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Chapter 3

University of Hail College of Engineering

ISE 320 - Quality Control and Industrial Statistics

Prof. Mohamed AichouniProf. Mohamed Aichouni

Chapter 3 Control Charts for Variables

Lectures notes adapted from: PowerPoint presentation to accompany Besterfield, Quality Improvement, 9th edition

Course Webpage: faculty.uoh.edu.sa/m.aichouni/ise320-quality/

Lectures notes adapted from: PowerPoint presentation to accompany Besterfield, Quality Improvement, 9th edition

Course Webpage: faculty.uoh.edu.sa/m.aichouni/ise320-quality/

• The variation concept is a law of nature in that no two natural items are the same.Th i ti b it l d il

variation

The variation may be quite large and easily noticeableThe variation may be very small. It may appear that items are identical; however, precision instruments will show differenceTh bilit t i ti i b f

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The ability to measure variation is necessary before it can be controlled

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There are three categories of variation in piece part production:

Variations in Manufacturing Products

1. Within-piece variation: variations in surface.2. Piece-to-piece variation: Among pieces produced at

the same time3. Time-to-time variation: Difference in product

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produced at different times of the day

Process Variations Causes

1.1. Common causesCommon causes are ever-present in the process;========= Natural Variations

2.2. Special causesSpecial causes are intermittent effects that must be investigated immediately.

========= Assignable Causes VariationsAssignable Causes Variations

Management and quality professionals (YOU)Management and quality professionals (YOU)•• Management and quality professionals (YOU) Management and quality professionals (YOU) should help manufacturing people to identify should help manufacturing people to identify

and remove special causes and remove special causes and reduce the and reduce the occurrence of common causesoccurrence of common causes in the process..

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Process Variation

Process Variability Variations due to:

Natural Causes:•Temperature variation

•Material variation•Customer differences•Operator performance

Special Causes:•Machine is breaking•Untrained operative•Machine movement•Process has changed

Must be monitored Early and visible warning required

Sources of Variation in Processes

Sources of Variation in production processes:

Materials OperatorsOperators MethodsMethods MeasurementMeasurementInstrumentsInstruments

INPUTSINPUTS PROCESSPROCESS OUTPUTSOUTPUTS

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ToolsTools HumanHumanInspectionInspection

PerformancePerformanceEnvironmentEnvironmentMachinesMachines

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Sources of variation are:Machines and Equipment:

Sources of Variation in Manufacturing

Methods• Toolwear• Machine vibration• Electrical fluctuations etc.

Material• Tensile strength• Ductility

Environment• Temperature• Light• Radiation

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• Ductility• Thickness• Porosity etc.

Measurements

• Humidity etc.

Operator / Man• Personal problem• Physical problem etc.

Of all the quality tools for analyzing data, the control chart is the most useful. No other tool captures

Control Charts

chart is the most useful. No other tool captures the voice of your process better.

Control charts are used to determine whether your process is operating in statistical control.

Until it is, any improvement efforts are, at best, mere process tampering.

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mere process tampering. Basically, a control chart is a run chart (described

earlier) that includes statistically generated upper and lower control limits.

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The control chart is a means of visualizing

Control Charts

Special causes variationthe variations that occur in the process data and its components.

It h h th th

Natural (common causes )variation

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It shows whether the process is in a stable state (in statistical control) or out of statistical control.

Figure 1 Example of a control chart

Control Charts

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ControlCharts

Continuous Numerical Data

Categorical or Discrete Numerical Data

Control Charts TypesControl Charts Types

Charts

VariablesCharts

AttributesCharts

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RChart

XChart

PChart

CChart

sChart

Other Charts: ImR, EWMA, CUSUM..

Control Charts

12Figure 2 - Example of a method of reporting inspection results

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The objectives of the variable control charts are:

Use of Variable Control Charts in Manufacturing

The objectives of the variable control charts are:For process improvementTo determine the process capability.For decisions regarding product specificationsFor current decisions on the production process

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For current decisions on recently produced items

control charts help to determine if the process is : (a) in statistical control ; or (b) out of statistical control.

Variable Control Charts Interpretation

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Procedure for establishing a pair of control charts for the average Xbar and the range R:

Control Chart Techniques

1. Select the quality characteristic2. Choose the rational subgroup3. Collect the data4. Determine the trial center line and control limits

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5. Establish the revised central line and control limits6. Achieve the objective

Quality Characteristic

• Variable - a single quality characteristic that can be measured on a numerical scale.

• When working with variables, we should monitor both the mean value ofshould monitor both the mean value of the characteristic and the variabilityassociated with the characteristic.

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The Quality characteristic must be measurable. It can expressed in terms of the seven basic units:

Quality Characteristic

1. Length2. Mass3. Time4. Electrical current5 Temperature

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5. Temperature6. Substance7. Luminosity

Control Charts for and R

Notation for variables control charts• n size of the sample (sometimes called a

x

• n - size of the sample (sometimes called a subgroup) chosen at a point in time

• m - number of samples selected• = average of the observations in the ith

sample (where i = 1, 2, ..., m)• = grand average or “average of the

ix

x grand average or average of the averages (this value is used as the center line of the control chart)

x

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Control Charts for and R

Notation and values

x

• Ri = range of the values in the ith sample

Ri = xmax - xmin

• = average range for all m samplesR g g p• μ is the true process mean• σ is the true process standard deviation

Control Charts for and R

Statistical Basis of the Charts

x

Statistical Basis of the Charts• Assume the quality characteristic of interest is

normally distributed with mean μ, and standard deviation, σ.

• If x1, x2, …, xn is a sample of size n, then he average of this sample is xxxx n21 +++

=L

• is normally distributed with mean, μ, and standard deviation,

nx

n/x σ=σ

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Control Charts for and R

Control Limits for the chart

x

x

RAxxLCLxLineCenter

RAxxUCL

2

2

−=

=

+=

• A2 is found in constants for various values of n.

2

Control Charts for and R

Control Limits for the R chart

x

RDLCLRLineCenter

RDUCL

R

R

3

4

=

=

=

• D3 and D4 are constants for various values of n.

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Control Charts Constants

Control Charts for and s

• The sample standards deviation can be a

x

more accurate estimation of the process variability process, especially if the sample size n>10.

• In this case control charts for Xbar and S can be used to monitor the process.

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Control Charts for and s

• Construction of the control charts for Xbar

x

and S follows the same procedure as for the Xbar-R charts.

• Control Limits for s chart are:

sBLCLsCenterLine

sBUCL

s

s

3

4

==

=

• Control Limits for Xbar chart:

• A3, B3, B4 are constants sAxLCL

xLineCentersAxUCL

3

3

−=

=

+=

Example of -R control charts A component part for a jet

aircraft engine is

x

manufactured by an investment casting process.

The vane opening on this casting is an important functional parameter of the part.

We will illustrate the use of Xbar and R control charts to assess the statistical stability of this process.

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Example of -R control charts

Determine the mean and the

x

mean and the range for each sample.

Determine the grand average of theaverage of the means and the average of the ranges.

Example of -R control charts

Calculate the control limits for the R chart:

x

Calculate the control limits for the Xbar chart:

080.5

27.12

3

4

==

==

==

RDLCLRLineCenter

RDUCL

R

R

Calculate the control limits for the Xbar chart:

97.2932.33

67.36

2

2

=−=

==

=+=

RAxxLCLxLineCenter

RAxxUCL

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Example of -R control charts

The process is Out of t ti ti l t l

x

statistical control;It is not stable.Special causes should

be investigated using cause and effect diagram and other quality tools.

Other Control Charts for variables

1. Individual Moving Range Charts2. Exponentially Weighted Mean Average

(EWMA) charts3. Cumulative Sum (CUSUM) chart.

Student should search on the net for the use of these charts

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Control Charts Selection

Source: Aichouni (2007), Quality Control.

Additional ExamplesExample 4-1The strength of a metallic

wire in a production process is given for 20 samples .

Study the stability of the production process using p p gthe Xbar-R charts.

Use both hand calculations and Minitab to produce the control charts.

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Additional ExamplesExample 4-2The thickness of a metal part

in the manufacturing process of a car is given for 25 samples .

Study the stability of the production process using p p gthe Xbar-s charts.

Use Minitab to produce the control charts.

Conclusion Conclusion

"Quality control truly begins and ends

Lecture Finished

Any Question?

Nogwith education",

K. Ishikawa (1990).

Question?

Ask questions

Teachers answers

Yes

Train your self (Google, YouTube, course webpage

End (See you next lecture)