Transcript StatMethodsForQualityControl

Slides by
JOHN
LOUCKS
&
SPIROS
VELIANITIS
Slide 1
Chapter 20
Statistical Methods for Quality Control
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Philosophies and Frameworks
Statistical Process Control
Acceptance Sampling
Slide 2
Quality
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Quality is “the totality of features and characteristics
of a product or service that bears on its ability to
satisfy given needs.”
Organizations recognize that they must strive for
high levels of quality
They have increased the emphasis on methods for
monitoring and maintaining quality.
Slide 3
Total Quality
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Total Quality (TQ) is a people-focused management system that aims at
continual increase in customer satisfaction at continually lower cost
TQ is a total system approach (not a separate work program) and an integral
part of high-level strategy.
TQ works horizontally across functions, involves all employees, top to
bottom, and extends backward and forward to include both the supply and
customer chains.
TQ stresses learning and adaptation to continual change as keys to
organization success.
Regardless of how it is implemented in different organizations, Total
Quality is based on three fundamental principles:
• a focus on customers and stakeholders
• participation and teamwork throughout the organization
• a focus on continuous improvement and learning
Slide 4
Quality Philosophies
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Dr. W. Edwards Deming
• One of Deming’s major contributions was to direct attention
away from inspection of the final product or service towards
monitoring the process that produces the final product or
service with emphasis of statistical quality control
techniques. In particular, Deming stressed that in order to
improve a process one needs to reduce the variation in the
process.
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Joseph Juran
• Proposed a simple definition of quality: fitness for
use
• His approach to quality focused on three quality
processes: quality planning, quality control, and
quality improvement
Slide 5
Quality Frameworks
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Malcolm Baldrige National Quality Award: Established in 1987
and given by the U.S. president to organizations that apply and
are judged to be outstanding in seven areas
ISO 9000: A series of five standards published in 1987 by the
International Organization for Standardization in Geneva,
Switzerland.
Six Sigma: Six sigma level of quality means that for every
million opportunities no more than 3.4 defects will occur.
• The methodology created to reach this quality goal is
referred to as Six Sigma.
• Six Sigma is a major tool in helping organizations achieve
Baldrige levels of business performance and process quality.
Slide 6
Quality Terminology
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Quality Assurance: QA refers to the entire system of
policies, procedures, and guidelines established by
an organization to achieve and maintain quality. QA
consists of two functions:
• Quality Engineering - Its objective is to include
quality in the design of products and processes
and to identify potential quality problems prior to
production.
• Quality Control - QC consists of making a series of
inspections and measurements to determine
whether quality standards are being met.
Slide 7
Statistical Process Control (SPC)
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In order to reduce the variation of a process, one needs to recognize that the
total variation is comprised of common causes and specific causes. At any
time there are numerous factors which individually and in interaction with
each other cause detectable variability in a process and its output. Those
factors that are not readily identifiable and occur randomly are referred to as
the common causes, while those that have large impact and can be
associated with special circumstances or factors are referred to as specific
causes.
When a process has variation made up of only common causes then the
process is said to be a stable process, which means that the process is in
statistical control and remains relatively the same over time. This implies
that the process is predictable, but does not necessarily suggest that the
process is producing outputs that are acceptable as the amount of common
variation may exceed the amount of acceptable variation. If a process has
variation that is comprised of both common causes and specific causes then
it is said to be an unstable process, which means that the process is not in
statistical control. An unstable process does not necessarily mean that the
process is producing unacceptable products since the total variation
(common variation + specific variation) may still be less than the acceptable
level of variation.
Slide 8
Statistical Process Control (SPC) Example
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Consider a manufacturing situation where a hole needs to be drilled into a
piece of steel. We are concerned with the size of the hole, in particular the
diameter, since the performance of the final product is a function of the
precision of the hole. As we measure consecutively drilled holes, with very
fine instruments, we will notice that there is variation from one hole to the
next. Some of the possible common sources can be associated with the
density of the steel, air temperature, and machine operator. As long as these
sources do not produce significant swings in the variation they can be
considered common sources. On the other hand, the changing of a drill bit
could be a specific source provided it produces a significant change in the
variation, especially if a wrong sized bit is used!
SPC Determination Steps:
• Sample and inspect the output of the production process.
• Using SPC methods, determined whether variations in output are due
to common causes or assignable causes.
• Decide whether the process can be continued or should be adjusted to
achieve a desired quality level.
Slide 9
SPC Hypotheses
SPC procedures are based on hypothesis-testing
methodology.
Null Hypothesis
H0 is formulated in terms of the production
process being in control.
Alternative Hypothesis
Ha is formulated in terms of the production
process being out of control.
Slide 10
Identification Tools
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There are a number of tools used in practice to determine
whether specific causes of variation exist within a process. In
the remaining part of this chapter we will discuss how time
series plots, the runs test, a test for normality and control charts
are used to identify specific sources of variation. As will
become evident there is a great deal of similarity between time
series plots and control charts. In particular, the control charts
are time series plots of statistics calculated from subgroups of
observations, whereas when we speak of time series plots we
are referring to plots of consecutive observations.
Slide 11
Time Series Plots
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A time series plot is a graph where the horizontal axis represents time and
the vertical axis represents the units in which the variable of concern is
measured. For example, consider the following series where the variable of
concern is the price of Anheuser Busch Co. stock on the last trading day for
each month from June 1995 to June 2000 inclusive. Using the computer we
are able to generate the following time series plot. Note that the horizontal
axis represents time and the vertical axis represents the price of the stock,
measured in dollars.
When using a time series plot to determine whether a process is stable, what
one is seeking is the answer to the following questions:
• 1. Is the mean constant?
• 2. Is the variance constant?
• 3. Is the series random (i.e. no pattern)?
Rather than initially showing the reader time series plots of stable processes,
we show examples of non stable processes commonly experienced in
practice.
Slide 12
Runs Test
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Frequently non-stable processes can be detected by visually
examining their time series plots. However, there are times
when patterns exist that are not easily detected. A tool that can
be used to identify nonrandom data in these cases is the runs
test.
To determine if the observed number significantly differs from
the expected number, we encourage the reader to rely on
statistical software (StatGraphics) and utilize the p-values that
are generated.
Slide 13
Test for Normality
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Another attribute of a stable process, which you may recall
lacks specific causes of variation, is that the series follows a
normal distribution. To determine whether a variable follows a
normal distribution one can examine the data via a graph,
called a histogram, and/or utilize a test which incorporates a
chi-square test statistic.
StatGraphics, will overlay the observed data with a theoretical
distribution calculated from the sample mean and sample
standard deviation in order to assist in the evaluation.
Slide 14
Example
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Stationarity? From the visual inspection (top
chart), one can tell the series is stationary.
Normality? From this, one can see that the
distribution of the middle chart appears
somewhat like a normal distribution. Not
exactly, but in order to see how closely it
does relate to theoretical normal distribution,
we rely on the Chi-square test. As we can see
from the table, the p-value (significance
level) equals 0.1356. Since the p-value is
greater than alpha (0.05), we retain the null
hypothesis.
Random? Relying upon the nonparametric
test for randomness. we can just look at the
p-value, which in this case is 0.086
(rounded). So, since the p-value again is
larger than our value of α = 0.05, we are able
to conclude that we cannot reject the null
hypothesis.
Slide 15
Control Charts
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SPC uses graphical displays known as control charts to
monitor a production process.
Control charts provide a basis for deciding whether the
variation in the output is due to common causes (in control)
or assignable causes (out of control).
Two important lines on a control chart are the upper control
limit (UCL) and lower control limit (LCL).
These lines are chosen so that when the process is in control,
there will be a high probability that the sample finding will
be between the two lines.
Values outside of the control limits provide strong evidence
that the process is out of control.
Slide 16
Control Chart Types
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Variables Control Charts
• X-bar Chart - This chart is used if the quality of the output is
measured in terms of a variable such as length, weight,
temperature, and so on. x represents the mean value found
in a sample of the output.
• R Chart - This chart is used to monitor the range of the
measurements in the sample.
• The X-Bar and R Charts procedure creates control charts for
a single numeric variable where the data have been collected
in subgroups.
Attributes Control Charts
• p Chart - This chart is used to monitor the proportion
defective in the sample.
• np Chart - This chart is used to monitor the number of
defective items in the sample.
Slide 17
x Chart Structure
x
Upper Control Limit
UCL
Center Line
Process Mean
When in Control
LCL
Time
Lower Control Limit
Slide 18
R Chart
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Because the control limits for the x chart depend on
the value of the average range, these limits will not
have much meaning unless the process variability is
in control.
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In practice, the R chart is usually constructed before
the x chart.
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If the R chart indicates that the process variability is
in control, then the x chart is constructed.
Slide 19
Control Limits for an R Chart: Process
Mean and Standard Deviation Unknown
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When Granite Rock’s packaging process is in control, the
weight of bags of cement filled by the process is normally
distributed with a mean of 50 pounds and a standard deviation
of 1.5 pounds. Suppose Granite does not know the true mean
and standard deviation for its bag filling process. It wants to
develop x and R charts based on twenty samples of 5 bags each.
The twenty samples, collected when the process was in control,
resulted in an overall sample mean of 50.01 pounds and an
average range of .322 pounds.
Slide 20
Control Limits for an R Chart: Process
Mean and Standard Deviation Unknown
R Chart for Granite Rock Co.
0.80
Sample Range R
0.70
UCL
0.60
0.50
0.40
0.30
0.20
0.10
LCL
0.00
0
5
10
15
20
Sample Number
Slide 21
Control Limits for an x Chart: Process
Mean and Standard Deviation Unknown
_
=
x = 50.01, R = .322, n = 5
=
_
UCL = x + A2R = 50.01 + .577(.322) = 50.196
_
LCL = x= - A2R = 50.01 - .577(.322) = 49.824
Slide 22
Control Limits for an x Chart: Process
Mean and Standard Deviation Unknown
x Chart for Granite Rock Co.
Sample Mean
50.3
UCL
50.2
50.1
50.0
49.9
49.8
LCL
49.7
0
5
10
15
Sample Number
20
Slide 23
Control Limits For a p Chart
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Example: Norwest Bank
Every check cashed or deposited at
Norwest Bank must be encoded with
the amount of the check before it can
begin the Federal Reserve clearing
process. The accuracy of the check
encoding process is of utmost
importance. If there is any discrepancy
between the amount a check is made
out for and the encoded amount, the check is
defective.
Slide 24
Control Limits For a p Chart
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Example: Norwest Bank
Twenty samples, each consisting of 400
checks, were selected and examined
when the encoding process was known
to be operating correctly. The number
of defective checks found in the 20
samples are listed below.
6 4 5
5 11 5
7
8
6
6
8
4
6
7
9
5
8
6
5
7
Slide 25
Control Limits For a p Chart
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Suppose Norwest does not know the proportion
of defective checks, p, for the encoding process when
it is in control.
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We will treat the data (20 samples) collected as one
large sample and compute the average number of
defective checks for all the data. That value can then
be used to estimate p.
Slide 26
Control Limits For a p Chart
Encoded Checks Proportion Defective
0.045
Sample Proportion p
0.040
0.035
UCL
0.030
0.025
0.020
0.015
0.010
0.005
LCL
0.000
0
5
10
15
20
Sample Number
Slide 27
NP Charts
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The NP Chart procedure creates a control chart for data that
describes the number of times an event occurs in m samples
taken from a product or process. The data might represent the number
of defective items in a manufacturing process, the number of
customers that return a product, or any other attribute that can
be classified as acceptable or unacceptable.
Slide 28
Interpretation of Control Charts
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The location and pattern of points in a control chart
enable us to determine, with a small probability of
error, whether a process is in statistical control.
A primary indication that a process may be out of
control is a data point outside the control limits.
Certain patterns of points within the control limits
can be warning signals of quality problems: a large
number of points on one side of center line OR six or
seven points in a row that indicate either an
increasing or decreasing trend.
Slide 29
Acceptance Sampling
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Acceptance sampling is a statistical method that
enables us to base the accept-reject decision on the
inspection of a sample of items from the lot.
The items of interest can be incoming shipments of
raw materials or purchased parts as well as finished
goods from final assembly.
Acceptance sampling has advantages over 100%
inspection.
Acceptance sampling is based on hypothesis-testing
methodology
• H0: Good-quality lot
• Ha: Poor-quality lot
Slide 30
Acceptance Sampling Procedure
Lot received
Sample selected
Sampled items
inspected for quality
Quality is
satisfactory
Results compared with
specified quality characteristics
Quality is not
satisfactory
Accept the lot
Reject the lot
Send to production
or customer
Decide on disposition
of the lot
Slide 31