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Chapter 36
Quality Engineering
(Review)
EIN 3390
Manufacturing Processes
Spring, 2011
36.1 Introduction
Objective of Quality Engineering:
Systematic reduction of variability, as shown
in Figure 36 – 1.
Variability is measured by sigma, s, standard
deviation, which decreases with reduction in variability.
Variation can be reduced by the application of
statistical techniques, such as multiple variable
analysis, ANOVA – Analysis of Variance, designed
experiments, and Taguchi methods.
36.1 Introduction
QE History:
- Acceptance sampling
- Statistical Process Control (SPC)
- Companywide Quality Control (CWQC) and Total Quality
Control (TQC)
- Six Sigma, DOE (Design of Experiment), Taguchi
methods
- Lean Manufacturing: “Lean" is a production practice that
considers the expenditure of resources for any goal other than the
creation of value for the end customer to be wasteful, and thus a
target for elimination
- Poka-Yoke: developed by a Japanese manufacturing engineer
named Shigeo Shingo who developed the concept. poka yoke
(pronounced "poh-kah yoh-kay") means to avoid (yokeru)
inadvertent errors (poka).
Process Control Methods
FIGURE 36-1 Over many years, many techniques have been used to reduce the variability in
products and processes.
36.1 Introduction

In manufacturing process, there are two
groups of causes for variations:
◦ Chance causes – produces random
variations, which are inherent and stable
source of variation
◦ Assignable causes – that can be detected
and eliminated to help improve the process.
36.1 Introduction
Manufacturing process is determined by
measuring the output of the process
 In quality control, the process is
examined to determine whether or not
the product conforms the design’s
specification, usually the nominal size
and tolerance

36.1 Introduction
Accuracy is reflected in your aim (the average
of all your shorts, see Fig 36 – 2)
Precision reflects the repeatability of the
process.
Process Capacity (PC) study quantifies the
inherent accuracy and precision.
Objectives:
- root out problems that can cause defective
products during production, and
- design the process to prevent the problem.
Accuracy vs. Precision
FIGURE 36-2 The concepts of
accuracy (aim) and precision
(repeatability) are shown in the
four target outcomes. Accuracy
refers to the ability of the
process to hit the true value
(nominal) on the average, while
precision is a measure of the
inherent variability of the
process.
Accuracy vs. Precision
FIGURE 36-2 The concepts of
accuracy (aim) and precision
(repeatability) are shown in the
four target outcomes. Accuracy
refers to the ability of the
process to hit the true value
(nominal) on the average, while
precision is a measure of the
inherent variability of the
process.
36.2 Determining Process Capability
The nature of process refers to both the
variability (or inherent uniformity) and
the accuracy or the aim of the process.
Examples of assignable causes of
variation in process : multiple machines
for the same components, operator
plunders, defective materials, progressive
wear in tools.
36.2 Determining Process Capability
Sources of inherent variability in the
process: variation in material properties,
operators variability, vibration and chatter.
These kinds of variations usually display a
random nature and often cannot be
eliminated. In quality control terms, these
variations are referred to as chance
causes.
36.2 Making PC Studies by Traditional Methods
The objective of PC study is to determine the
inherent nature of the process as compared to
the desired specifications.
The output of the process must be examined under
normal conditions, the inputs (e.g. materials,
setups, cycle times, temperature, pressure, and
operator) are fixed or standardized.
The process is allowed to run without tinkering
or adjusting, while output is documented
including time, source, and order production.
36.2 Making PC Studies by Traditional Methods
Histogram is a frequency distribution.
Histogram shows raw data and desired value,
along with the upper specification limit (USL)
and lower specification limit (LSL).
A run chart shows the same data but the data are
plotted against time.
The statistical data are used to estimate the mean
and standard deviation of the distribution.
Process Capability
1.001
FIGURE 36-3 The process capability study compares the
part as made by the manufacturing process to the
specifications called for by the designer. Measurements from
the parts are collected for run charts and for histograms for
analysis—see Figure 36-4.
Example of Process Control
FIGURE 36-4 Example of
calculations to obtain estimates
of the mean (m) and standard
deviation (s) of a process
36.2 Making PC Studies by Traditional Methods
m +-3s defines the natural capacity limits of the
process, assuming the process is approximately
normally distributed.
A sample is of a specified, limited size and is
drawn from the population.
Population is the large source of items, which
can include all items the process will produce
under specified condition.
Fig. 36 – 5 shows a typical normal curve and the
areas under the curve is defined by the standard
deviation.
Fig. 36 – 6 shows other distributions.
Normal Distribution
FIGURE 36-5 The normal or
bell-shaped curve with the areas
within 1s, 2s, and 3s for
a normal distribution; 68.26% of
the observations will fall within
1s from the mean, and
99.73% will fall within 3s
from the mean.
36.2 Histograms
A histogram is a representation of a frequency
distribution that uses rectangles whose widths represent
class intervals and whose heights are proportional to the
corresponding frequencies.
All the observations within in an interval are considered to
have the same value, which is the midpoint of the
interval.
A histogram is a picture that describes the variation in a
progress.
Histogram is used to 1) determine the process capacity, 2)
compare the process with specification, 3) to suggest
the shape of the population, and 4) indicate
discrepancy in data.
Disadvantages: 1) Trends aren’t shown, and 2) Time
isn’t counted.
Mean vs. Nominal
FIGURE 36-7
Histogram shows
the output mean m
from the process
versus nominal
and the tolerance
specified by the
designer versus
the spread as
measured by the
standard
deviation s. Here
nominal =49.2,
USL =62, LSL
=38, m =50.2, s
=2.
36.2 Run Chart or Diagram
A run chart is a plot of a quality characteristic
as a function of time. It provides some idea of
general trends and degree of variability.
Run chart is very important at startup to identify
the basic nature of a process. Without this
information , one may use an inappropriate tool
in analyzing the data.
For example, a histogram might hide tool wear if
frequent tool change and adjustment are made
between groups and observations.
Example of a Run Chart
FIGURE 36-8 An example of a
run chart or graph, which can
reveal trends in the process
behavior not shown by the
histogram.
36.2 Process Capability Indexes
The most popular PC index indicates if the process
has the ability to meet specifications.
The process capacity index, Cp, is computed as
follows:
Cp = (tolerance spread) / (6s)
= (USL – LSL) / (6s)
A value of Cp >= 1.33 is considered good.
The example in Fig 36-7:
Cp = (USL – LSL)/(6s) = (62 – 38)/(6 x 2) =2
36.2 Process Capability Indexes
The process capability ratio, Cp, only looks at
variability or spread of process (compared to
specifications) in term of sigmas. It doesn’t take
into account the location of the process mean, m.
Another process capability ratio Cpk for off-center
processes:
Cpk = min (Cpu, Cpl)
= min[Cpu= (USL – m)/(3s), Cpl= (m – LSL)/(3s)]
Output Shift
FIGURE 36-9 The output from the process is shifting
toward the USL, which changes the Cpk ratio but not
the Cp ratio.
Output Shift
FIGURE 36-9 The output from the process is shifting
toward the USL, which changes the Cpk ratio but not
the Cp ratio.
When s = 2.0
36.2 Process Capability Indexes
In Fig. 36 – 10, the following five cases are covered.
6s < USL –LSL or Cp > 1
b) 6s < USL –LSL, but process has shifted.
c) 6s = USL –LSL, or Cp = 1
d) 6s > USL –LSL or Cp < 1
e) The mean and variability of the process have both
changed.
If a process capability is on the order of 2/3 to
3/4 of the design tolerance, there is a high
probability that the process will produce all good
parts over a long time period.
a)
FIGURE 36-10 Five different
scenarios for a process output
versus the designer’s
specifications for the minimal
(50) and upper and lower
specifications of 65 and 38
respectively.
FIGURE 36-10 Five different
scenarios for a process output
versus the designer’s
specifications for the minimal
(50) and upper and lower
specifications of 65 and 38
respectively.
36.3 Inspection to Control Quality
Inspection is the function that controls
the quality manually, or automatically.
How much should be inspected:
Inspect every item being made
2. Sample
3. None. Assume that everything is
acceptable or the product is inspected by
customer, who will exchange it in case it
is defective.
1.
36.3.1 Statistical Process Control (SPC)
Sampling requires statistical techniques
for decisions about the acceptability of the
whole based on sample’s quality. This is
known as statistical process control
(SPC).
The most widely used basic SPC techniques
is the control charts.
Control charts for variables are used to
monitor the output of a process by
sampling, by measuring selected quality
characteristics, by plotting the sample
data on the chart, and then by making
decisions about the performance of the
process.
Figure 36 – 13 shows the basic structure of
two charts commonly used for variable
types of measurements.
The X chart tracks the aim (accuracy) of
the process.
The R chart (or s chart) tracks the
precision or variability of the process.
Usually, only X chart and R chart are
used unless the sample size is large,
and then s chart are used in place of R
chart.
36.3 Inspection to Control Quality
Quality Calculations
Sx/n
R = Xhigh – X low
FIGURE 36-13
Quality control chart
calculations. On the
charts, X plot and R
values over time. The
constants for
calculating UCL and
LCL values for the X
and R charts are
based on 3 standard
deviations.
s= R/d2
A2 = 3/[d2 SQRT(n)]
Where, n – sample size
Samples are drawn over time.
Because some sample statistics tend to be
normally distributed about their own
mean, x value are normally distributed
about x, and R values are normally
distributed about R, and s values are
normally distributed s.
Quality control charts are widely used as
aids in maintaining quality and
detecting trends in quality variation
before defective parts are actually
produced.
When sampling inspection is used, the typical
sample sizes are from 3 to about 12.
Fig 16 – 4 shows one example of X and R charts
for measuring a dimension of a gap on a part
with 25 samples of size 5 over 6 days.
FIGURE 36-14 Example of X
and R charts and the data set
of 25 samples [k 25 of size 5
(n = 5)].
(Source : Continuing Process
Critical and Process
Capability Improvement,
Statistical Methods Office,
Ford Motor Co., 1985.)
0.178
FIGURE 36-14 Example of X
and R charts and the data set
of 25 samples [k 25 of size 5
(n = 5)].
(Source : Continuing Process
Critical and Process
Capability Improvement,
Statistical Methods Office,
Ford Motor Co., 1985.)
Cp = ? Cpk = ?
0.178
Errors in
Textbook
After control charts have been established, the
charts act as a control indicator for the process.
 If the process is operating under chance cause
conditions, the data will appear random (no
trends or pattern).
 If X, R or s values fall outside the control limits
or if nonrandom trends occur (like 7 points on
one side of the central line or 6 successive
increasing or decreasing points appear), an
assignable cause or change may have
occurred, and action should be taken to correct
the problem.

36.4 Process Capability Determination from
Control Chart Data
36.4 Process Capability Determination
from Control Chart Data



After the process is determined to be “under
control”, the data can be used to estimate the
process capability parameters.
A sample size 5 was used in the example, so n = 5
(Fig 36 – 14). 25 groups of samples were drawn
from the process, so K = 25.
For each sample, the sample mean x and sample
range R are computed. For large samples, N > 12,
the standard deviation of each sample should be
computed rather than the range.
36.5 Determining Causes For
Problems in Quality
Fishbone diagram developed by Kaorw Ishikowa
in 1943 is used in conjunction with control chart
to root out the causes of problems.
Fishbone diagram is also known as Cause-andeffect.
Fishbone lines are drawn from the main line. These
lines organize the main factors. Branching from
each of these factors are even more detailed
factors.
36.5 Determining Causes For
Problems in Quality
Four “M” are often used in fishbone diagram:
Men, Machines, Materials, and Methods.
CEDAC – Cause-and-effect diagram with the
additional of cards. The effect is often tracked
with a control chart. The possible causes of
defects or problems are written on cards and
inserted in slots in the cards.
Fishbone Diagram
FIGURE 36-15 Example of a
fishbone diagram using a control
chart to show effects.
Fishbone Diagram
FIGURE 36-15 Example of a
fishbone diagram using a control
chart to show effects.
36.5.1 Sampling Errors
Two kinds of decision errors:
Type I Error (a error): process is running
perfectly, but sample data indicate that
something is wrong.
Type II error (b error): process is not running
perfectly and was making defective products, but
sample data didn’t indicate that anything was
wrong.
Errors
FIGURE 36-16 When you look
at some of the output from a
process and decide about the
whole (i.e., the quality of the
process), you can make two
kinds of errors.
36.5.3 Design of Experiments (DOE)
and Taguchi Methods
SPC looks at processes and control, Taguchi
methods loosely implies “improvement”.
DOE and Taguchi methods span a much wider
scope of functions and include the design
aspects of products and processes, areas
that were seldom treated from quality standpoint
view. Consumer is the focus on quality, and the
methods of quality design and controls have
been incorporated into all phases of production.
Taguchi Method
FIGURE 36-18 The use of
Taguchi methods can reduce the
inherent process variability, as
shown in the upper figure.
Factors A, B, C, and D versus
process variable V are shown in
the lower figure.
36.5.4 Six Sigma
FIGURE 36-19 To move to six
sigma capability from four sigma
capability requires that the
process capability (variability) be
greatly improved (s reduced). The
curves in these figures represent
histograms or curves fitted to
histograms.
36.5.5 Total Quality Control (TQC)
Total Quality Control (TQC) was first used by A.
V. Feigenbaum in may 1957.
TQC means that all departments of a company
must participate in quality control (Table 36 – 1).
Final Exam
Date:
April 26, 2011 (Tuesday)
Time:
12:00 pm– 2:00pm
Classroom: EC 2410