The document provides a comprehensive overview of reliability engineering concepts, including definitions of reliability, failure, mean time between failures (MTBF), and maintainability. It discusses the factors leading to item failures, such as design complexity, overstressing, and errors, and outlines methods for reliability assessment like fault tree analysis and parametric analysis. Additionally, it covers statistical methods for estimating reliability parameters and the significance of warranty and guarantee in engineering products.

1. Reliability
engineering

2. Definitions
 Reliability
- The ability of an item to
perform a required function under stated
conditions for a stated period of time. It is
usually denoted as probability or as a
success .
 Failure
– The termination of ability of an
item to perform a required function.

3.  Observed
Failure Rate – For a stated period in life of
an item, the ratio of the total number of failures in a
sample to the cumulative of the time on that
sample. The observed failure rate is associated with
particular and stated time intervals(or summation
of intervals) in the life of the item and under stated
conditions.
 Observed
Mean Time Between Failures(MTBF) – For
a stated period in the life of an item, the mean
value of the length of time between consecutive
failures computed as the ratio of the cumulative
observed time to the number failures under stated
conditions.

4.  Observed
mean time to failure (MTTF)For a stated period in the life of an item, the
ratio of the cumulative time for a sample to
the total number of failure in the sample
during the period under stated condition

5. Name
Definition
Guarantee
An assurance given by the manufacturer to the vendor that the product will
work without failure for a stated period of time
Warranty
A written guarantee given to the purchaser of a new appliance,
automobile, or other item by the manufacturer or dealer, usually specifying
that the manufacturer will make any repairs or replace defective parts free
of charge for a stated period of time.
Maintainability
The measure of the ability of an item to be retained in or retained in or
restored to a specified condition when maintenance is performed by
personnel having specified skill levels, using prescribed procedures and
resources
Applies to a major tasks where many repetitions are expected and where
considerable time is required
Availability
A tool for measuring the percent of time an item or system is in a state of readiness
where it is operable and can be committed to use when called upon. Availability
ceases because of a downing event that causes the item/to system become
unavailable to initiate a mission when called upon
Availability=MTBF/(MTBF+MTTR)
Reliability
The ability of an item to perform a required function under stated
conditions for a stated period of time. It is usually denoted as probability
or as a success .

6. Guarantee
Warranty
Maintainability
Availability
Reliability
An assurance
given by the
manufacturer
to the vendor
that the
product will
work without
failure for a
stated period
of time
A written guarantee
given to the
purchaser of a new
appliance,
automobile, or
other item by the
manufacturer or
dealer, usually
specifying that the
manufacturer will
make any repairs or
replace defective
parts free of charge
for a stated period
of time.
The measure of the
ability of an item
to be retained in or
retained in or
restored to a
specified condition
when
maintenance is
performed by
personnel having
specified skill
levels, using
prescribed
procedures and
resources
Applies to a major
tasks where many
repetitions are
expected and
where
considerable time
is required
A tool for
measuring the
percent of time
an item or
system is in a
state of
readiness where
it is operable
and can be
committed to
use when called
upon.
Availability
ceases because
of a downing
event that
causes the item
to become
unavailable to
initiate a mission
when called
upon
The ability of an
item to perform
a required
function under
stated
conditions for a
stated period
of time. It is
usually
denoted as
probability or
as a success .
Availability=MT
BF/(MTBF+MTTR)

7. Why engineering items failed?




The design might be inherently incapable, the
more complex the design ,more the difficult
to overcome the problem
The item might be overstressed in some way
Failures can be caused by wear out.
Sufficiently strong at the start of the life and
become weaker with age
Failures can be caused by other time
dependent mechanism such as battery run
down, creep in turbine caused simultaneously
by high temperature and tensile stress

8. 




Failures can be caused by sneaks . Sneak is
the condition in which the system does not
work properly even though every part does
Failures can be caused by errors such as
incorrect specification, design ,fault assembly
or test
There are many other potential causes to
failure such as oil leaks noisy ,display
flickering etc.
Knowing ,as far as is practicable, the potential
causes of failures is fundamental to
preventing them
Failures might be caused by variation

9. What is reliability engineering





Manufacturers often suffer high costs of failure
under warranty
Reliability is usually concerned with failures in the
time domain. This distinction marks the difference
between traditional quality control and reliability
engineering
Whether failures occur or not and their times to
occurrence can seldom be forecast accurately
.reliability is therefore an aspect of engineering
uncertainty
Whether an item will work for a particular period is a
question which can be answered as a probability.
Ultimately reliability engineering is effective
management of engineering

10. Need for
Reliability

11. Non-Repairable items





Reliability is the survival probability over the items
expected life ,or for a period during its life, when
only one failure can occur
The instantaneous probability of the first and only
failure is called hazard rate
MTTF , the expected life by which a certain
percentage might have failed is used here.
The non repairable parts may be individual parts
such as bulb, transistor or systems comprised of
many parts such as spacecraft, microprocessor
When a part fails in a non repairable system, the
system fails, hence the reliability is function of the
time to the first part failure

12. Repairable items




Reliability is the probability that the failure will
not occur in the period of interest, when more
than one failure can occur .
It can also be expressed as failure rate or the
rate of occurrence of failures
Reliability is characterized by MTBF, but only
under the particular condition of a constant
failure rate
In a repairable system which contains which
contains a part type ,the part will contribute
by that amount to the system failure rate

13. Bath tub curve
 What:
the concept is derived from the
human life experience involving infant
mortality, chances of failures, plus a wear
out period of life since data for births and
deaths is accumulated by government
agencies. Most equipment lacks the
birth/death recording by govt. and most
non-human systems can be regenerated
to live/die many times before relegation
to the scrap heap

14. Bath Tub Curve

15.  Why:
failures rate are different for both
people and equipment at different phase
of operation and the medicine to be
applied to both humans and equipment
need to be considered for effectively
treating the roots of the problem

16. Mean
Median
Mode
The sample mean
can be used to
estimate the
population mean ,
which is the
average of all
possible outcomes
It is the measure
of the central
tendency, which
is the mid point of
the distribution
It is the point at
which half the
measured values
fall to either side
It is the value at
which the
distribution peaks.

18. Distribution Plots

20. Parametric Analysis
Parametric Analysis is fitting the data to a known
distribution and estimating the parameters of the
distribution.
 Parametric Analysis is done by using two most
commonly used methods :
-Regression Analysis
-Most Likelihood Method
 Having got a fit, a statistic is calculated to estimate
the goodness of the fit after which a confidence
interval of the parameters can be found.


21. Regression Analysis
Most commonly used continuous distribution
are
- Weibull Distribution
- Normal Distribution
- Lognormal Distribution
- Exponential Distribution
 First we linearize the basic CDF by making the
required transformation. From that we find
parameters of the distribution.


22. Linearized Formulae for
Weibull Distribution
 Xi=ln(ti)
 Yi=ln
ln[1/( 1-F(ti) )]
where F(ti) is Cumulative Failure Function
 F(ti)= (i-0.3)/(n+4)
(For ith failure out of n components)
 β= Slope
 η = exp(-abs[intercept]/ β)

23. A
straight line is fitted using the X and
Y data points by minimizing the sum of
squares of the distance of the data
points from the fitted line. The
distance can be in vertical or
horizontal direction.
 There
is a correlation coefficient,
referred to as r whose values varies
from -1 to 1. The more the value of r^2
reaches 1 the more linear is the
relation between X and Y.

24. To see the
complete solution
click here

25. Most Likelihood Method(MLE)
 It
also helps in estimating the
parameters of distribution.
 It does that by defining a likelihood
function which is function of
parameters of the distribution.
 The Likelihood function is maximized
to find the parameters of the
distribution.

26. Life Testing Data Types Used
for MLE Estimates
TYPE I
Time Terminated
With
Replacement
Without
Replacement
Life Testing
TYPE II
Failure
Terminated
With
Replacement
Without
Replacement

27. MLE Weibull Parameter
Estimation
r
g ( ) 
t

i

ln t i  ( n  r ) t s ln t s
i 1
r



ti  ( n  r )t s

i 1
1 


     ti  ( n  r )t s
 r  i 1
r



1/ 
1


1
r
 ln t
r
i 1
i
0

28.  ts
 ti
=1
=Test time
= tr
For Complete Data
For TYPE I Data
For TYPE II Data
is time taken for ith failure
 r is the number of failures
 n is total number of components
 Find β for g(β)=0
 Substitute that in second equation
and find η

29. For Completely
Solved Solution
Click Here

30. Goodness Of Fit (GOF)
 r^2
value in the case of Regression
analysis is used to find goodness of fit.
 For MLE we use the following GOF statistic.
• Chi-Square Method
• Kolmogorov-Smirnov Test
 Often data would fit many distribution.
Hence we have to find GOF so as to find
the perfect distribution.

31. Chi Square Test
 Applicable
to all distributions having large
sample size.
 Applied
data.
 The
to both discrete and continuous
probabilities are based on null
hypothesis

32. Formula Used


33. Example
There are 35 failure times listed below. Check
if the distribution follows exponential
distribution.
GIVEN DATA
1476
300
98
221
157
182
499
552
1563
36
246
442
20
796
31
47
438
400
279
247
210
284
553
767
1297
214
428
597
2025
185
467
401
210
289
1024

34. Group the result in specific
bounds
Upper Bound
Number of failure times
observed in that bound
350
18
750
10
2026
7

35.  Cumulative
Failure Function, F(ti)=1-
exp(-λti)
for exponential distribution.
Thus expected number of failures in
the
bound is given by
E(ti)=number of
components*expected
failure(F(ti))
Let λ=0.00206
E1=35*(1-exp(-350*0.00206))=17.98
E2=35*(1-exp(-350*0.00206)-P1)=9.55
E3=35*(1-P2-P1)=7.47

36.  From
χ^2

the formula, we find the value of
Degree of Freedoms, k=3-1-1=1
 From
the Statistic table for Chi-Square
we get, for k=1 and χ^2=0.0496, α is
between 10% to 20% (α should be less
than 90%). Hence, the Null Hypothesis
is accepted. Thus, we can say that
the distribution is Exponential.

37. For completely
solved solution
click here

38. Kolmogorov-Smirnov Test
 It
is also used to find the GOF but that it
can be used even to small sample size.
 Formulae
Sn(tn)=0
=i/n
=1
Used
For -∞<t1
For ti<t< ∞;i=1,2….n-1
For tn<t<∞

39. K – S = max(|F(ti)-Sn(ti)|,|F(ti)-Sn(ti-1)|)
Where
F(ti) is Cumulative failure of the
distribution
ti is the Time taken for ith Failure
n is sample size

40. Example

The following 14 observations are on the failure
time of a component in hours. Test the
hypothesis that the failure time is normal.
For normal distribution,
z= (x-μ)/σ
where μ is the mean
σ is the standard deviation
Cumulative Failure Function,
F(ti)=(1/σ √2)℮^(-0.5)[(x- μ)/σ]^2

41. GIVEN DATA
i
TTF
i
TTF
1
61.6
8
72.7
2
63.4
9
73
3
65.1
10
75.3
4
65.5
11
77.1
5
70
12
78.4
6
72.3
13
83.2
7
72.5
14
83.5

42. For Completely
Solved Solution
Click Below
K-S Test.xlsx

43. Reliability Block Diagram
 Systems
are composed of components
 RBD is a method of evaluating
the
reliability of the system by the establishing
following relationship
 Series
 Parallel
 Combination of both
 These structure helps in understanding
logic relationship

44. Series configuration
1






2
n
Failure of any one component in the block will
lead to the failure of the entire system
Rs - system reliability
E1 - event where component 1 does not fail
E2 - event where component 2 does not fail
R1 - reliability of component 1
R2 – reliability of component 2

45. Formula
Rs = P(E1 E2 )
= P(E1) P(E2)
= R1 (R2 )
Therefore the system reliability must be
greater than the individual component
reliability
i.e. All component's must have high reliability
in this configuration

46. Parallel configuration
 In
a parallel system all elements must fail
for the system to fail
1
2
n

47. formula
RS=1-(1-R1)(1-R2)
Generalizing
Rs=1- [1- Ri (t) ]

48. Combination of parallel and
series

49. Example
If R1=R2 =0.90,R3=R6=0.98,R4=R5=0.99
considering as constant failure rate
Solution:
Ra=1-(0.10)^2
Rb=[1-(0.10)^2](0.98)
=0.9702
Rc=(0.99)^2
=0.9801
& Rs=[1-(1-0.9702)(1-0.98)](0.98)
=0.9794


50. FAULT TREE ANALYSIS
 An
undesired event is defined
 The event is resolved into its immediate
causes
 This resolution of events continues until
basic causes are identified
 A logical diagram called a fault tree is
constructed showing the logical event
relationships

51. ELEMENTS





FTA is a deductive analysis approach for
resolving an undesired event into its causes
FTA is a backward looking analysis, looking
backward at the causes of a given event
Specific stepwise logic is used in the process
Specific logic symbols are used to to illustrate
the event relationships
A logic diagram is constructed showing the
event relationships.

52. USES






FTA is used to resolve the causes of system
failure
FTA is used to quantify system failure
probability
FTA is used to evaluate potential upgrades to
a system
FTA is used to optimize resources in assuring
system safety
FTA is used to resolve causes of an incident
FTA is used to model system failures in risk
assessments

53. FOUR STEPS
1. Define the undesired event to be
analyzed (the focus of the FTA)
2. Define the boundary of the system (the
scope of the FTA)
3. Define the basic causal events to be
considered (the resolution of the FTA)
4. Define the initial state of the system

54. BASIC EVENTS

55. BASIC GATES

56. Example

57. Specifications
 Undesired
top event: Motor does not start
when switch is closed
 Boundary of the FT: The circuit containing
the motor, battery, and switch
 Resolution of the FT: The basic
components in the circuit excluding the
wiring
 Initial State of System: Switch open,
normal operating conditions

58. Fault tree

61. The Top Event of the Fault Tree
 The
top event should describe WHAT the
event is and WHEN it happens
 The top event is the specific event to be
resolved into its basic causes
EX:
1. Fuel Supply System Fails to Shutoff after
the fueling phase
2. Launch Vehicle Fails to Ignite at Launch

62. OR gate




The OR Gate represents the logical union of
the inputs: the output occurs if any of the
inputs occur
The OR gate is used when an event is resolved
into more specific causes or scenarios
The OR gate is used when a component
failure is resolved into an inherent failure or a
command failure
The OR gate is used when an event is
described in terms of equivalent, more
specific events

63. AND gate




The AND Gate represents the logical intersection
of the inputs, the output occurs if all of the inputs
occur
The OR gate is used when an event is resolved into
combinations of events that need to occur
The AND gate is used when a redundant system is
resolved into multiple subsystems that need to fail
The AND gate is used when a system failure is
resolved into conditions and events needed to
occur

64. Developing FTA
1.Define the top event as a rectangle
2.Determine the immediate necessary and sufficient
events which result in the top event
3.Draw the appropriate gate to describe the logic for
the intermediate events resulting in the top event
4. Treat each intermediate event as an intermediate
level top event
5. Determine the immediate, necessary and sufficient
causes for each intermediate event
6. Determine the appropriate gate and continue the
process

65. Key attributes
 Top
Event-What specific event is being
analyzed?
 Boundary-What is inside and outside the
analysis?
 Resolution-What are the primary causes
to be resolved to?
 Initial State-What is assumed for the initial
conditions and states?

66. FAULT VS FAILURE
•The intermediate events in a fault tree are
called faults
•The basic events, or primary events , are called
failures if they represent failures of components
•It is important is to clearly define each event as
a fault or failure so it can be further resolved or
be identified as a basic cause
*Write the statements that are entered in the
event boxes as faults; state precisely what the
fault is and the conditions under which it occurs.
Do not mix successes with faults*

67. Petri nets

A petri nets is general purpose graphical and
mathematical tool describing relations existing
between conditions and events. The basic symbol
of petri nets include
: place , denotes events
: immediate transition , denotes event transfer
with no delay
: timed transition , denotes event transfer the
period of tie delay
: arc, between places and transitions
: token, contained in places , denotes the data
: inhibitor arc , between places and transitions

68. Basic Structure :

69. 
The transition is said to fire if input places
satisfy an enabled condition. Transition firing
will remove one token from each of its input
places and put one token into all of its output
places. There are two types of input place for
the transition namely specified type and
conditional type. The former one has single
output arc whereas the latter one has
multiples. Tokens in the specified type place
have only one outgoing destination I,e if the
input places holds a token then the transition
fires and gives the output places a token.
However tokens in conditional type place
have more than one outgoing paths that may
lead the system to different situations.

70. 
There are three types of transitions that are
classified based on time. Transition with no
time delay are called immediate transitions
while those need a certain time delay are
called timed transition. The third type is called
a stochastic transition. It is used for modeling
a process with random time. Owing to variety
of logical relations that can be represented
with petri nets, it is powerful tool for modeling
system. Petri nets an be used not only for
simulation, reliability analysis, and failure
monitoring, but also for dynamic behavior
observation. This greatly helps fault tracing
and failure state analysis. Moreover, the use if
petri nets can improve the dialogue bet
analysis and designer of a system.

71. Minimum cut sets
To identify the minimum cut sets in a petri net the
matrix method is used, as follows
1.Put down the number of the input places in the
row if the output place is connected by multi arcs
from transition . This accounts for OR models
2.If the output place is connected by one arc from a
transition then numbers of the input places should be
put down in a column. This accounts for the and
models

72. 3. The common entry located in rows is the entry
shared by each row
4. Starting from the top event down to the basic
event s until all the places are replaced by basic
events , the matrix is thus formed, called the basic
event matrix, the column vector of the matrix
constitute cut sets
5. Remove the super sets from the basics event
matrix and the remaining column vector become
the minimum cut sets

73. 
Minimum cut sets can be derived in an
opposite, bottom up , direction , that is from
basics places to the top place . Transition with
T=0 are called immediate transition . If the
petri nets is immediate transition , i.e. the
token transfer between places do not take
time, then can be absorbed to a simplified
form called the equivalent petri net. After
absorption, all the remaining place are basic
events . The equivalent petri nets exactly
constitutes the minimum cut sets, i.e. the input
of each transition represents a minimum cut
sets

74. Monte Carlo simulation
 In
a Monte Carlo simulation, a logical
model of the system being analyzed is
repeatedly evaluated, each run using
different values of the distributed
parameters
 The selection of parameters values is
made randomly but with probabilities
governed by the relevant distribute
functions

75. 

Monte carlo simulation can be used for
system reliability and availability modeling ,
using suitable computer programs. Since
Monte carlo simulation involves no complex
mathematical analysis, it is an attractive
alternative approach.it is relatively easy way
to model complex systems , and the input
algorithm are easy to understand
One problem in this methods is that its
expensive use of compute time

76.  Since
the simulation of probabilistic events
generates variable results, in effect
simulating the variability of real life, it is
usually necessary to perform a number of
runs in order to obtain estimates of mean
and variance of the output parameters of
interest such as availability number of
repairs arising and facility utilization on the
other hand , the effect of variation can
be assessed .

77. Design analysis methods




Design analysis methods have been developed to
highlight critical aspects and to focus attention on
possible shortfalls
Design analyses are sometimes considered tedious
and expensive
In most case the analyses will show that nearly all
aspects of the design are satisfactory, and much
more effort will have been expended in showing
this than in highlighting a few deficiencies
The tedium and expense can be greatly reduced
by good planning and preparation and by the use
of computerized methods ,.

78. The main reliability design analysis technique
described
1.Quality function deployment
2.Reliability prediction
3.Load-strength analysis
4.Failure modes, effects and critically analysis
5.Fault tree analysis
6.Hazard and operability study
7.Parts materials and process review
8.Others, including human aspects
manufacturing, maintenance, etc..

79. Quality function development


QFD is a bad transition of a good reliability
technique for getting the voice of the
customer into the design process so the
product the customer desires.in particular ,it is
applicable to soft issues that are difficult to
specify
This method helps to pinpoint what to do, the
best way to accomplish the objective the
best order for achieving the design objective
and staffing asserts to complete the task

80.  It
is a major up front effort to learn and
understand the customer’s requirement
and the approach that will satisfy their
objectives
 The methodology is used as a team
approach to solving problems and
satisfying customers , beginning with a
listing

81. Failure Mode and Effect Analysis(FMEA)



Failure mode and effect analysis is the study
of potential failures that might occur in any
part of a system to determine the probable
operation success.
When criticality analysis is added for
sophisticated studies the method is known as
FMECA.
The basic thrust of the analysis tool is to
prevent failures using a simple and cost
effective analysis that draws on the collective
information of the team to find problem and
resolve them before they occur

82. 


The analysis is known as a bottom-up
(inductive) approach to finding each
potential mode of failure that might occur for
every component of a system .it also used for
determining the probable effect on the
system operation of each failure mode and ,
in turn on probable operational success
FMEA can be performed from different
viewpoints such as safety, mission success,
repair costs, failure modes, reliability
reputation
FMEA is most productive when performed
during the design process to eliminate
potential failures it can also be performed on
existing systems

83.  The
analysis can be conducted in the
design room or on the shop floor and it is
an excellent tool for sharing the
experience to make the team aware of
details that are known to one person but
seldom shared with the team .

84. Accelerated testing




A test method of increasing loads to quickly
produce age to failure data with only a few
data points are then scaled to reflect normal
loads
The benefits of this testing is to save time and
money while quantifying the relationship
between stress and performance along with
identifying design at low cost
It is used to correlate with real life conditions
It is useful method for solving old, nagging
problems within a production process

85. Accelerated testing shortens the test tie as
the tests are conducted at higher stress levels
to expediting the failure tie to be days instead
of month or years
 Challenges faced by designer :
1.Long test time to complete life testing of
product
2.Constraints on timelines
3.Cost as function of time
4.Reliability growth


86.  Care
has to be taken that the stress or the
agent of failure does not results in failure
in another failure mode than the one
being evaluated
 Acceleration rate must be uniform

87. Types of ALT
Qualitative Accelerated Testing
 HALT
 HASS
 Quantitative Accelerated Testing
 SSALT
 CSALT
 CISALT


88. Highly Accelerated
Testing(HALT)





To identify potential failure modes or uncover
defects of a product.
Test the component to failure under highly
stressed conditions.
Study the failure modes and analyze to the
root cause.
Fix the root cause to make the product more
robust.
Does not help in predicting the life of the
product.

89. Highly Accelerated Stress
Screening (HASS)
 Used
to monitor the production process.
 All
products are subjected to the same
stresses during HALT but, at a lower level.
 It
identifies process related defects.

90. Quantitative Accelerated
Testing





Planned/Controlled accelerated testing from
which TTF under normal usage conditions can
be derived.
Models to be used for a specific agent of
failure have been postulated.
Accelerated Factor(AF)=TTFnormal/TTFstress
AF is used to derive the normal TTF from
accelerated TTF.
Quantitative ALT helps predict the life of the
product.

91. Improving the process








Continuous improvement nearly always leads to
reduced costs , higher producitvity,and higher
reliability
Methods that are available for process
development are as follows
Simple charts
Control charts
Multi-vari charts
Statistical methods
Quality circles
Zero defects

92. Simple charts
A
variety of simple charting techniques can
be used to help to identify and solve process
variability problems.
 the pareto chart is often is used as starting
point to identify most important problems
and most likely causes.
 Measles chart is used when problems are
distributed over an area
 The cause and effect diagram also called
fishbone or ishikawa diagram can be used
to structure and record problem solving and
process improvement efforts. The main
problem is indicated on the horizontal line
and possible causes are shown as branches
which inturn can have subcases

93. Control charts
While using control charts it is monitored
continually to find trends that might
indicate special causes of variation .trends
can be continually run high or low or it can
be a cyclic pattern. A continuous high or
low trend indicates a need for process or
measurement adjustment. A cyclic trend
might be caused by temperature
fluctuation, process drifts between settings
change of materials etc…

94. Multi-vari charts
A
multi-vari chart is a graphical method
for identifying the major causes of
variation in a process. Multi vari charts
can be used for process development
and for problem solving, and they can be
very effective in reducing the number of
variables to include in a statistical
experiment.

95. Multi-vari charts show whether the major
causes of variation are spatial, cyclic or
temporal. A parameter being monitored is
measured in different position s at different
points in the production cycle at different
times. The results are plotted against two
measurement locations, e.g. diameter at
each end of the shaft, plotted against
batch number from setup. It shows that
batch to batch variation is the most
significant cause, with a significant pattern
of end to end variation(taper).

96. Statistical Methods
This method for analysis of variation can be used
effectively for variation reduction in production
process. They should be used for process
improvement, in the same way as for product and
process initial design. If a particular process has been
the subject of such experiments during
development, then the results can be used to guide
studies for further experiments.
It is also used to identify the major causes of
variation, prior to setting up statistical experiments.
This way the number of variables to be investigated
can be reduced leading to cost savings .

97. Quality Circles
It is the most widely used method world wide. A
quality circle team consisting of operators is
formed. This manage themselves, select leaders
and members, and address the problems. They
also suggest improvement if it under their
control or they recommend it to the
management.
The quality circle are taught to use
analytical techniques to help identify problems
and generate solutions. These are called the
seven tools of quality.

98. The Seven tools of quality are
1. Brainstorm, to identify and prioritize
problems
2. Data collection
3. Data analysis methods, including
measles chart, trend charts and
regression analysis
4. Pareto chart
5. Histogram
6. Cause and Effect diagram
7. Statistical Process Control(SPC) chart

99. Failure Reporting Analysis and
Corrective Action System(FRACAS)
Failure reporting and analysis is an important
part of the QA function. The system must
provide for
1.Reporting of all production test and inspection
failures with sufficient detail to enable
investigation and corrective action to be taken
2.Reporting the results of investigation and
action
3. Analysis of failures pattern and trends, and
reporting on these
4.Continuos improvement by removal of causes


100. 

The data system must be computerized for
economy and accuracy modern ATE sometimes
includes direct test data recordings and inputting
to the central system by networking the data
analysis must provide pareto analysis , probability
plots and trend analysis for management
Production defect data reporting and analysis
must be very quick to be effective. Trends should
be analyzed daily , or weekly atmost, particularly
for high rates of production , to enable timely
corrective action to be taken . The data analysis
system also necessary for indicating areas for
priority action, using the pareto principle of
concentrating action on the few problem area
that contribute to the most to the quality cost . For
this purpose longer term analysis is necessary

101.  Defective
component should not be
scrapped immediately, but should be
labeled and stored for the period , say
one or two months , so that they are
available for more detail investigation if
necessary.
 Production defect data should not be
analyzed in isolation by people whose
task is primarily the data management.
the people involved must participate to
ensure that the data interpreted by those
involved and that practical results are
derived . the quality circle approach
provides very effectively for this

102. 
Production defect data are important for
highlighting possible in service reliability
problems. Many in-service failure modes
manifest themselves during production
inspection and testing. For ex, if a component
or process generates failure on the final
functional test, and these are connected
before delivery , it is possible that the failure
mechanism exist in product which pass test
and are shipped . Metal surface protection
and soldering processes present such risks .
Therefore production defects should always
be analyzed to determine the likely effects on
reliability , external failure cost and all internal
production quality cost.