STATISTICAL QUALITY CONTROL
Statistical
methods are analytical tools used to evaluate men, materials, Machines, or processes.
Evaluations obtained by these methods assist in maintaining desired result by
using past history to predict capabilities or trends. Such analytical methods
are management tools which furnish data to all levels supervision for
appropriate action. Some advantages of statistical techniques in interpreting
engineering data and controlling manufactured products are:
More
uniform at a higher level.
Less
waste by reduction of rework and scrap
Improved
inspection by better planning and better execution.
Higher
production of good parts per man per machine hour.
Improved
design tolerance.
Better
plant relations through coordinated effort.Control through statistical methods
differs from the procedures of manufacturing a product according to schedule and
then sorting the products into acceptable and non-acceptable lots. Eventually
these control methods help to decide.
When
the process is operating at a satisfactory level.
When
the process level is not satisfactory and corrective action is required to
prevent the manufacture of unacceptable products.In order to ensure high levels
of quality, elementary statistical techniques have been developed to‘control’
or ‘monitor’ the quality of a product. These techniques and the actions of
implementing the mare referred to as Statistical Quality Control (S.Q.C.).
Statistical quality control has traditionally been divided into two categories,
namely; acceptance sampling and statistical process control.
Acceptance sampling
Acceptance
sampling is
an attempt to judge the quality of lots that have been made from samples
from those lots. While Process Controlis
the use of techniques to monitor the process as the product is being made to
ensure that defectives are not being made to begin with
UNIT 1 QUALITY
The
word ‘quality’ is often used to signify ‘excellence’ of a product or service –
we hear talk about‘ Rolls-Royce quality’ and ‘top quality’. In some
manufacturing companies, quality may be used to indicates that a product
conforms to certain physical characteristics set down with a particularly
‘tight ’specification. But if we are to manage quality, it must be defined in a
way, which recognizes the true requirements of the customers. The ability to
meet the customers’ requirements is vital, not only between two separate
organizations, but within the same organization. There exists in every factory,
every department, every office, a series of suppliers and customers.
The typist
is a supplier to the boss – is the typist meeting the requirements ?Does the
boss receive error-free typing set out as he wants it, when he wants it? If so,
then we have a quality typing service. Does the factory receive from its
supplier defect-free parts which conform to there requirements of the assembly
process? If so, then we have a quality supplier. For industrial and commercial
organizations, which are viable only if they provide satisfaction to the consumer,
competitiveness in quality is not only central to profitability, but crucial to
business survival .The consumers should not be required to make a choice
between price and quality, and for manufacturing or service organizations to
continue to exist, they must learn how to manage quality. In today’s tough and challenging
business environment, the development and implementation of a comprehensive
quality policy is not merely desirable – it is essential. Every day, people in
certain factories scrutinize together the results of the examination of the
previous day’s production, and commence the ritual battle
over whether the material is suitable for despatch to the customer. One may be
called the Production Manager and another the Quality Control Manager. They may argue
and debate the evidence before them, the rights and wrongs of the
specification, and each tries to convince the other of the validity of their
argument. Sometimes they nearly break into fighting. This ritual is associated
with trying to answer the question:
correctly’
being a flexible word depending on the interpretation given to the
specification on that particular day. This is not quality control,
it
is post-production detection wasteful detection of bad product before it hits
the customers. There is a belief in some quarters that to achieve quality we
must check, test, inspect or measure – the ritual pouring on of quality at the
end of the process – and that quality, therefore, is expensive.
This is
nonsense, but it is frequently encountered. In the office we find staff
checking other people’s work before it goes out, validating computer input
data, checking invoices, typing, etc. There is also quite a lot of looking for
things, chasing things that are late, apologizing to customers for
non-delivery, and so on – waste, waste and more waste. Quality is now beyond
conformance to specification as a measure of evaluating excellence, it is now evaluation
of target value and continuously striving to decrease this variability about
the target value to make more uniform product. Quality is defined simply as meeting
the requirements of the customer and this has been expressed inmany ways by
other authors:
Fitness
for purpose or use (Juran).The
totality of features and characteristics of a product or service that bear on
its ability to satisfy stated or implied needs (BS 4778: Part 1: 1987 (ISO 8402:
1986).
QUALITY
The word ‘quality’ is often used to signify
‘excellence’ of a product or service – we hear talk about‘ Rolls-Royce quality’
and ‘top quality’. In some manufacturing companies, quality may be used to indicates
that a product conforms to certain physical characteristics set down with a
particularly ‘tight ’specification. But if we are to manage quality, it must be
defined in a way, which recognizes the true requirements of the customers. The
ability to meet the customers’ requirements is vital, not only between two
separate organizations, but within the same organization. There exists in every
factory, every department, every office, a series of suppliers and customers.
The typist is a supplier to the boss – is the typist meeting the requirements ?
Does the boss receive error-free typing set out as
he wants it, when he wants it? If so, then we have a quality typing service.
Does the factory receive from its supplier defect-free parts which conform to
the requirements of the assembly process? If so, then we have a quality
supplier. For industrial and commercial organizations, which are viable only if
they provide satisfaction to the consumer, competitiveness in quality is not
only central to profitability, but crucial to business survival .The consumers
should not be required to make a choice between price and quality, and for manufacturing
or service organizations to continue to exist, they must learn how to manage
quality. In today’s tough and challenging business environment, the development
and implementation of a comprehensive quality policy is not merely desirable –
it is essential. Every day, people in certain factories scrutinize together the
results of the examination of the previous day’s production, and commence the ritual battle
over whether the material is suitable for despatch to the customer. One may be
called the Production Manager and another the Quality Control Manager. They may argue
and debate the evidence before them, the rights and wrongs of the
specification, and each tries to convince the other of the validity of their
argument. Sometimes they nearly break into fighting. This ritual is associated
with trying to answer the question: ‘
Have we done
the job correctly?
correctly’ being a flexible word depending on the
interpretation given to the specification on that particular day. This is not
quality control,
it is post-production detection wasteful detection
of bad product before it hits the customers. There is a belief in some quarters
that to achieve quality we must check, test, inspect or measure – the ritual
pouring on of quality at the end of the process – and that quality, therefore,
is expensive. This is nonsense, but it is frequently encountered. In the office
we find staff checking other people’s work before it goes out, validating
computer input data, checking invoices, typing, etc. There is also quite a lot
of looking for things, chasing things that are late, apologizing to customers
for non-delivery, and so on – waste, waste and more waste. Quality is now
beyond conformance to specification as a measure of evaluating excellence, it
is now evaluation of target value and continuously striving to decrease this
variability about the target value to make more uniform product. Quality is
defined simply as meeting the requirements of the customer and this has been
expressed inmany ways by other authors:
Fitness for purpose or use (Juran).
The totality of features and characteristics of a
product or service that bear on its ability to satisfystated or implied needs
(BS 4778: Part 1: 1987 (ISO 8402: 1986))
Most people will have some concept of what
reliability is from everyday life, for example, people may discuss how reliable
their washing machine has been over the length of time they have owned it.
Similarly, a car that doesn’t need to go to the garage for repairs often,
during its lifetime, would be said to have been reliable. It can be said that
reliability is quality over time. Quality is associated with workmanship and
manufacturing and therefore if a product doesn’t work or breaks as soon as you
buy it you would consider the product to have poor quality.
However if over time parts of the product wear-out
before you expect them to then this would be termed poor reliability. The
difference therefore between quality and reliability is concerned with time and
more specifically product life time. Reliability engineering has both
quantitative and qualitative aspects; measurements of reliability are necessary
for customer requirements compliance. However measuring reliability does not
make a product reliable, only by designing in reliability can a product achieve
its reliability targets. These lecture notes will therefore introduce some of
the terminology used in reliability engineering. It will provide information
about measuring reliability as well as designing for reliability. Moreover it
will emphasise the importance of good engineering principles to ensure product
reliability. By identifying possible causes of failure and elimination will
obviously help to improve product reliability. The formal definition of
reliability is as follows: The ability of an item to perform a required
function under stated conditions for a stated period of time. BS4778 Another
definition concerns the probabilistic nature of measuring reliability, i.e. the
probability of an item to perform a required function under specified
conditions for a stated period of time. It is therefore a measure of
engineering uncertainty and to quantify reliability involves the use of
statistics and more specifically probability theory. These notes will also
describe some useful probability distributions that can describe the lifetime
behaviour of products.
What is reliability? Reliability is associated with
unexpected failures of products or services and understanding why these
failures occur is key to improving reliability. The main reasons why failures
occur include: • The product is not fit for purpose or more specifically the
design is inherently incapable. • The item may be overstressed in some way.
Warwick Manufacturing Group Introduction to Reliability Engineering Page 2 •
Failures can be caused by wear-out • Failures might be caused by variation. •
Wrong specifications may cause failures. • Misuse of the item may cause
failure. • Items are designed for a specific operating environment and if they
are then used outside this environment then failure can occur. There are many
reasons for failure in items the list above is a generic list. The load and
strength of an item may be generally known, however there will always be an
element of uncertainty. The actual strength values of any population of
components will vary; there will be some that are relatively strong, others
that are relatively weak, but most will be of nearly average strength.
Similarly there will be some loads greater than others but mostly they will be
average. the load strength relationship with no overlaps. Load Strength Probability
: load strength relationship , no overlaps However there is an overlap of the two distributions then
failures will occur. There therefore needs to be a safety margin to ensure that
there is no overlap of these distributions. Load Strength Probability Failure load
strength relationship - overlaps Warwick Manufacturing Group Introduction to
Reliability Engineering It is clear that to ensure good reliability the causes
of failure need to be identified and eliminated. Indeed the objectives of
reliability engineering are: • To apply engineering knowledge to prevent or
reduce the likelihood or frequency of failures; • To identify and correct the
causes of failure that do occur; • To determine ways of coping with failures
that do occur; • To apply methods of estimating the likely reliability of new
designs, and for analysing reliability data. These notes will discuss some of
the techniques that can be used to identify failures as well as the statistical
techniques for analysing reliability important? Unreliability has a number of
unfortunate consequences and therefore for many products and services is a
serious threat. For example poor reliability can have implications for: •
Safety • Competitiveness • Profit margins • Cost of repair and maintenance •
Delays further up supply chain • Reputation • Good will KEY POINTS •
Reliability is a measure of uncertainty and therefore estimating reliability
means using statistics and probability theory • Reliability is quality over
time • Reliability must be designed into a product or service • Most important
aspect of reliability is to identify cause of failure and eliminate in design
if possible otherwise identify ways of accommodation • Reliability is defined
as the ability of an item to perform a required function without failure under
stated conditions for a stated period of time • The costs of unreliability can
be damaging to a company Warwick Manufacturing Group Introduction to
Reliability Engineering
Measuring reliability Requirements Many customers
will produce a statement of the reliability requirements that is included in
the specification of the product. This statement should include the following:
• The definition of failure related to the product’s function and should cover
all failure modes relevant to the function; • A full description of the
environments in which the product will be stored, transported, operated and
maintained; • A statement of the reliability requirement Care must be given in
defining failure to ensure that the failure criteria are unambiguous. Failure
should always relate to a measurable parameter or to a clear indication. For
example, a definition of failure could include ‘failure of a function to
operate’. To be able to design for the load of the product the design team must
have accurate information concerning the environment of the product. If an item
must fully operate at high altitude with extreme changes in temperature then
the design must be robust enough to withstand such environmental factors.
Similarly if a product is stored in extreme conditions prior to use then the
design must accommodate for the storage conditions. The reliability requirement
should be stated in a way which can be verified, and which makes sense relative
to the use of the product. The simplest requirement is to state that no failure
will occur under stated conditions. Reliability requirements based on life
parameters must be based on the corresponding life distributions. A common
parameter used is MTBF, when a constant failure rate is assumed. Reliability
and Maintainability casE has recently moved away from prescriptive reliability
requirements and now requests a reliability case from their suppliers. The
reliability and maintainability (R&M) case is defines as
“A reasoned, auditable argument created to support
the contention that a defined system satisfies the R&M requirements” . DEF
STAN 0042 part 3 is a document produced by the UK MOD that gives guidance on
what goes into an R&M The bath tub curve The bath-tub curve is a
representation of the reliability performance of components or non repaired
items. It observes the reliability performance of a large sample of homogenous
items entering the field at some start time (usually zero). If we observe the
items over their lifetime without replacement then we can observe three distinct
shapes or periods curve and these 3 periods. The infant mortality or early
failures portion shows that the population will initially experience a high
hazard function that starts to decrease. This Warwick Manufacturing Group
Introduction to Reliability Engineering Page 5 period of time represents the
burn-in or debugging period where weak items are weeded out. After the initial
phase when the weak components have been weeded out and mistakes corrected, the
remaining population reaches a relatively constant hazard function period,
known as the useful life period. you can see that the hazard function is
constant, this shape can be modelled by the exponential distribution when
failure are occurring randomly through time. The final portion of the bath-tub
curve is called the wear-out phase, this is when the hazard function increases
with time. Useful Life Infant Mortality Wear Out Hazard function Time Useful
Life Infant Mortality Wear Out The bath-tub curve 2.3 Life distributions 2.3.1
Distribution functions If you take a large number of measurements you can draw
a histogram to show the how the measurements vary. A more useful diagram, for
continuous data, is the probability density function. engineering; these are
called, the exponential, Weibull and lognormal distributions. The normal
distribution as discussed in both the Six Sigma and SPC lectures is not
generally used in reliability engineering (although it is sometimes used).
Warwick Manufacturing Group Introduction to Reliability Engineering Page 8 The
Exponential Distribution When an item is subject to failures that occur in
random intervals and the expected number of failures is the same for long
periods of time then the distribution of failures is said to fit an exponential
distribution. the total operating time. The exponential distribution is the
most commonly used distribution in reliability engineering and models the
useful life portion of the bath-tub curve. The Weibull Distribution can be
modelled by an exponential distribution with η=1/λ . When β<1, we get a decreasing hazard function and When β>1,
we get a increasing hazard function Figure 7, below, shows the Weibull shape
parameters superimposed on the bath-tub curve. Warwick Manufacturing Group
Introduction to Reliability Engineering Page 9 Useful Life Infant Mortality
Wear Out Hazard function Time Useful Life Infant Mortality.
UNIT 4
UNIT 4
Reliability in statistics and psychometrics is the overall
consistency of a measure. A measure is said to have a high reliability if
it produces similar results under consistent conditions.
WARWICK MANUFACTURING GROUP Product Excellence using
6 Sigma (PEUSS) Introduction to Reliability Section 7 Warwick Manufacturing
Group AN INTRODUCTION TO RELIABILITY ENGINEERING
Contents 1 Introduction 1 2 Measuring reliability 4
3 Design for reliability 12 4 Reliability management 34 5 Summary 35 Copyright
© 2007 University of Warwick Warwick Manufacturing Group Introduction to
Reliability Engineering
RELIABILITY ENGINEERING 1
Introduction
Definition Most people will have some concept of
what reliability is from everyday life, for example, people may discuss how
reliable their washing machine has been over the length of time they have owned
it. Similarly, a car that doesn’t need to go to the garage for repairs often,
during its lifetime, would be said to have been reliable. It can be said that
reliability is quality over time. Quality is associated with workmanship and
manufacturing and therefore if a product doesn’t work or breaks as soon as you
buy it you would consider the product to have poor quality. However if over time
parts of the product wear-out before you expect them to then this would be
termed poor reliability. The difference therefore between quality and
reliability is concerned with time and more specifically product life time.
Reliability engineering has both quantitative and qualitative aspects;
measurements of reliability are necessary for customer requirements compliance.
However measuring reliability does not make a product reliable, only by
designing in reliability can a product achieve its reliability targets. These
lecture notes will therefore introduce some of the terminology used in
reliability engineering.
It will provide information about measuring
reliability as well as designing for reliability. Moreover it will emphasise
the importance of good engineering principles to ensure product reliability. By
identifying possible causes of failure and elimination will obviously help to
improve product reliability. The formal definition of reliability is as
follows: The ability of an item to perform a required function under stated
conditions for a stated period of time. BS4778 Another definition concerns the
probabilistic nature of measuring reliability, i.e. the probability of an item
to perform a required function under specified conditions for a stated period
of time. It is therefore a measure of engineering uncertainty and to quantify
reliability involves the use of statistics and more specifically probability
theory. These notes will also describe some useful probability distributions
that can describe the lifetime behaviour of products.
What is reliability?
Reliability
is associated with unexpected failures of products or services and
understanding why these failures occur is key to improving reliability. The
main reasons why failures occur include: • The product is not fit for purpose
or more specifically the design is inherently incapable. • The item may be
overstressed in some way. Warwick Manufacturing Group Introduction to
Reliability Engineering • Failures can be caused by wear-out • Failures
might be caused by variation. • Wrong specifications may cause failures. •
Misuse of the item may cause failure. • Items are designed for a specific
operating environment and if they are then used outside this environment then
failure can occur. There are many reasons for failure in items the list above
is a generic list. The load and strength of an item may be generally known,
however there will always be an element of uncertainty. The actual strength
values of any population of components will vary; there will be some that are
relatively strong, others that are relatively weak, but most will be of nearly
average strength. Similarly there will be some loads greater than others but
mostly they will be average. likely reliability of new designs, and for
analysing reliability data. These notes will discuss some of the techniques
that can be used to identify failures as well as the statistical techniques for
analysing reliability .Why is Reliability important? Unreliability has a number
of unfortunate consequences and therefore for many products and services is a
serious threat. For example poor reliability can have implications for: •
Safety • Competitiveness • Profit margins • Cost of repair and maintenance •
Delays further up supply chain • Reputation • Good will KEY POINTS •
Reliability is a measure of uncertainty and
therefore estimating reliability means using statistics and probability theory
• Reliability is quality over time • Reliability must be designed into a
product or service • Most important aspect of reliability is to identify cause
of failure and eliminate in design if possible otherwise identify ways of
accommodation • Reliability is defined as the ability of an item to perform a
required function without failure under stated conditions for a stated period
of time • The costs of unreliability can be damaging to a company Warwick Manufacturing
Group Introduction to Reliability Engineering Measuring reliability
Requirements Many customers will produce a
statement of the reliability requirements that is included in the specification
of the product. This statement should include the following: • The definition
of failure related to the product’s function and should cover all failure modes
relevant to the function; • A full description of the environments in which the
product will be stored, transported, operated and maintained; • A statement of
the reliability requirement Care must be given in defining failure to ensure
that the failure criteria are unambiguous. Failure should always relate to a
measurable parameter or to a clear indication. For example, a definition of
failure could include ‘failure of a function to operate’. To be able to design
for the load of the product the design team must have accurate information
concerning the environment of the product. If an item must fully operate at
high altitude with extreme changes in temperature then the design must be
robust enough to withstand such environmental factors. Similarly if a product
is stored in extreme conditions prior to use then the design must accommodate
for the storage conditions.
The reliability requirement should be stated in a
way which can be verified, and which makes sense relative to the use of the
product. The simplest requirement is to state that no failure will occur under
stated conditions. Reliability requirements based on life parameters (see
section 2.3) must be based on the corresponding life distributions. A common
parameter used is MTBF, when a constant failure rate is assumed. Reliability
and Maintainability case The UK MOD has recently moved away from prescriptive
reliability requirements and now requests a reliability case from their
suppliers.
The reliability and maintainability (R&M) case
is defines as “A reasoned, auditable argument created to support the contention
that a defined system satisfies the R&M requirements” . DEF STAN 0042 part
3 is a document produced by the UK MOD that gives guidance on what goes into an
R&M case. 2.2 The bath tub curve The bath-tub curve is a representation of
the reliability performance of components or nonrepaired items hazard function
is constant, this shape can be modelled by the exponential distribution (see
section 2.3) when failure are occurring randomly through time. The final
portion of the bath-tub curve is called the wear-out phase, this is when the
hazard function increases with time. Useful Life Infant Mortality Wear Out
Hazard function Time Useful Life Infant Mortality Wear Out Figure 3 The
bath-tub curve 2.3 Life distributions.
SQC&R BOOK BY Douglas C. Montgomery
SQC&R BOOK BY Douglas C. Montgomery
