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S6 Statistical Process Control

SCM 352

Outline

• Statistical Quality Control• Common causes vs. assignable causes• Different types of data – attributes and

variables• Central limit theorem• SPC charts

– Control charts for variables– Control charts for attribute

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Statistical Process Control (SPC)

• The objective of a process control system is to provides a statistical signal when assignable causes are present

• Variability is inherent in every process• Natural or common causes• Special or assignable causes

• Detect and eliminate assignable causes of variation

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Natural Variations

• Also called common causes• Affect virtually all production processes• Expected amount of variation• Output measures follow a probability distribution• For any distribution there is a measure of central

tendency and dispersion• If the distribution of outputs falls within acceptable

limits, the process is said to be “in control”• A process with only natural variations is in statistical

control

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• Also called special causes of variation– Generally this is some change in the process

• Variations that can be traced to a specific reason– Operators errors– Defective raw materials– Improperly adjusted machines

• The objective is to discover when assignable causes are present– Eliminate the bad causes– Incorporate the good causes

Assignable Variations

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Natural & Assignable Variation

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• Characteristics for which you focus on defects

• Classify products as either ‘good’ or ‘bad’, or count number of defects– e.g., radio works or not

• Categorical or discrete random variables

AttributesVariables

Types of Data

• Characteristics that you measure, e.g., weight, length

• May be in whole or in fractional numbers

• Continuous random variables

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X

As sample size gets large enough,

sampling distribution becomes almost normal regardless of population distribution.

Central Limit Theorem

X

Theoretical Basis of Control Charts

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-3σ -2σ -1σ +1σ +2σ +3σMean

68.26%95.44%99.74%

σ = Standard deviation

The Normal Distribution

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For variables that have continuous dimensions

Weight, speed, length, etc.

x-charts are to control the central tendency of the processR-charts are to control the dispersion of the processThese two charts must be used together

Control Charts for Variables

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For x-Charts

Lower control limit (LCL) = x - A2R

Upper control limit (UCL) = x + A2R

where R = average range of the samplesA2 = control chart factor found in Table S6.1 x = mean of the sample means

Setting Chart Limits

© 2011 Pearson Education, Inc. publishing as Prentice HallTable S6.1

Sample Size Mean Factor Upper Range Lower Rangen A2 D4 D3

2 1.880 3.268 03 1.023 2.574 04 .729 2.282 05 .577 2.115 06 .483 2.004 07 .419 1.924 0.0768 .373 1.864 0.1369 .337 1.816 0.184

10 .308 1.777 0.22312 .266 1.716 0.284

Control Chart Factors

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For R-Charts

Lower control limit (LCLR) = D3R

Upper control limit (UCLR) = D4R

whereR = average range of the samples

D3 and D4 = control chart factors from Table S6.1

Setting Chart Limits

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Control Charts for Variables

Time SampleTaken 1 2 3 4 Range Mean

7 am 0.5014 0.5022 0.5009 0.50278 am 0.5021 0.5041 0.5024 0.50209 am 0.5018 0.5026 0.5035 0.5023

10 am 0.5008 0.5034 0.5024 0.501511 am 0.5041 0.5056 0.5034 0.5047

Average

Special Metal Screw

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Time SampleTaken 1 2 3 4 Range Mean

7 am 0.5014 0.5022 0.5009 0.5027 0.0018 0.50188 am 0.5021 0.5041 0.5024 0.5020 0.0021 0.50279 am 0.5018 0.5026 0.5035 0.5023 0.0017 0.5026

10 am 0.5008 0.5034 0.5024 0.5015 0.0026 0.502011 am 0.5041 0.5056 0.5034 0.5047 0.0022 0.5045

Average 0.0021 0.5027

Special Metal Screw

Control Charts for Variables

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Control Charts - Special Metal ScrewR - Charts R = 0.0021

UCLR = D4R = 2.282(0.0021) = 0.00479LCLR = D3R = 0(0.0021) = 0

Control Charts for Variables

© 2011 Pearson Education, Inc. publishing as Prentice HallTable S6.1

Sample Size Mean Factor Upper Range Lower Rangen A2 D4 D3

2 1.880 3.268 03 1.023 2.574 04 .729 2.282 05 .577 2.115 06 .483 2.004 07 .419 1.924 0.0768 .373 1.864 0.1369 .337 1.816 0.184

10 .308 1.777 0.22312 .266 1.716 0.284

Control Chart Factors

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0.005

0.004

0.003

0.002

0.001

01 2 3 4 5 6

Ran

ge (i

n.)

Sample number

UCLR = 0.00479

LCLR = 0

R = 0.0021

Range Chart - Special Metal Screw

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Control Charts - Special Metal ScrewR = 0.0021x = 0.5027

x - Charts

UCLx = x + A2R = 0.5027 + 0.729(0.0021)LCLx = x - A2R = 0.5027 - 0.729(0.0021)UCL = 0.5042LCL = 0.5012

Control Charts for Variables

© 2011 Pearson Education, Inc. publishing as Prentice HallTable S6.1

Sample Size Mean Factor Upper Range Lower Rangen A2 D4 D3

2 1.880 3.268 03 1.023 2.574 04 .729 2.282 05 .577 2.115 06 .483 2.004 07 .419 1.924 0.0768 .373 1.864 0.1369 .337 1.816 0.184

10 .308 1.777 0.22312 .266 1.716 0.284

Control Chart Factors

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0.5050

0.5040

0.5030

0.5020

0.5010

1 2 3 4 5

Aver

age

(in.)

Sample number

x = 0.5027

UCLx = 0.5042

LCLx = 0.5012

0.5045

x Chart - Special Metal Screw

Thank You

Questions? ?