5. Defect Detection Vs. Prevention
• What is a defect?
• Defect is deviation from the engineering
specifications.
• In reality defect is deviation from the targeted
value of a characteristics.
• The closer we go to the target , more is the
customer satisfied and farther we go, we have
dissatisfied customer.
SPC
5
7. 7
Defect Detection
• It uses customer as final inspector
• Is reactionary
• Tolerates waste such as scrap/rework
• Relies on inspection, audits, or checks
of large samples of output
• Treats all defects the same
• Focuses on specs.
• Involves action only on output
• Provides late feedback for defect
• Detection is not cost effective
SPC
8. 8
Voice of process
Every process generates information that can be
used to measure it. The most effective way to take
advantage of this is to:
determine the process quality characteristics &
respective target value
Collect data about process.
Compare process characteristics to pre-established
target values.
Act based on results of comparison.
Following this procedure results in early feedback
which leads to improvement
SPC
10. 10
Defect Prevention
Is pro-active
Avoids waste
Uses small samples of product and
process information
Is analytically based
Discriminates between potential
defects based on causes
Involves action on the process or
process parameters
Provides timely feedback
It is cost effective
Focuses on target value
SPC
11. 11
Test for 100% inspection
You are given a paper and in the
paragraph written there , you have
to find out how many times letter
‘ f ‘ has appeared in the paragraph.
Time for visual inspection is 2
minutes
SPC
12. 12
What is statistics?
Even though theory behind statistics is hard to
understand, we use it everyday extensively.
To talk about sports.
To shop intelligently.
To complete tasks at home or at work.
SPC
13. 13
Few fundamentals of Statistics
Mean - It is arithmetic average of all
observations.
Mode -It is most commonly occurring
observations.
Median - It is the middle observation
when all observations are arranged
in order of magnitude
SPC
14. 14
SPREAD
Spread is how far apart the ends of
the group are.
Bowling average
4, 2 , 6 , 0 , 3 , 5 , 2 , 1 , 3 , 4
Average / mean = 3 Spread = 6
Income Rs.
400, 200 , 660 , 90 , 300 , 250 , 100 , 300 , 480 ,180
Average / Mean = 296 Spread=570
Another term that relates spread is Standard Deviation
SPC
15. 15
Standard Deviation
is a statistical measure of spread or variation that
is present in the group data.
To calculate SD(Sigma : )there are six steps
1. Calculate the average of all the observations.
2. Subtract this average from each observations.
3. Square each number obtained in step 2.
4. Find the sum of all numbers obtained in step 3.
5. Divide the number obtained instep 4 by number of
observations minus one.
6. Take the square root of the number obtained in 5.
= i=1 (xi-)2 = Average; n= no.of observations
n-1
SPC
17. Variation
• Variation is Natural
• No two things are alike or identical
• Variation is the cause of inconsistency
• Variation is reason that components do
not always fit together
• Variations is the reason that quality levels of same
product ,produced on the same line using parts of
same suppliers are different.
Our goal is to manage Variation
SPC
17
18. To manage Variation we must understand it.
• Where from variation comes ?
• Variation can result from different procedures
used by a manufacturer or an operator.
• Variation can result from different machines used
by us.
• Variation can result from wear in mechanism of
machine.
• Variation can result from different batches of
material used.
Variation can be result of endless list of reasons.
SPC
18
19. Main sources of variation
• In all processes variation is inevitable ,difference
between individual outputs of a process.
• A process contains many sources of variability.
• The main sources of variability are Machine ,
Method , Material , Men, Environment etc.
SPC
19
20. Variation
There are two causes of variation
Common cause
Special causes
• Common Causes :- A source of variation that affect all
the individual values of the process output and
inherent in the process itself and can not be
eliminated totally.
• Special Causes:- A source of variation that is
intermittent, unpredictable, unstable. These causes
can be identified and can be eliminated permanently.
SPC
20
21. Variation
Characteristics of processes with only common
causes of variation
The processes are stable I.e. under control
Process outcomes are predictable
The effects of common cause variation can only
be eliminated by action on the system.
Common causes of variation
Are associated with the majority 85% of process
concerns
Arise from many small sources.
SPC
21
22. Variation
If only common causes of variation are present ,the
output of a process forms a distribution that is stable
over time. It is predictable.
Variation from common cause is predictable.
Variation from common cause is stable
The shape is unchanged over time
SPC
22
23. Variation
• If special causes of variation are present ,the
output of a process forms a distribution that is not
stable over time. It is not predictable.
• Variation from special cause is unpredictable.
• Variation from special cause is unstable
The mean changes over time
The spread changes over time
• The shape varies over time
SPC
23
24. Variation
• If special causes of variation are present ,the
output of a process forms a distribution that is not
stable over time. It is not predictable.
• Variation from special cause is unpredictable.
• Variation from special cause is unstable
The mean changes over time
The spread changes over time
• The shape varies over time
SPC
24
25. Stable Process
• A stable process is the one with no indication of
special cause of variation.
• Behaviour of stable process is predictable
• A process may be stable, but may produce defective
output.
• A stable process is not an end to improvement.
SPC
25
26. Variation
• The variation due to common causes contributes to
85 % and variation due to special causes contributes
to 15 %.
• Common causes are management responsibility &
hence 85 % it is management responsibility to reduce
variation.
• Only 15% is workers responsibility.
SPC
26
27. Principles & Objectives of SPC:
-- Variation is inevitable
-- Variation is predictable
-- Variation is measurable
• Statistical process control: 10% is statistics and 90% is product & process
knowledge
• SPC means applying statistics for output of a process in order to control the
process
• SPC is preventive technique
• Economic control over process
SPC
27
28. • PROCESS CONTROL:- A process is said to be operating in state of
statistical control when the only source of variation is common causes.
• PROCESS STABILITY:- A process is said to be stable when the process
is in control and variation is constant with respect to time.
• PROCESS CAPABILITY:- The measure of inherent variation of the
process when it is in stable condition is called as process capability
• OVER ADJUSTMENT:- It is the practice of adjusting each deviation from
the target as if it were due to a special cause of variation in the
process. If stable process is adjusted on the basis of each
measurement made, then adjustment comes an additional source of
variation.
SPC
28
29. Techniques for Process control:
• Mistake proofing :- In this technique 100% process control is achieved by
sealing all types of failures by using modern techniques to get defect free
product. Here causes are prevented from making the effect.
• 100 % Inspection:- In this technique 100% checking of all the parameters
of all products have been done to get defect free product. Here only
defect is detected.
• Statistical Process Control:- In this Statistical technique such as Control
Chart, Histogram etc are used so as to analyse the process and achieve
and maintain state of statistical control to get defect free product. Causes
are detected and prompting CA before detect occurs.
SPC
29
30. It is a technique whose aim is to prevent defective work
being produced by focusing on the process rather than on
the final product ,by using various statistical tools.
SPC provides the operator an opportunity of
correcting/tuning the process in time.
It encourages continual improvement ,which is reflected in
the product & the equipment.
Statistical Methods are not only control charts. Some of the
tools include
Pareto Diagrams
Check sheets
Scatter Diagram
Design of Experiments
Histogram
SPC
30
31. Histogram
• It provides the information about the distribution of
data
• It provides information about the spread or
variation of data.
• It provides information about the location or
centrality of distribution.
• to display large amounts of data values in a relatively
simple chart form.
• to tell relative frequency of occurrence.
• to easily see the distribution of the data.
• to see if there is variation in the data.
• to make future predictions based on the data.
SPC
31
32. Histogram Making
Step 1: Gather Data
Step 2 : Tabulate data
Step 3 : Count the number of data points ‘ n ‘
Step 4 : Determine the Range
Range (R) = Max. reading - Min. reading
Step 5 : Determine class width ‘ k ’
k = R/ Root of n
Step 6 : Determine class boundaries
Step 7 : Determine frequency .. Number of readings
in each class boundary.
Step 8 : Draw histogram with Class width on X axis
and frequency on Y axis.
SPC
32
36. Types of data:
• Variable data – Are quantitative data that can be
counted. Eg. – Distance, diameter, thickness,
hardness, length etc.
• Attribute data – Are qualitative data that can not
be counted. Eg. – Colour, texture, microstructure,
go-no-go checking results, yes/no results
SPC
36
37. SPC
1 2 3 4 5 6 7 8
Sample Number
Sample
Mean
UCLx
LCLx
UCLr
Control Charts
38. Control Charts:
• Variable Charts – Commonly X-Bar – R Chart is used. X Bar-R
chart (Average and Range) explains process data in terms of both
its spread (piece to piece variability) and its location (process
average).
Other variable control charts:
Average and SD Chart
Median and Range Chart
Individual and Moving Range Chart
• Attribute Charts – Pass/Fail type measurements.
P Chart for proportion of nonconforming
nP Chart for number of nonconforming
c Chart for number of non conformities
u Chart for Non conformities per unit
SPC
38
39. Control Charts: Benefits
• Can be used by operators for ongoing control of a process
• Can Help the process perform consistently, predictably for quality
and cost
• Allow the process to achieve
- Higher Quality
- Lower Unit cost
• Provide a common language for discussing the performance of the
process
• Distinguish special from common causes of variation, as guide to
local action or action on the system
SPC
39
40. Control Charts
In ‘ Statistical Process Control ‘ we have to
Gather Data
Plot data
Calculate and plot control limits
Interpret for process control
corrective action
Calculate process capability
Continual Improvement
SPC
40
41. DATA PLOTTED OVER TIME
MONITORED
CHARACTERISTIC
UCL
Center Line
LCL
UCL = Upper Control Limit / LCL = Lower Control Limit
Plotted Data
SPC
Key Component - Control Charts
42. Control Charts for Variables
Average and Range Charts
(X bar and R)
SPC
42
43. X bar- R Chart
• Preparatory Steps
– Establish an environment suitable for action
– Define process
– Define characteristics to be charted
– Define measurement system, do MSA
– Minimize unnecessary variation
SPC
43
44. X bar- R Chart
• Gather Data
• Choose sub group size
o Sensitivity increases with the sub group size
o Cost of sampling increases with size
o Normally sub group size can be 4 or 5
o Subgroups should be collected often enough & at appropriate
times such that they should reflect the potential opportunities for
change.
For example :Different shifts, Different operators, Different material
lots
o No. of subgroups :
Ensure that the major sources of variation are captured
Suggested is 25 nos. or more
SPC
44
45. X bar- R Chart
• Collect the data
• Calculate average (X bar) and range (R) of each
sub-group
• X bar = (X1+X2+……+Xn)/n
• R = Xhighest - Xlowest
SPC
45
46. X bar- R Chart
• Collect the data
• Calculate average (X bar) and range (R) of each
sub-group
• X bar = (X1+X2+……+Xn)/n
• R = Xhighest - Xlowest
SPC
46
Part Operation Other Details
Measurement
SN Date Time
X1 X2 X3 X4
Mean
(X
bar)
Range
(R)
1 12/12 10.25 35 40 32 33 35.0 8
2 12/12 13.45 46 42 40 38 41.5 8
3 12/12 15.34 34 40 34 36 36.0 6
…..
25 15/12 10.30 38 34 44 40 39 10
47. X bar- R Chart
Select proper scales for control charts
Plot Averages and Ranges on control charts
Calculate X double bar and R bar:
X double bar = (X1 bar + X2 bar + ………..+Xn bar) / n
R bar = (R1 + R2 +……….+ Rn) / n
SPC
47
48. X bar- R Chart
• Calculate control limits
• For Average control chart
Upper Control Limit, UCL = X(Double bar) + A2 x R bar
Lower Control Limit, LCL = X(Double bar) - A2 x R bar
• For range control chart
Upper Control Limit, UCL = D4 x R bar
Lower Control Limit, LCL = D3 x R bar
SPC
48
49. X bar- R Chart
• Calculate control limits
• For Average control chart
Upper Control Limit, UCL = X(Double bar) + A2 x R bar
Lower Control Limit, LCL = X(Double bar) - A2 x R bar
• For range control chart
Upper Control Limit, UCL = D4 x R bar
Lower Control Limit, LCL = D3 x R bar
SPC
49
Sub Group
Size
A2 D4 D3
2 1.880 3.267 0
3 1.023 2.527 0
4 0.729 2.282 0
5 0.577 2.115 0
6 0.483 2.004 0
7 0.419 1.924 0.076
50. X bar- R Chart
Draw lines for the following on the control chart
X double bar
R bar
control limits
SPC
50
53. X bar- R Chart
SPC
53
UCL
LCL
1 Sigma (Zone C)
2 Sigma (Zone B)
3 Sigma (Zone A)
1 Sigma (Zone C)
2 Sigma (Zone B)
3 Sigma (Zone A)
The Item
We Are
Measuring
TIME
54. X bar- R Chart
SPC
54
The Item
We Are
Measuring
TIME
1 Sigma
2 Sigma
3 Sigma
1 Sigma
2 Sigma
3 Sigma
60-75%
90-98%
99-99.9%
UCL
LCL
Rules of Standard Deviation
“Where should the data lie?”
55. X bar- R Chart
What does Out-of-Control mean?
Tests for Detecting Lack of Control
(For variable control charts)
1) One point more than 3 sigmas from center line- beyond control line
2) Seven points in a row on same side of center line
3) Seven points in a row, all increasing or all decreasing
4) Fourteen points in a row alternating up and down
5) Two out of three points more than two sigmas from center line (Same
side)
6) Four out of five points more than one sigma from center line (Same
side)
7) Fifteen points in a row within 1 sigma of center line (Either side)
8) Eight points in a row more than one sigma from center line (Either
side)
SPC
55
56. X bar- R Chart
SPC
56
30
20
10
0
10
5
0
-5
Observation Number
Individual
Value
I Chart for C1
X=0.2800
3.0SL=5.416
-3.0SL=-4.856
UCL
LCL
One point more than 3 sigmas from center line
57. X bar- R Chart
SPC
57
30
20
10
0
10
0
-10
Observation Number
Individual
Value
I Chart for C1
X=0.000
3.0SL=9.000
-3.0SL=-9.000
UCL
LCL
Fifteen points in a row within 1 sigma of center line
(either side)
58. X bar- R Chart
SPC
58
Therefore, based on what you know so far, what percent of data points
should fall between the upper control limit (UCL) and lower control
limit (LCL) if your process is in-control?
99 to 99.9 %
UCL
LCL
TIME
59. X bar- R Chart
Corrective Action
Find and address special causes
Use
Pareto analysis or
Cause and effect analysis or
Any problem solving technique
SPC
59
What should you do if you determine that your process is
“Out of Control?”
60. X bar- R Chart
Corrective Action
Take corrective action on identified special causes
Exclude any out of control points for which special causes
have been found & removed
Recalculate & plot the process average and control limits
Confirm that all data points show control when compared
to the new limits
Otherwise repeat the cycle of corrective action
SPC
60
61. X bar- R Chart
Ongoing Control
Ensure that process is in control
(For trial control limits)
Adjust the process to the target, if the process
center is off target
Extend the control limits to cover future periods
Monitor for ongoing control
SPC
61
62. X bar- R Chart
Prepare X bar - R chart using following
SPC
62
10.4 13.0 10.4 7.4 6.3 6.1 11.9 9.6 8.2 8.8
10.6 8.6 11.9 11.0 10.0 6.6 8.2 9.5 12.4 9.4
9.6 10.3 8.9 9.1 10.6 11.7 9.4 11.4 10.9 9.3
10.9 9.4 9.1 8.7 11.2 9.7 10.2 9.2 9.8 8.4
9.3 10.5 10.6 8.5 9.5 10.4 10.4 9.8 9.9 5.8
63. X bar- R Chart
SPC
63
10
9
8
7
6
5
4
3
2
1
Subgroup 0
12
11
10
9
8
7
Sample
Mean
Mean=9.660
UCL=11.78
LCL=7.541
8
7
6
5
4
3
2
1
0
Sample
Range
R=3.674
UCL=7.768
LCL=0
Xbar/R Chart for C1
64. Control Charts for Attributes
p Chart for proportion Nonconforming
SPC
64
65. p Chart
• It is important that
– Each component / part / or item being checked is
recorded as either conforming or non conforming
– Results of these inspections are grouped on a
meaningful basis, and non conforming items are
expressed as a decimal fraction of the subgroup
size.
– meaningful basis, and non conforming items are
expressed as a decimal fraction of the subgroup
SPC
65
66. p Chart
• Choose sub group size
Sensitivity increases with the sub group
size
Cost of sampling increases with size
Normally sub group size can be 50
to 200 or more
– are expressed as a decimal fraction of the subgroup
SPC
66
67. p Chart
Subgroups should be collected often enough & at
appropriate times such that they should reflect the
potential opportunities for change.
For example :
Different shifts
Different operators
Different material lots
No. of subgroups :
Ensure that the major sources of variation are captured
Suggested is 25 nos. or more
SPC
67
68. p Chart
Typical Data Collection Sheet
– are expressed as a decimal fraction of the subgroup
size
SPC
68
art Operation Other Details
SN Date Time
Sample (n)
No. of non
conforming
items in a
sample (np)
Proportion
nonconforming
(p = np/n)
1 12/12 10.25
2 12/12 13.45
3 12/12 15.34
…..
25 15/12 10.30
69. p Chart
• Select proper scales for control charts
• Plot values of p for each subgroup
on control charts
• Calculate Process Average Proportion Nonconforming
(p bar)
n1p1, n2p2 : no. of non conforming items in subgroup
n1,n2 : Subgroup size
SPC
69
p bar = (n1p1 + n2p2 + …+nkpk)
(n1 + n2 + …+ nk)
70. p Chart
Formula for Control Limits
– are expressed as a decimal fraction of the subgroup size
SPC
70
Upper Control Limit, UCLp = p bar + 3 * Sq. root {p bar (1-p bar)}
Sq. root (n)
Lower Control Limit, LCLp = p bar - 3 * Sq. root {p bar (1-p bar)}
Sq. root (n)
n is constant sample size
n
n is constant sample size
71. p Chart
Formula for Control Limits
– are expressed as a decimal fraction of the subgroup size
SPC
71
Upper Control Limit, UCLp = p bar + 3 * Sq. root {p bar (1-p bar)}
Sq. root (n bar)
Lower Control Limit, LCLp = p bar - 3 * Sq. root {p bar (1-p bar)}
Sq. root (n bar)
n is not constant sample size
It is varying between +/- 25%
72. p Chart
Formula for Control Limits
– are expressed as a decimal fraction of the subgroup size
SPC
72
If n is not constant sample size and varying beyond +/-25%,
then recalculate the precise control limits by using following
formula
Upper Control Limit, UCLp = p bar + 3 * Sq. root {p bar (1-p bar)}
Sq. root (n)
Lower Control Limit, LCLp = p bar - 3 * Sq. root {p bar (1-p bar)}
Sq. root (n)
73. p Chart
SPC
73
Draw lines for the following on the control chart
Process average (p bar)
control limits
74. p Chart
Interpret for Process Control
1) One point more than 3 sigmas from center line
2) Nine points in a row on same side of center line
3) Six points in a row, all increasing or all decreasing
4) Fourteen points in a row alternating up and down
To be interpreted same as charts for variables
SPC
74
75. p Chart
Interpret for Process Control
1) Find and correct special causes
2) Recalculate control limits
3) Monitor for on going control
Refer slides in X bar - R chart section
SPC
75
78. SPC
78
Control Limits vs. Specification Limits
• Process Control Limits are calculated based on data from the
process itself
• They are based on +/- 3 (99.73% of the process variation is
expected to fall between these limits)
• Product Specification Limits ARE NOT found on the control chart
• Understanding how the process matches up against customer
requirements IS important to know
To determine how the process performs to Customer Expectations, a
Process Capability Study is required
79. SPC
79
Control Limits vs. Specification Limits
TWO BIG CONTROL CHART ERRORS
1) Putting specification limits on a Control Chart
2 ) Treating UCL and LCL as a specification limit
When you do either of these the control chart becomes just an
inspection tool - it’s no longer a control chart
UCL / LCL are not directly tied to customer defects !
80. Relationship between Control Limits & Spec. Limits
USL
LSL
+ 3
- 3
Process natural limits are inside specification limits
and the process is centered nominal
Nominal
SPC
81. 81
Relationship between Control Limits & Spec. Limits
USL
LSL
+ 3
- 3
Process natural limits are inside specification limits
and the process is not centered nominal
Nominal
SPC
82. 82
Relationship between Control Limits & Spec. Limits
USL
LSL
+ 3
- 3
Process natural limits are outside specification limits
and the process is centered nominal
Nominal
Out of
spec
Out of
spec
SPC
83. 83
Relationship between Control Limits & Spec. Limits
USL
LSL
+ 3
- 3
Process natural limits are outside specification limits
and the process is not centered nominal
Nominal
SPC
84. 84
PROCESS CAPABILTY RATIOS
SPC
Cp & Cpk are two key measures of process capability
Cp = USL – LSL ie Total Tolerance
6 Sigma Process Spread
Cpk = Min X bar - LSL , USL – X bar Cpk accounts for process centering and spread
3 sigma 3 sigma
Cpk will always be equal to or less than Cp
Standard Deviation, Sigma = R bar/ d2
d2 is a constant varying by sample size,
n 2 3 4 5 6 7 8 9 10
d2 1.13 1.69 2.06 2.33 2.53 2.70 2.85 2.97 3.08
85. 27 mm = LSL USL = 33 mm
xbar = 30 mm
s = 1
3 3
Cp = __________
s s
C
USL - LSL
6
p
s
SPC
85
86. 3 3s
s
xbar = 35 mm
s = 1 mm
Cp = __________
C
USL - LSL
6
p
s
27 mm = LSL USL = 33 mm
SPC
87. CpU = ___________
CpL = ___________
Cpk = ____________
3 3 s
s
xbar = 35 mm
s = 1 mm
28 mm = LSL USL = 33 mm
SPC
88. SPC
Pre control Chart :
Out of specifications
Out of specifications
Specifications
Specifications
½ Specifications
½ Specifications
89. SPC
Pre control: The logic:-probability based on normal distribution
Specifications/2
GREEN ZONE
Yellow zone Yellow zone
RED ZONE RED ZONE
1/14 for 1
point out of
green zone
1/14 * 1/14
= 1/196 for 2
consecutive
points
If even one point falls in Red zone, Stop and reset!!
90. SPC
Pre control: The logic:-contd…
If two consecutive points are outside the two pre control
lines : May mean that the process variation has increased!
Use a sample of two consecutive measurements A & B. If A
is green , continue. If A is yellow check B and if B is also
yellow, STOPAND INVESTIGATE.
To qualify the process / set up:
Take two consecutive measurements. If both Green, O.K. If
one yellow, Restart the count. If both Yellow, Reset.
91. 92
Short term Capability Study
SPC
Short term capability :
Based on measurements collected from say one operating run. The
data are analyzed and checked further for the state of statistical
control.
If no special causes are found, a short term capability index can be
calculated.
This is useful for PPAP submissions, machine capability studies,
check for process modifications, etc.
Process Performance indices calculated are called Pp and Ppk
92. 93
Short term Capability Study
SPC
Pp & Ppk Cp &Cpk
PROCESS
PERFORMANCE INDEX
PROCESS CAPABILITY
INDEX
USED DURING INITIAL
PROCESS STUDY
DURING PPAP
ONGOING PROCESS
CAPABILITY STUDY
CAN BE CAPTURED
FOR STABLE AND
CHRONICALLY
UNSTABLE PROCESSES
USED ONLY FOR
STABLE PROCESSES
93. 94
Short term Capability Study
SPC
Pp & Ppk Cp &Cpk
CAPTURES VARIATION
DUE TO BOTH
COMMON & SPECIAL
CAUSES
CAPTURES VARIATION
DUE TO COMMON
CAUSES ONLY
SIGMA IS CALCULATED
USING n-1 FORMULA
USING ALL INDIVIDUAL
READINGS
SIGMA IS CALCULATED
USING R bar / d2
FORMULA
Ppk > 1.67 Cpk 1.33 – 1.67
