percent of all measurements lie within
and; this is why
the limits on control charts are called three-sigma limits.
**
****Figure 38.15: **
The Control Chart and Normal Curve
Companies like Motorola have embarked upon a six-sigma limit
rather than a threesigma
limit. The benefit is shown in Table 38.1 below. With a
six-sigma limit, only
two defects per billion are allowed. The cost to maintain a
six-sigma limit can be
extremely expensive unless the cost can be spread out over, say,
1 billion units
produced
Control chart analysis determines whether the inherent process
variability and the
process average are at stable levels, whether one or both are
out of statistical control
290
(not stable), or whether appropriate action needs to be taken.
Another purpose of
using control charts is to distinguish between the inherent,
random variability of a
process and the variability attributed to an assignable cause.
The sources of random
variability are often referred to as common causes. These are
the sources that
cannot be changed readily, without significant restructuring of
the process. Special
cause variability, by contrast, is subject to correction within
the process under
process control.
*
**Common cause variability or variation: *
This source of random variation is
always
present in any process. It is that part of the variability
inherent in the process itself.
The cause of this variation can be corrected only by a
management decision to
change the basic process.
*
**Special cause variability or variation: *
This variation can be controlled at the
local
or operational level. Special causes are indicated by a point on
the control chart that
is beyond the control limit or by a persistent trend approaching
the control limit.
**
****Table 38.1: ****
Attributes of the Normal (Standard) Distribution**
To use process control measurement data effectively, it is
important to understand
the concept of variation. No two product or process
characteristics are exactly alike,
because any process contains many sources of variability. The
differences between
products may be large, or they may be almost immeasurably small,
but they are
always present. Some sources of variation in the process can
cause immediate
differences in the product, such as a change in suppliers or the
accuracy of an
individual's work. Other sources of variation, such as tool
wear, environmental
changes, or increased administrative control, tend to cause
changes in the product
or service only over a longer period of time.
To control and improve a process, we must trace the total
variation back to its
sources. Again the sources are common cause and special cause
variability.
Common causes are the many sources of variation that always
exist within a
process that is in a state of statistical control. Special
causes (often called assignable
causes) are any factors causing variation that cannot be
adequately explained by any
single distribution of the process output, as would be the case
if the process were in
statistical control. Unless all the special causes of variation
are identified and
corrected, they will continue to affect the process output in
unpredictable ways.
The factors that cause the most variability in the process are
the main factors found
on cause-and-effect analysis charts: people, machines,
methodology, materials,
measurement, and environment. These causes can either result
from special causes
or be common causes inherent in the process.
291
The theory of control charts suggests that if the source of
variation is from chance
alone, the process will remain within the three-sigma limits.
When the process goes
out of control, special causes exist. These need to be
investigated and corrective
action must be taken.
• **Control
Chart Types:** **
**
Just as there are two types of data, continuous and discrete,
there are two types of
control charts: variable charts for use with continuous data and
attribute charts for
use with discrete data. Each type of control chart can be used
with specific types of
data. Table 38.2 provides a brief overview of the types of
control charts and their
applications.
**
****Variables charts: **
Control charts for variables are
powerful tools that we can use
when measurements from a process are variable. Examples of
variable data are the
diameter of a bearing, electrical output, or the torque on a
fastener.
**
****Table 38.2: **
Types of Control Charts and Application
As shown in Table 38.2, and R charts are used to measure control
processes
whose characteristics are continuous variables such as weight,
length, ohms, time,
or volume. The p and NP charts are used to measure and control
processes
displaying attribute characteristics in a sample. We use p
charts when the number of
failures is expressed as a fraction, or NP charts when the
failures are expressed as a
number. The c and u charts are used to measure the number or
portion of defects in
a single item. The c control chart is applied when the sample
size or area is fixed,
and the u chart when the sample size or area is not fixed.
**
****Attribute charts: **
Although control charts are most often
thought of in terms of
variables, there are also versions for attributes. Attribute
data have only two values
(conforming/nonconforming, pass/fail, go/no-go, present/absent),
but they can still
be counted, recorded, and analyzed. Some examples are: the
presence of a required
label, the installation of all required fasteners, the presence
of solder drips, or the
continuity of an electrical circuit. We also use attribute
charts for characteristics
that are measurable, if the results are recorded in a simple
yes/no fashion, such as
the conformance of a shaft diameter when measured on a go/no-go
gauge, or the
acceptability of threshold margins to a visual or gauge check.
It is possible to use control charts for operations in which
attributes are the basis for
inspection, in a manner similar to that for variables but with
certain differences. If
292
we deal with the fraction rejected out of a sample, the type of
control chart used is
called a p chart. If we deal with the actual number rejected,
the control chart is
called an NP chart. If articles can have more than one
nonconformity, and all are
counted for subgroups of fixed size, the control chart is called
a c chart. Finally, if
the number of nonconformities per unit is the quantity of
interest, the control chart
is called a u chart.
The power of control charts (Shewhart techniques) lies in their
ability to determine
if the cause of variation is a special cause that can be
affected at the process level,
or a common cause that requires a change at the management
level. The
information from the control chart can then be used to direct
the efforts of
engineers, technicians, and managers to achieve preventive or
corrective action.
The use of statistical control charts is aimed at studying
specific ongoing processes
in order to keep them in satisfactory control. By contrast,
downstream inspection
aims to identify defects. In other words, control charts focus
on prevention of
defects rather than detection and rejection. It seems
reasonable, and it has been
confirmed in practice, that economy and efficiency are better
served by prevention
rather than detection.
**• ****Control
Chart Components:**
**
**
All control charts have certain features in common (Figure
38.16). Each control
chart has a centerline, statistical control limits, and the
calculated attribute or
control data. Additionally, some control charts contain
specification limits.
The centerline is a solid (unbroken) line that represents the
mean or arithmetic
average of the measurements or counts. This line is also
referred to as the X bar line
( ). There are two statistical control limits: the upper control
limit for values greater
than the mean and the lower control limit for values less than
the mean.
**
****Figure 38.16: **
Control Chart Elements
Specification limits are used when specific parametric
requirements exist for a
process, product, or operation. These limits usually apply to
the data and are the
pass/fail criteria for the operation. They differ from
statistical control limits in that
they are prescribed for a process, rather than resulting from
the measurement of the
process.
The data element of control charts varies somewhat among
variable and attribute
control charts. We will discuss specific examples as a part of
the discussion on
individual control charts.
293
**• ****Control
Chart Interpretation:**
**
**
There are many possibilities for interpreting various kinds of
patterns and shifts on
control charts. If properly interpreted, a control chart can
tell us much more than
simply whether the process is in or out of control. Experience
and training can lead
to much greater skill in extracting clues regarding process
behavior, such as that
shown in Figure 38.17. Statistical guidance is invaluable, but
an intimate
knowledge of the process being studied is vital in bringing
about improvements.
A control chart can tell us when to look for trouble, but it
cannot by itself tell us
where to look, or what cause will be found. Actually, in many
cases, one of the
greatest benefits from a control chart is that it tells when to
leave a process alone.
Sometimes the variability is increased unnecessarily when an
operator keeps trying
to make small corrections, rather than letting the natural range
of variability
stabilize. The following paragraphs describe some of the ways
the underlying
distribution patterns can behave or misbehave.
**
****Figure 38.17: **
Control Chart Interpretation
**
****Runs: **
When several successive points line up on one side of the central line, this
pattern is called a run. The number of points in that run is
called the length of the
run. As a rule of thumb, if the run has a length of seven
points, there is an
abnormality in the process. Figure 38.18 demonstrates an example
of a run.
**
****Figure 38.18: **
Process Run
**
****Trends**:
If there is a continued rise of all in a series of points, this pattern is
called a
trend. In general, if seven consecutive points continue to rise
or fall, there is an
abnormality. Often, the points go beyond one of the control
limits before reaching
seven. Figure 38.19 demonstrates an example of trends.
294
**
****Figure 38.19: **
Control Chart Trends
**
****Periodicity: **
Points that show the same pattern of
change (rise or fall) over
equal intervals denote periodicity. Figure 38.20 demonstrates an
example of
periodicity.
**
****Figure 38.20: **
Control Chart Periodicity
**
****Hugging the centerline or control limit. **
Points on the control chart that are
close to
the central line or to the control limit are said to hug the
line. Often, in this
situation, different types of data or data from different
factors have been mixed into
the subgroup. In such cases it is necessary to change the
sub-grouping, reassemble
the data, and redraw the control chart. To decide whether there
is hugging of the
center line, draw two lines on the control chart, one between
the centerline and the
UCL and the other between the center line and the LCL. If most
of the points are
between these two lines, there is an abnormality. To see whether
there is hugging of
one of the control limits; draw line two-thirds of the distance
between the center
line and each of the control lines. There is abnormality if 2
out of 3 points, 3 out of
7 points, or 4 out of 10 points lie within the outer one-third
zone. The abnormalities
should be evaluated for their cause(s) ad the corrective action
taken. Figure 38.21
demonstrates data hugging the LCL.
**
****Figure 38.21: **
Hugging the Centerline
295
**
****Out of control: **
An abnormality exists when data points
exceed either the
upper or lower control limits. Figure 38.22 illustrates this
occurrence.
**
**Figure 38.22: Control Chart Out of Control
*
**In control: *
No obvious abnormalities appear in the
control chart. Figure 38.23
demonstrates this desirable process state. |