The document discusses risk management and quality control through statistical process control charts. It defines key risk management terms and outlines different types of risks. It then covers control charts for variables, including how to calculate control limits and determine whether a process is in or out of control. The document provides examples of X-bar and R charts and discusses how to revise control limits over time.

1. RISK MANAGEMENT
Topic: Managing Quality Risk
through control chart
Presented By:
Ritesh Agarwal
Sunam Pal 1

2. Is Risk a symbol of danger
or
symbol of opportunity
Answer: Both

3. Risk Management
Risk
Uncertainty of outcome
Terminologies
•Pure Risk- Always leads to loss
•Speculative Risk- May Result in loss or Gain
•Static Risk- Results in loss
•Dynamic Risk- May Result in loss or Gain
•Acceptable Risk
•Non Acceptable Risk

4. Control Charts for
Variables

5. Types of Risks
• Material Risk- Building,Plant & Machinery,
Furniture,Fixtures,fittings,Stocks.
• Consequential Risk- Loss of production,Loss of
profit,Loss of market,Good will.
• Social Risk
• Legal Risk- Product liability,Public liability.
• Political Risk- Subsidies,Sanctions etc.

6. Best Practice Risk Management
• Framework for Risk Management
can be benchmarked in terms of:
METHO
DO LOGIE
»Policies S S
»Methodologies POLICIE
»Resources
RESOURCES
6

7. Risk Evaluation
• Arrange them in order of priority
• Provide information for deciding the most
appropriate way of handling.
Ranking risks according to :
2. Frequency of loss
3. Potential severity of loss.

8. Risk Analysis
Risk and Human behavior looks into
psychology of risk.
 How others look at the risk?
 How they behave in the face of risk?
 How they behave in groups?
Perception of Risk.

9. Risk analysis is to be carried out with proper
perception of risk of risk and cost involved in
Analysis.
Not to stick to one method
Understand company and industry
Should be financially reasonable
Accurate record keeping
Amount of imagination of required

10. Risk Reduction / Loss
Prevention
1. Reduce probability of loss and its severity.
2. Most important for PM process.
3. Risk Reduction / Prevention can be from –
• Loss prevention
• Ensuring Safety
• Fire protection / Detection
• Environmental protection

11. Variation
• It is the measure of deviation from
mean/average value
• Variation may be quite large or very small.
• If variation is very small, it may appear that
items are identical, but precision instruments
will show differences.

12. Categories of variation
• Within-piece variation
• One portion of surface is rougher than another
portion.
• A piece-to-piece variation
• Variation among pieces produced at the same
time.
• Time-to-time variation
• Service given early would be different from that
given later in the day.

13. Source of variation
• Equipment
• Tool wear, machine vibration, …
• Material
• Raw material quality
• Environment
• Temperature, pressure, humadity
• Operator
• Operator performs- physical & emotional

14. Control Chart Viewpoint
 Variation due to
 Common or chance causes
 Assignable causes
 Control chart may be used to discover
“assignable causes”

15.  Run chart - without any upper/lower
limits
 Specification/tolerance limits
 Control limits - statistical

16. Control chart functions
• Control charts are powerful aids to understanding the
performance of a process over time.
Noise
Input Output
PROCESS
What’s causing variability?

17. Control charts identify
variation
• Chance causes - “common cause”
• inherent to the process or random and not
controllable
• if only common cause present, the process is
considered stable or “in control”
• Assignable causes - “special cause”
• variation due to outside influences
• if present, the process is “out of control”

18. Types of Data
• Continuous data
• Product characteristic that can be measured
• Length, size, weight, height, time, velocity
• Discrete data
Product characteristic evaluated with a discrete choice
• Good/bad, yes/no

19. Control chart for variables
• Variables are the measurable characteristics
of a product or service.
• Measurement data is taken and arrayed on
charts.

20. Control charts for variables
• X-bar chart
• In this chart the sample means are plotted in order to
control the mean value of a variable (e.g., size of piston
rings, strength of materials, etc.).
• R chart
• In this chart, the sample ranges are plotted in order to
control the variability of a variable.
• S chart
• In this chart, the sample standard deviations are plotted
in order to control the variability of a variable.
• S2 chart
• In this chart, the sample variances are plotted in order
to control the variability of a variable.

21. Control chart components
• Centerline
• shows where the process average is
centered or the central tendency of the
data
• Upper control limit (UCL) and Lower
control limit (LCL)
• describes the process spread

22. The Control Chart Method
X bar Control Chart:
UCL = XDmean + A2 x Rmean
LCL = XDmean - A2 x Rmean
CL = XDmean
R Control Chart:
UCL = D4 x Rmean
LCL = D3 x Rmean
CL = Rmean
Capability Study:
PCR = (USL - LSL)/(6s); where s = Rmean /d2

23. Control Chart Examples
UCL
Variations
Nominal
LCL
Sample number

24. Determine trial centerline
• The centerline should be the population mean, µ
• Since it is unknown, we use X Double bar, or the grand average of
the subgroup averages.
m
∑X i
X = i=1
m

25. UCL & LCL calculation
UCL = X + 3σ
LCL = X − 3σ
σ = standard deviation

26. Determining an alternative value for
the standard deviation
m
∑R i
R = i=
1
m
UCL = + 2 R
X A
LCL = − 2 R
X A

27. Example: Control Charts for Variable Data
Slip Ring Diameter (cm)
Sample 1 2 3 4 5 X R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.08
2 5.01 5.03 5.07 4.95 4.96 5.00 0.12
3 4.99 5.00 4.93 4.92 4.99 4.97 0.08
4 5.03 4.91 5.01 4.98 4.89 4.96 0.14
5 4.95 4.92 5.03 5.05 5.01 4.99 0.13
6 4.97 5.06 5.06 4.96 5.03 5.01 0.10
7 5.05 5.01 5.10 4.96 4.99 5.02 0.14
8 5.09 5.10 5.00 4.99 5.08 5.05 0.11
9 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15

28. Calculation
From Table above:
• Sigma X-bar = 50.09
• Sigma R = 1.15
• m = 10
Thus;
• X-Double bar = 50.09/10 = 5.009 cm
• R-bar = 1.15/10 = 0.115 cm
Note: The control limits are only preliminary with 10 samples.
It is desirable to have at least 25 samples.

29. 3-Sigma Control Chart Factors
Sample size X-chart R-chart
n A2 D3 D4
2 1.88 0 3.27
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86

30. Trial control limit
X-bar chart
•UCLx-bar = X-D bar + A2 R-bar
= 5.009 + (0.577)(0.115) = 5.075 cm
•LCLx-bar = X-D bar - A2 R-bar
= 5.009 - (0.577)(0.115) = 4.943 cm
R-chart
•UCLR = D4R-bar = (2.114)(0.115) = 0.243 cm
•LCLR = D3R-bar = (0)(0.115) = 0 cm

31. X-bar Chart
5.10
UCL
5.08
5.06
5.04
X bar
5.02
5.00 CL
4.98
4.96 LCL
4.94
0 1 2 3 4 5 6 7 8 9 10 11
Subgroup

32. R Chart
0.25 UCL
0.20
0.15
Range
CL
0.10
0.05
LCL
0.00
0 1 2 3 4 5 6 7 8 9 10 11
Subgroup

33. 6.70
6.65
Run Chart 6.60
Mean, X-bar
6.55
6.50
6.45
6.40
6.35
6.30
0 5 10 15 20 25
Subgroup number
0.35
0.3
0.25
Range, R
0.2
0.15
0.1
0.05
0
0 5 10 15 20 25
Subgroup number

34. X-bar Chart

35. R Chart

36. Trial Control Limits & Revised Control Limit
6.65
6.60 Revised control limits
6.55
Mean, X-bar
6.50
UCL = 6.46
6.45
6.40 CL = 6.40
6.35
6.30 LCL = 6.34
0 2 4 6 8
Subgroup
0.20 UCL = 0.18
0.15
Range, R
0.10 CL = 0.08
0.05
0.00
0 2 4 6 8
LCL = 0
Subgroup

37. Revise the charts
In certain cases, control limits are revised
because:
1. out-of-control points were included in
the calculation of the control limits.
2. the process is in-control but the within
subgroup variation significantly
improves.

38. The Normal
Distribution
σ = Standard deviation
Mean
-3σ -2σ -1σ +1σ +2σ +3σ
68.26%
95.44%
LSL USL 99.74%
-3σ +3σ
CL

39. • 34.13% of data lie between µ and 1σ above the mean (µ).
• 34.13% between µ and 1σ below the mean.
• Approximately two-thirds (68.28 %) within 1σ of the mean.
• 13.59% of the data lie between one and two standard deviations
• Finally, almost all of the data (99.74%) are within 3σ of the mean.

40. Normal Distribution Review
 Define the 3-sigma limits for sample means as follows:
3σ 3(0.05)
Upper Limit = µ + = 5.01 + = 5.077
n 5
3σ 3(0.05)
Lower Limit = µ − = 5.01 − = 4.943
n 5
 What is the probability that the sample means will lie
outside 3-sigma limits?
 Note that the 3-sigma limits for sample means are
different from natural tolerances which are at
µ ± 3σ

41. Common Causes

42. Process Out of Control
• The term out of control is a change in the process due to an
assignable cause.
• When a point (subgroup value) falls outside its control limits,
the process is out of control.

43. Assignable Causes
Average (a) Mean
Grams

44. Assignable Causes
Average
(b) Spread
Grams

45. Assignable Causes
Average
(c) Shape
Grams

46. Improvement

47. Chart zones
• Based on our knowledge of the normal curve, a
control chart exhibits a state of control when:
♥ Two thirds of all points are near the center value.
♥ The points appear to float back and forth across
the centerline.
♥ The points are balanced on both sides of the
centerline.
♥ No points beyond the control limits.
♥ No patterns or trends.

48. σ What Is Six Sigma?
Sigma is a letter • Degree of variation;
in the Greek • Level of performance in terms of defects;
Alphabet
• Statistical measurement of process
capability;
• Benchmark for comparison;
• Process improvement methodology;
• It is a Goal;
• Strategy for change;
• A commitment to customers to achieve
an acceptable level of performance
48

49. Six Sigma Definitions
• Business Definition
 A break through strategy to significantly improve
customer satisfaction and shareholder value by
reducing variability in every aspect of business.
• Technical Definition
 A statistical term signifying 3.4 defects per million
opportunities.
49

50. Sigma Defects Per Million Rate of
Level Opportunities Improveme
nt
1σ 690,000
2σ 308,000 2 times
3σ 66,800 5 times
4σ 6,210 11 times
5σ 230 27 times
6σ 3.4 68 times
50

51. Six Sigma Project Methodology
Project Phases
Define Measure Analyze Improve Control
 Identify,  Collect data  Analyze  Improvemen  Establish
evaluate on size of data, t strategy standards to
and select the selected establish  Develop maintain
projects for problem, and confirm ideas to process;
improvemen  identify key the “ vital remove root  Design the
t customer few “ causes controls,
 Set goals requirement determinant  Design and implement
 Form teams. s, s of the carry out and
 Determine performance experiments monitor.
key product . ,  Evaluate
and process  Validate  Optimize financial
characteristi hypothesis the process. impact of
c.  Final the project
solutions
51

52. Learning Outcome
3.Risk can fixed only when it is scalable
4.More than one form of risk can be present in a
project
5.100% assurance on risk control can be guranteed
6.Reduction in Risk automatically enhances the
quality of product

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