Topic: Managing Quality Risk through control chart

Presented By:

Ritesh AgarwalSunam Pal

1

RISK MANAGEMENT

Is Risk a symbol of danger or

symbol of opportunity

Answer: Both

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

Control Charts for Variables

Types of Risks

1. Material Risk- Building,Plant & Machinery, Furniture,Fixtures,fittings,Stocks.

2. Consequential Risk- Loss of production,Loss of profit,Loss of market,Good will.

3. Social Risk4. Legal Risk- Product liability,Public liability.5. Political Risk- Subsidies,Sanctions etc.

Best Practice Risk Management

• Framework for Risk Managementcan be benchmarked in terms of:

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POLICIES

METHODOLOGIES

RESOURCES

»Policies»Methodologies»Resources

Risk Evaluation

• Arrange them in order of priority• Provide information for deciding the most

appropriate way of handling.

Ranking risks according to :1. Frequency of loss 2. Potential severity of loss.

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.

Risk analysis is to be carried out with proper perception of risk of risk and cost involved in Analysis.Not to stick to one methodUnderstand company and industryShould be financially reasonableAccurate record keepingAmount of imagination of required

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

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.

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.

Source of variation• Equipment

• Tool wear, machine vibration, …• Material

• Raw material quality• Environment

• Temperature, pressure, humadity• Operator

• Operator performs- physical & emotional

Control Chart Viewpoint

Variation due to Common or chance causes Assignable causes

Control chart may be used to discover “assignable causes”

Run chart - without any upper/lower limits

Specification/tolerance limits Control limits - statistical

Control chart functions• Control charts are powerful aids to understanding the

performance of a process over time.

PROCESSPROCESS

Input Output

What’s causing variability?

Noise

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”

Types of Data

• Continuous data• Product characteristic that can be measured

• Length, size, weight, height, time, velocity

• Discrete dataProduct characteristic evaluated with a discrete choice

• Good/bad, yes/no

Control chart for variables

• Variables are the measurablemeasurable characteristics of a product or service.

• Measurement data is taken and arrayed on charts.

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.

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

The Control Chart Method

R Control Chart: UCL = D4 x Rmean LCL = D3 x Rmean CL = Rmean Capability Study:PCR = (USL - LSL)/(6s); where s = Rmean /d2

X bar Control Chart: UCL = XDmean + A2 x Rmean LCL = XDmean - A2 x Rmean CL = XDmean 

Control Chart ExamplesControl Chart Examples

Nominal

UCL

LCL

Sample number

Var

iati

on

s

Determine trial centerline• The centerline should be the population mean, • Since it is unknown, we use X Double bar, or the grand average of

the subgroup averages.

m

m

i

i 1

XX

UCL & LCL calculation

deviation standard

3XLCL

3XUCL

Determining an alternative value for the standard deviation

m

m

ii

1

RR

RAXUCL 2

RAXLCL 2

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 0.082 5.01 5.03 5.07 4.95 4.96 5.00 0.123 4.99 5.00 4.93 4.92 4.99 4.97 0.084 5.03 4.91 5.01 4.98 4.89 4.96 0.145 4.95 4.92 5.03 5.05 5.01 4.99 0.136 4.97 5.06 5.06 4.96 5.03 5.01 0.107 5.05 5.01 5.10 4.96 4.99 5.02 0.148 5.09 5.10 5.00 4.99 5.08 5.05 0.119 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

Calculation

From Table above:• Sigma X-bar = 50.09• Sigma R = 1.15• m = 10Thus;• 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.

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

Trial control limitTrial 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

X-bar Chart

4.94

4.96

4.98

5.00

5.02

5.04

5.06

5.08

5.10

0 1 2 3 4 5 6 7 8 9 10 11

Subgroup

X b

ar

LCL

CL

UCL

R Chart

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8 9 10 11

Subgroup

Ran

ge

LCL

CL

UCL

Run Chart

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20 25

Subgroup number

Ra

ng

e, R

6.30

6.35

6.40

6.45

6.50

6.55

6.60

6.65

6.70

0 5 10 15 20 25

Subgroup numberM

ean

, X

-bar

X-bar ChartX-bar Chart

R ChartR Chart

Trial Control Limits & Revised Control Limit

6.30

6.35

6.40

6.45

6.50

6.55

6.60

6.65

0 2 4 6 8

Subgroup

Mea

n, X

-bar

0.00

0.05

0.10

0.15

0.20

0 2 4 6 8

Subgroup

Ran

ge,

R

UCL = 6.46

CL = 6.40

LCL = 6.34

LCL = 0

CL = 0.08

UCL = 0.18

Revised control limits

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.

The NormalThe NormalDistributionDistribution

-3 -2 -1 +1 +2 +3Mean

68.26%95.44%99.74%

= Standard deviation

LSL USL

-3 +3CL

• 34.13% of data lie between and 1 above the mean (). • 34.13% between and 1 below the mean. • Approximately two-thirds (68.28 %) within 1 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 3 of the mean.

Define the 3-sigma limits for sample means as follows:

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

Normal Distribution Review

94345

0503015

3

07755

0503015

3

.).(

. Limit Lower

.).(

. Limit Upper

n

n

3

Common CausesCommon Causes

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.

Assignable CausesAssignable Causes

(a) Mean

Grams

Average

Assignable CausesAssignable Causes

(b) Spread

Grams

Average

Assignable CausesAssignable Causes

(c) Shape

Grams

Average

Improvement

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.

What Is Six Sigma?

• Degree of variation;• Level of performance in terms of defects;• 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

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Sigma is a letter

in the Greek Alphabet

Six Sigma Definitions

• Business DefinitionA break through strategy to significantly improve

customer satisfaction and shareholder value by reducing variability in every aspect of business.

• Technical DefinitionA statistical term signifying 3.4 defects per million

opportunities.

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Sigma Level

Defects Per Million Opportunities

Rate of Improvement

1 690,000

2 308,000 2 times

3 66,800 5 times

4 6,210 11 times

5 230 27 times

6 3.4 68 times

50

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Six Sigma Project Methodology

ControlControlDefineDefine MeasureMeasure AnalyzeAnalyze ImproveImprove

Establish standards to maintain process;

Design the controls, implement and monitor.

Evaluate financial impact of the project

Identify, evaluate and select projects for improvement

Set goalsForm

teams.

Collect data on size of the selected problem,

identify key customer requirements,

Determine key product and process characteristic.

Analyze data, establish and confirm the “ vital few “ determinants of the performance.

Validate hypothesis

Improvement strategy

Develop ideas to remove root causes

Design and carry out experiments,

Optimize the process.

Final solutions

Project Phases

Learning Outcome1.Risk can fixed only when it is scalable2.More than one form of risk can be present in a project3.100% assurance on risk control can be guranteed4.Reduction in Risk automatically enhances the quality of product

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