Variation thinking

2WS02 Industrial Statistics

A. Di Bucchianico

SPC: Philosophy

Let the process do the talking:

Goal: realize constant quality by controlling the

process with quantitative information

Constant quality means: quality with controlled and

known variation around a fixed target

Operator should be able to do the routine

controlling

Variation I

Variation II

Variation III

109876543210

-1-2-3-4-5-6-7-8-9

-10

Example: Dartec

disqualificationwhen outside range

Examples of variation patterns10

9876543210

-1-2-3-4-5-6-7-8-9

-10

Metric for sample variation: range

easy to compute (pre-computer era!)

rather accurate for sample size < 10

minimum maximumrange

Metric for sample variation: standard deviation

11

1

22

1

2

n

XnX

n

XXS

n

ii

n

ii

• 2nd formula easier to compute by hand • 2nd formula less rounding errors• correct dimension of units• n-1 to ensure that average value equals

population variance (“unbiased estimator”)

Visualisation of sample variation

Box-and Whisker plot

Histogram for dartecok

-9 -6 -3 0 3 6 9

dartecok

0

5

10

15

20

25

30fr

equen

cy

histogram

Box-and-Whisker Plot

-8 -4 0 4 8

dartecok

all observations first 60 observationsHistogram for dartecnotok

dartecnotok

frequency

-6 -3 0 3 6 90369

121518

dart

ecn

oto

k

0 20 40 60 80 100-6-30369

Histogram for dartecnotok

dartecnotok

frequency

-7 -4 -1 2 5 8 1105

1015202530

Variation and stability

Can variation be stable?

yes, if we mean that observations

– follow fixed probability distribution

– do not influence each other (independence)

stability -> predictability

How to handle a stable production process?

Why stable processes?

• behaviour is predictable

• processes can be left on itself: intervention may

be expensive

Deming’s funnel experiment

Lessons from funnel experiment

• tampering a stable process may lead to increase

of variation

• adjustments should be based on understanding of

process (engineering knowledge)

•we need a tool to check for stability

Attributive versus variable

two main types of measurements:

– attributive (yes/no, categories)

– variable (continuous data)

hybrid type:

– classes or bins

use variable data whenever possible!

Statistically in control

•Constant mean and spread

•Process-inherent variation only

•Do not intervene

Measurement

Tijd

XX

XX

X

X

X

X

XX

X

XX

X

X

XX

Intervene?

Statistically versus technically in control

“Statistically in

control”

– stable over

time /predictable

“Technically in control”

– within

specifications

Statistically in control vs technically in control

statistically controlled process:

– inhibits only natural random fluctuations (common causes)

– is stable

– is predictable

– may yield products out of specification

technically controlled process:

– presently yields products within specification

– need not be stable nor predictable

Priorities

what is preferable:

– statistical control or

– technically in control ??

process must first be in statistical control

Variation and production processes

Shewhart distinguishes two forms of variation in production

processes:

• common causes

– inherent to process

– cannot be removed, but are harmless

• special causes

– external causes

– must be detected and eliminated

Chance or noise

How do we detect special causes ?

use statistics to distinguish between chance and

real cause

Shewhart control chart

graphical display of product characteristic which is important for

product quality

X-bar Chart for yield

Subgroup

X-b

ar

0 4 8 12 16 2013,6

13,8

14

14,2

14,4

UpperControl Limit

Centre Line

Lower Control

Limit

Control charts

Why control charts?

•control charts are effective preventive device

•control charts avoid tampering of processes

•control charts yield diagnostic information

Basic principles

• take samples and compute statistic

• if statistic falls above UCL or below LCL, then out-of-control signal: e.g.,

X-bar Chart for yield

Subgroup

X-b

ar

0 4 8 12 16 2013,6

13,8

14

14,2

14,4

how to choose control limits?

Normal distribution

•often used in SPC

•“justification” by Central Limit Theorem:

– accumulation of many small errors

Meaning of control limits

•limits at 3 x standard deviation of plotted statistic

•basic example:

9973.0)33(

)33(

)33(

)(

ZP

XP

XP

UCLXLCLP

XX

XX

UCL

LCL

Example

• diameters of piston rings

• process mean: 74 mm

• process standard deviation: 0.01 mm

• measurements via repeated samples of 5 rings yields:

mmLCL

mmUCL

mmn

x

9865.73)0045.0(374

0135.74)0045.0(374

0045.05

01.0

Specifications vs. natural tolerance limits

never put specification limits on a control chart

control chart displays inherent process variance

during trial run charts (also called tolerance chart of tier chart) often

yields useful graphical information