08 FD SPC Overview

7/29/2019 08 FD SPC Overview

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An Introduction To SPC

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visit to www.e1procedures.com


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An Introduction to ControlCharts


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Basic Conceptions

What is a control chart? The control chart is a graph used to study how a process

changes over time. Data are plotted in time order.

A control chart always has a central line for the average, anupper line for the upper control limit and a lower line for the

lower control limit. Lines are determined from historical data. By comparingcurrent data to these lines, you can draw conclusions aboutwhether the process variation is consistent (in control) or isunpredictable (out of control, affected by special causes ofvariation).


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Basic Conceptions

When to use a control chart?

Controlling ongoing processes by finding and

correcting problems as they occur.

Predicting the expected range of outcomes from a

process.

Determining whether a process is stable (in statistical

control).

Analyzing patterns of process variation from special

causes (non-routine events) or common causes (builtinto the process).

Determining whether the quality improvement project

should aim to prevent specific problems or to make

fundamental changes to the process.


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Basic Conceptions

Control Chart Basic Procedure Choose the appropriate control chart for the data.

Determine the appropriate time period for collectingand plotting data.

Collect data, construct the chart and analyze thedata.

Look for out-of-control signals on the control chart.When one is identified, mark it on the chart andinvestigate the cause. Document how youinvestigated, what you learned, the cause and howit was corrected.

Continue to plot data as they are generated. Aseach new data point is plotted, check for new out-

of-control signals.


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Basic Principles

Basic components of control charts

A centerline, usually the mathematical average of all

the samples plotted;

Lower and upper control limits defining the

constraints of common cause variations;

Performance data plotted over time.


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Basic Principles

General model for a control chartUCL = + k

CL =

LCL = kwhere is the mean of the variable, and is the standarddeviation

of the variable. UCL=upper control limit; LCL = lower control limit;

CL = center line. where kis the distance of the control limits

from thecenter line, expressed in terms of standard deviation units.

When k

is set to 3, we speak of 3-sigma control charts. Historically, k = 3has

become an accepted standard in industry.


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Basic Principles of Control Charts

Types of the control charts

Variables control charts

Variable data are measured on a continuous scale. Forexample: time, weight, distance or temperature can be

measured in fractions or decimals.Applied to data with continuous distribution

Attributes control charts

Attribute data are counted and cannot have fractions or

decimals. Attribute data arise when you are determiningonly the presence or absence of something: success orfailure, accept or reject, correct or not correct. Forexample, a report can have four errors or five errors, but itcannot have four and a half errors.

Applied to data following discrete distribution


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Variables control charts

X-bar and R chart (also called averages

and range chart)

X-bar and s chart


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An Introduction

toProcess capability


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Have you ever

Shot a rifle?

Played darts?

Played basketball?

Shot a round of golf?

What is the point of these sports?

What makes them hard?



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Have you ever

Shot a rifle?

Played darts?

Shot a round of golf?

Played basketball?

Emmett

Jake

Who is the better shot?



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Discussion

What do you measure in your process?

Why do those measures matter?

Are those measures consistently the

same?

Why not?


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Variability

Deviation = distance between

observations and the mean (or

average)

Emmett

Jake

Observations

10

9

8

8

7

averages 8.4

Deviations

10 - 8.4 = 1.6

9 8.4 = 0.6

8 8.4 = -0.4

8 8.4 = -0.4

7 8.4 = -1.4

0.0

8

7

10

8

9


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Variability

Deviation = distance between

observations and the mean (or

average)

Emmett

Jake

Observations

7

7

7

6

6

averages 6.6

Deviations

7 6.6 = 0.4

7 6.6 = 0.4

7 6.6 = 0.4

6 6.6 = -0.6

6 6.6 = -0.6

0.0

7

6

7

76


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Variability

Variance = average distance

between observations and the

mean squared

Emmett

Jake

Observations

10

9

8

8

7

averages 8.4

Deviations

10 - 8.4 = 1.6

9 8.4 = 0.6

8 8.4 = -0.4

8 8.4 = -0.4

7 8.4 = -1.4

0.0

8

7

10

8

9

Squared Deviations

2.56

0.36

0.16

0.16

1.96

1.0 Variance


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Variability



mean squared

Emmett

Jake

Observations

7

7

7

6

6

averages

Deviations Squared Deviations7

6

7

76


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Variability



mean squared

Emmett

Jake

Observations

7

7

7

6

6

averages 6.6

Deviations

7 - 6.6 = 0.4

7 - 6.6 = 0.4

7 - 6.6 = 0.4

6 6.6 = -0.6

6 6.6 = -0.6

0.0

Squared Deviations

0.16

0.16

0.16

0.36

0.36

0.24

7

6

7

76

Variance


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Variability

Standard deviation = square root

of variance Emmett

Jake

Variance Standard

Deviation

Emmett 1.0 1.0

Jake 0.24 0.4898979

But what good is a standard deviation


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Variability

The world tends to

be bell-shaped

Most

outcomes

occur in the

middle

Fewer

in the

tails

(lower)

Fewer

in the

tails

(upper)

Even very rare

outcomes are

possible

(probability > 0)

Even very rare

outcomes are

possible

(probability > 0)


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Variability

Add up the dots on the dice

0

0.05

0.1

0.15

0.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Sum of dots

Probability

1 die

2 dice

3 dice

Here is why: Even outcomes that are equally

likely (like dice), when you add

them up, become bell shaped


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Normal bell shaped curve

Add up about 30 of most things

and you start to be normal

Normal distributions are divide up

into 3 standard deviations on

each side of the mean

Once your that, you

know a lot aboutwhat is going on

And that is what a standard deviation

is good for


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Usual or unusual?

1. One observation falls

outside 3 standard

deviations?

2. One observation falls inzone A?

3. 2 out of 3 observations fall in

one zone A?

4. 2 out of 3 observations fall in

one zone B or beyond?

5. 4 out of 5 observations fall inone zone B or beyond?

6. 8 consecutive points above

the mean, rising, or falling? X XXXX XX X XX1 2 3 4 5 6 7 8


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Causes of Variability

Common Causes: Random variation (usual)

No pattern

Inherent in process adjusting the process increases its variation

Special Causes Non-random variation (unusual)

May exhibit a patternAssignable, explainable, controllable

adjusting the process decreases its variation

SPC uses samples to identify that special causes have occurred


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Limits

Process and Control limits: Statistical

Process limits are used for individual items

Control limits are used with averages Limits = 3

Define usual (common causes) & unusual (specialcauses)

Specification limits: Engineered

Limits = target tolerance

Define acceptable & unacceptable


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Process vs. control limits

Variance of averages < variance of individual items

Distribution of averages

Control limits

Process limits

Distribution of individuals

Specification limits


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Usual v. Unusual,

Acceptable v. Defective

Target

A B C D E


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More about limits

Good quality:

defects are

rare (Cpk>1)

Poor quality:

defects are

common (Cpk


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Process capability

Good quality: defects are rare (Cpk>1)

Poor quality: defects are common (Cpk


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Going out of control

When an observation is unusual, what

can we conclude?

2

The mean

has changed

X1


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Going out of control

When an observation is unusual, what

can we conclude?

The standard deviation

has changed

2

X

1


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Setting up control charts:

Calculating the limits

1. Sample n items (often 4 or 5)

2. Find the mean of the sample (x-bar)

3. Find the range of the sample R4. Plot on the chart

5. Plot the R on an R chart

6. Repeat steps 1-5 thirty times

7. Average the s to create (x-bar-bar)

8. Average the Rs to create (R-bar)

x

x

x

xxR


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Setting up control charts:

Calculating the limits

9. Find A2 on table (A2 times R estimates 3)

10. Use formula to find limits for x-bar chart:

11. Use formulas to find limits for R chart:

RAX 2

RDLCL 3 RDUCL 4


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Lets try a small problem

smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6

observation 1 7 11 6 7 10 10

observation 2 7 8 10 8 5 5


x-bar

R

X-bar chart R chart

UCL

Centerline

LCL


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Lets try a small problem

smpl 1 smpl 2 smpl 3 smpl 4 smpl 5 smpl 6 Avg.

observation 1 7 11 6 7 10 10



X-bar 7.3333 9.6667 9.3333 7.3333 7 7.6667 8.0556

R 1 3 6 1 5 5 3.5

X-bar chart R chart

UCL 11.6361 9.0125

Centerline 8.0556 3.5

LCL 4.4751 0


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X-bar chart

0.0000

2.0000

4.0000

6.0000

8.0000

10.0000

12.0000

14.0000

1 2 3 4 5 6

11.6361

8.0556

4.4751


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R chart

0

2

4

6

8

10

1 2 3 4 5 6

9.0125

3.5

0


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Interpreting charts

Observations outside control limitsindicate the process isprobablyout-of-

control Significant patterns in the observations

indicate the process isprobablyout-of-control

Random causes will on rare occasionsindicate the process is probably out-of-control when it actually is not


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Interpreting charts

In the excel spreadsheet, look for these

shifts:

A B

C D

Show real time examples of charts here
http://j/My%20Documents/class%20files/BUS%20453%20files/spc%20shift%20catcher%20worksheet.xlshttp://j/My%20Documents/class%20files/BUS%20453%20files/spc%20shift%20catcher%20worksheet.xls


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Lots of other charts exist

P chart C charts U charts Cusum & EWMA

For yes-no

questions likeis it defective?

(binomial data)

For counting

number defectswhere most items

have 1 defects

(eg. custom built

houses)

Average count

per unit (similarto C chart)

Advanced charts

V shaped orCurved controllimits (calculate

them by hiring a

statistician)

nppp )1(3

cc 3

n

uu 3


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Selecting rational samples

Chosen so that variation within the sample isconsidered to be from common causes

Special causes should only occur between

samples Special causes to avoid in sampling

passage of time

workers

shiftsmachines

Locations


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Chart advice

Larger samples are more accurate

Sample costs money, but so does being out-of-control

Dont convert measurement data to yes/no binomial

data (Xs to Ps) Not all out-of control points are bad

Dont combine data (or mix product)

Have out-of-control procedures (what do I do now?)

Actual production volume matters (Average Run Length)


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THANK YOU

e1Procedures Software House provides a full

range of consulting, public and in-house training in

international standards, regulatory requirements,and process improvement techniques which

maximizes performance and profitability for your

company

Contact us and we can help support yourorganizations implementation or transition or other

business process improvement activities

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visit to www.e1procedures.com