Process capability
Process
The term specication refers to the requirements that a
capability
Cp index
product must satisfy to meet the clients needs.
Example
Criticism
Cpk
Example
Criticism
Given a quality characteristic, these specications often
take the
ANOVA
Designed experiments are typically analyzed using ANOVA
techniques.
ANOVA is an abbreviation referring to
analysis of variance.
The purpose of these slides is to provide a gentle
introduction to ANOVA. It may also serve as a handy
reminder for those
Welcome to MATH 427
Introduction
Chapter 1
Welcome to MATH 427 (Statistical Quality Control).
Denitions
Motivation
The course will meet Tue/Thu, 12:35 13:55.
Variability
Tolerance
Course material (slides, assignments, solutions, etc.)
Inspection
will be p
Acceptance sampling
Acceptance
Acceptance sampling (AS) refers to statistical techniques
sampling
Types of AS plans
Advantages
Disadvantages
whose ultimate purpose is the acceptance or rejection of lot
of items based on the analysis of items from that lot
Process capability
Process
The term specication refers to the requirements that a
capability
Cp index
product must satisfy to meet the clients needs.
Example
Criticism
Cpk
Example
Criticism
Given a quality characteristic, these specications often
take the
Solving problems
Issues faced
Companies typically face two types of quality problems:
Examples
Quality circles
sporadic quality problems;
Role of data
Problem
chronic quality problems.
solving
The fab seven
Sporadic problems require immediate action. They
Introduction to control charts
Introduction
Principle
A control chart is a graphical tool designed to track the
changes in a quality characteristic over time. It is used to
Denitions
Type of
variation
assess the past performance of the process;
Control li
Rational sub-groups revisited
Introduction
To be useful, a control chart must address the right
Allocation of
question.
the variation
Example
Data must be collected and organized in rational sub-groups
Option 1
Option 2
that truly reect the characteristic
EWMA charts
EWMA charts
CUSUM
charts
Suppose X1 , . . . , Xn are collected at regular time intervals. If
the process mean drifts slowly over time, the overall mean
V-masks
Design
Example
ARL
Tabular
CUSUM
CUSUM
status charts
Discussion
1
X=
n
n
Xi
i=1
wil
General procedure for X - and R-charts
Introduction
Revising limits
Using the
median range
Example
Robustness
Simulation
study
Other
detection
rules
Assume that the process is stable;
this justies the use of X and R.
Predict the stochastic behavior of X
Welcome to MATH 427
Introduction
Chapter 1
Welcome to MATH 427 (Statistical Quality Control).
Denitions
Motivation
We will meet here every Wednesday, 11:35 14:25.
Variability
Tolerance
Course material (slides, assignments, solutions, etc.)
Inspection
will
Factor allocation in a fractional plan
Recall that fractional plans are factorial designs in which
only a fraction of the runs is carried out.
Consequently, only a fraction of the main effects and
interactions can be estimated reliably from such plans.
It
Double-sampling plans
A double-sampling plan is a procedure in which, under
Doublesampling
certain circumstances, a second sample is required before
plans
the lot can be sentenced.
OC curves
Example
It involves four parameters, viz.
ASN curve
Grubbs table
General procedure for X - and R -charts
Introduction
Revising limits
Using the
median range
Example
Robustness
Simulation
study
Other
detection
rules
Assume that the process is stable;
this justies the use of X and R .
Predict the stochastic behavior of
Rational sub-groups revisited
Introduction
To be useful, a control chart must address the right
Allocation of
question.
the variation
Example
Data must be collected and organized in rational sub-groups
Option 1
Option 2
that truly reect the characteristic
Control charts for attributes
Introduction
The np-chart
So far, we focussed on control charts for measurements.
The p-chart
The c -chart
We will now consider control charts for attributes.
The u -chart
Such charts are used when the data are dichotomous
(p
Solving problems
Issues faced
Companies typically face two types of quality problems:
Examples
Quality circles
sporadic quality problems;
Role of data
Problem
chronic quality problems.
solving
The fab seven
Sporadic problems require immediate action. They
EWMA charts
Suppose X1 , . . . , Xn are collected at regular time intervals. If
the process mean drifts slowly over time, the overall mean
1
X=
n
n
Xi
i =1
will not give an accurate estimate of the process at any
given time, because all observations have
Introduction to experimental design
A designed experiment is a series of tests in which changes
are made on purpose to the input variables of a process.
The objective is to observe and identify corresponding
changes in the output response.
The bases of ex
Introduction to control charts
Introduction
Principle
Denitions
Type of
variation
A control chart is a graphical tool designed to track the
changes in a quality characteristic over time. It is used to
assess the past performance of the process;
Control li
CUSUM charts
Introduction
Example
The CUSUM chart was introduced by E.S. Page, from the
V-masks
University of Cambridge (Page 1954, Biometrika).
Design
Example
ARL
Tabular
Much like EWMA charts, its purpose is to detect drifts in the
process mean.
CUSUM
C
Blocking techniques
A blocking factor is an external variable that is used to group
units into blocks so that the experimental group and the
control group are matched.
In the previous example, suppose that we must carry out
the experiment over two days, v
Two-way ANOVA model
Suppose that we wish to study the effect of two factors A
and B on a response variable Y .
Assume that factor A can take a different values, and that
factor B can take b different values.
Each combination (i , j ) of A and B is called
Double-sampling plans
A double-sampling plan is a procedure in which, under
Doublesampling
certain circumstances, a second sample is required before
plans
the lot can be sentenced.
OC curves
Example
It involves four parameters, viz.
ASN curve
Grubbs table