variables control charts for subgroups (x-r & x- s charts)

Variables Control ChartsVariables Control Chartsfor Subgroupsfor Subgroups

(X-R & X-(X-R & X-ss Charts) Charts)

2

Basic SPC

What is “SPC”?What is “SPC”?

You Think You Know ... You Think You Know ...But Do You Really?But Do You Really?

3

Basic SPC

Enough of Teasing ..Enough of Teasing ..

Let’s start to undo the Let’s start to undo the confusion.confusion.

X =X

n

Distribution of Sampling Averages

XX

4

Basic SPC

VariabilityVariability The Devil is in the Deviations. No two things

can ever be made exactly alike, just like no two things are alike in nature.

Variation cannot be avoided in life! Every process has variation. Every measurement. Every sample!

LSL USLT

Time 1

Time 2

Time 3

Time 4

5

Basic SPC

Sources of VariationSources of Variation Variability can come about due to changes in:

Material quality

Machine settings or conditions

Manpower standards

Methods of processing

Measurement

Environment

6

Basic SPC

Types of VariationTypes of Variation

One way of classifying variation is:

within unit (positional variation)

between units (unit-unit variation)

between lots (lot-lot variation)

between lines (line-line variation)

across time (time-time variation)

measurement (gage repeatability & reproducibility)

7

Basic SPC

Quality and VariabilityQuality and Variability

yVariabilit

1Quality

Quality is fitness for use

What is “Quality”?

8

Basic SPC

Product ControlProduct Control Model for Model for Quality ControlQuality Control

Raw Material, Components & Sub-Assemblies

Process

Product

InspectionPass

Ship

Fail

Rework Scrap

ShipRecycle Disposal

9

Basic SPC

Process ControlProcess Control Model for Model for Quality ControlQuality Control

Raw Material, Components & Sub-Assemblies

Process

Product

Observation: Data Collection

Evaluation: Data Analysis

Diagnosis: Fault Discovery

Decision: Formulate Action

Implementation: Take Action

Uncontrollable Inputs

Controllable Inputs

10

Basic SPC

Statistical Process ControlStatistical Process Control The process control model shifts focus to the

home front, i.e. the manufacturing process, taking a preventive instead of reactive mode.

It also has something which the old concept of product control lacked - statistics. This allows use of samples to understand the entire process.

The new emphasis had to have a name - Statistical Process Control (SPC).

We owe the application of statistics as a tool for manufacturing to Dr Walter A. Shewhart.

11

Basic SPC

Dr Walter A. ShewhartDr Walter A. ShewhartFather of Control ChartsFather of Control Charts

Physicist at Bell Telephone Labs., specializing in the Brownian movement.

Asked to help in the war effort to design standard radio headset for army troops.

Developed important descriptive statisticsto aid in manufacturing, the most important of which was the X-R chart (invented in 1924).

Presented to the outside world in a series of lectures at Stevens Institute of Technology. The lecture material became his well-known book, Economic Control of Quality of Manufactured Product (1931).

12

Basic SPC

Success in ManufacturingSuccess in Manufacturing

The key to success in manufacturing is an effective SPC program that continuously finds and eliminates problems.

Central to an SPC program are the following:

Understand the causes of variability: Shewhart found two basic causes of variability:

Chance causes of variabilityAssignable causes of variability

Develop methods of recognizing these causes: SPC charts

13

Basic SPC

Introduction to SPC ChartsIntroduction to SPC Charts

Concepts and Principles of Control Charts

Let’s dive into them now ...

14

Basic SPC

Two Basic Causes of Two Basic Causes of VariabilityVariability

Chance Causes of Variation

Due to the cumulative effect of many small unavoidable sources of variation.

Also known as: common variation random variation inherent variation natural variation

A process operating with only chance causes of variation present is said to be “in statistical control”.

15

Basic SPC

Two Basic Causes of Two Basic Causes of VariabilityVariability

Assignable (or Special) Causes of Variation

Variation in a process that is different from from chance variation; disturbs a process so that what it produces seems unnatural.

Examples of such causes of variation are: improperly adjusted machine excessive tool wear defective raw material

A process operating in the presenceof assignable causes of variation issaid to be “out-of-control”.

16

Basic SPC

Objectives of SPC ChartsObjectives of SPC Charts All control charts have one primary purpose!

To detect assignable causes of variationthat cause significant process shift, so that:

investigation and corrective action may be undertaken to rid the process of the assignable causes of variation before too many non-conforming units are produced.

in other words, to keep the process in statistical control.

17

Basic SPC

Objectives of SPC ChartsObjectives of SPC Charts The following are secondary objectives or

direct benefits of the primary objective:

To reduce variability in a process.

To help estimate the parameters of a process and establish its process capability.

18

Basic SPC

Graphical comparison of a quality characteristic against computed control limits.

Usually, its sample statistic is plotted over time. Sometimes, the actual value of the quality characteristic is plotted.

Lower Control Limit

Upper Control Limit

Center Line

Sample Number or TimeSam

ple

Qua

lity

Cha

ract

eris

tic

Each point is usually a sample statistic (such as subgroup average) of the

quality characteristic

General Form of SPC ChartsGeneral Form of SPC Charts

19

Basic SPC

Control charts plot variation over time.

Control limits, Upper Control Limit (UCL) and Lower Control Limit (LCL), help us distinguish between the two basic causes of variability.

Lower Control Limit

Upper Control Limit

Center Line

Sample Number or Time

Sam

ple

Qua

lity

Cha

ract

eris

tic


Center Line represents mean operating level of

process

UCL & LCL are vital guidelines for deciding when

action should be taken in a process

20

Basic SPC

A point outside of UCL or LCL is evidence that process is out of control: Investigation and corrective action are required to

eliminate the assignable cause(s). Assignable cause(s) may be measuring error, plotting

error, special variation from some process input, etc.

Lower Control Limit

Upper Control Limit

Center Line


Sam

ple

Qua

lity

Cha

ract

eris

tic


Out-of-control signal: Investigate assignable cause(s).

21

Basic SPC

Process Control vs Process Control vs Process Capability Process Capability

At this juncture, let’s distinguish between process control and

process capability ...

22

Basic SPC

Process ControlProcess Control

Means that chance causes are the only source of variation present.

Refers to “voice of the process”, i.e. we only need data from the process to determine if a process is in control.

Quality characteristic is monitored to verify if it forms a stable distribution over time, with control limits computed from the process data only.

Just because a process is in control does not necessarily mean it is a capable process.

23

Basic SPC

The “goodness” of a process is measured by its process capability.

Compares “voice of the process” with “voice of the customer”, which is given in terms of customer specs. or requirements.

Measures how well a stable distribution (process in control) meets customer requirements by the proportion of products within or out of customer specs.

Process CapabilityProcess Capability

Usl-lsl

24

Basic SPC

Control Limits vs Spec. LimitsControl Limits vs Spec. Limits

Specification Limits (USL , LSL) determined by design considerations represent the tolerable limits of individual

values of a product usually external to variability of the process

Control Limits (UCL , LCL) base on data derived based on variability of the process usually apply to sample statistics such as

subgroup average or range, rather than individual values

25

Basic SPC

Shewhart Control Charts - OverviewShewhart Control Charts - Overview

26

Basic SPC

Shewhart control charts are characterized by having control limits set at k distance from process mean. A usual value of k is 3, giving:

Upper Control Limit = w + 3w

Center Line = w

Lower Control Limit = w – 3w

Whether the data is variable or attribute, Shewhart control charts plot the sample statistic of the quality characteristic of interest.

Shewhart Control Charts - OverviewShewhart Control Charts - Overview

27

Basic SPC

Shewhart Variables Control Shewhart Variables Control Charts for SubgroupsCharts for Subgroups

28

Basic SPC

Introduction to Introduction to X-R ChartsX-R Charts

29

Basic SPC

Central Limit Theorem and Normal Central Limit Theorem and Normal DistributionDistribution

Shewhart variables control charts for subgroups work because of two important principles:

Central Limit Theorem Normal Distribution

Shewhart found that when the averages of subgroups from a constant-cause system are plotted in the form of a histogram, the normal distribution appears.

30

Basic SPC


The constant-cause system does not itself have to be normally distributed. It can be skewed, rectangular or even inverted pyramid.

As long as the sample size is adequately large, the averages of the subgroups will show a central tendency and variation that tend to follow the normal curve.

This is called the Central Limit Theorem.

31

Basic SPC


This discovery means that a process can be monitored over time by measuring the averages of a subgroup of parts (basis for X-chart).

If the process is a constant-cause system, these averages would fall within a normal curve. The variability is entirely due to common causes.

When assignable causes appear, they will affect the averages to the point where these averages will probably not fit within the normal curve.

32

Basic SPC


Important Information from Central Limit Theorem:

If k observations of sample size n are taken, the distribution of x1, x2, … , xk will approximate a normal distribution N(x,x) distribution, with

n

k

x

xx

x

k

1ii

x

33

Basic SPC

Construction of X-R ChartsConstruction of X-R Charts

The X-R chart is the most versatile of control charts, and is used in most applications.

Charting of averages and charting of ranges are used to check if a constant-cause system exists.

2010Subgroup 0

74.015

74.005

73.995

73.985

Sam

ple

Mea

n

X=74.00

3.0SL=74.01

-3.0SL=73.99

0.05

0.04

0.03

0.02

0.01

0.00

Sam

ple

Ran

ge

R=0.02235

3.0SL=0.04726

-3.0SL=0.000

X-bar-R Charts X-chart measures variability between

samples

R-chart measures variability within

samples

R Always screw

34

Basic SPC

The control limits are the estimated +/-3 sigma limits for the process.

Tables of constants were developed to make the sigma calculations simple and to reduce error.

2010Subgroup 0

74.015

74.005

73.995

73.985

Sam

ple

Mea

n

X=74.00

3.0SL=74.01

-3.0SL=73.99

0.05

0.04

0.03

0.02

0.01

0.00

Sam

ple

Ran

ge

R=0.02235

3.0SL=0.04726

-3.0SL=0.000

X-bar-R Charts


35

Basic SPC

The Center Line and Control Limits of a X-chart:

The Center Line and Control Limits of a R-chart:

XX2

X

XX2

3RAXLCL

XLineCenter

3RAXUCL

R3

R4

3RRDLCL

RLineCenter

3RRDUCL


36

Basic SPC

n A2 A3 d2 c4 B3 B4 D3 D4

2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267

3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575

4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282

5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115

6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004

7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924

8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864

9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816

10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777

11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744

12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717

13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693

14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672

15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653

16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637

17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622

18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608

19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597

20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585

21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575

22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566

23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557

24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548

25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541

For sample size n > 10, R loses its efficiency in

estimating process sigma and R-chart may not be

appropriate.


Shewhart Constants

37

Basic SPC

Control Charts – Sampling RisksControl Charts – Sampling Risks

Since the control limits are the +/-3 sigma limits for the process, the interval between the limits cover 99.73% of the normal distribution.

Output43210-1-2-3-4

0.4

0.3

0.2

0.1

0.0

Normal Curve and Probability Areas

68%

95%

99.73%

38

Basic SPC


If there is no change in the process, there is still a chance of getting a point out of the 3 control limits. What is the implication?

3

3

99.73%

Lower Control Limit

Center Line

Upper Control Limit

What does each area of 0.135%

mean?

0.135%

0.135%

39

Basic SPC

Control Charts – Sampling RisksControl Charts – Sampling RisksType I Error = reject good lot = over reject Concluding that the process is out of control when it is

really in control

= probability of making Type I error = commonly known as the producer’s risk = total of 0.27% for control limits of +/- 3

Lower Control Limit

Upper Control Limit

Center Line


0.135%

0.135%

Is process really out of control? Or is the

point outside due to random variation?

40

Basic SPC


Type I Error and Tampering

If the process is really in control, and process adjustment is made because of Type I error, it is called tampering with the process.

Tampering has been shown to actually increase the variability of the process!

41

Basic SPC

Control Charts – Sampling RisksControl Charts – Sampling RisksType II Error = accept fail lot Concluding that the process is in control when it is really

out of control

= probability of making Type II error = commonly known as the consumer’s risk

Lower Control Limit

Upper Control Limit

Center Line


0.135%

0.135%

Is process really in control? Or is the point inside due to

random variation of the shifted process?

Shifted Process

42

Basic SPC


The control chart is a test of the hypothesis that the process is in statistical control.

Lower Control Limit

Upper Control Limit

Center Line


Sam

ple

Qua

lity

Cha

ract

eris

tic Out-of-control signal Reject H0:- Process has shifted- Assignable causes present

In-control signalAccept H0:- Process remains unchanged- No assignable causes present

43

Basic SPC

Control Limits & Sampling RisksControl Limits & Sampling Risks

By moving the control limits further from the center line, the risk of a Type I error is reduced.

However, widening the control limits will increase the risk of a Type II error.

For a given Type I error (control limits interval), the risk of a Type II error canbe reduced by increasing the sample size.

44

Basic SPC

Let’s try an example of

X-R chart

45

Basic SPC

Example 1: X-R ChartExample 1: X-R ChartS/N X1 X2 X3 X4 X5 1 74.030 74.002 74.019 73.992 74.008 2 73.995 73.992 74.001 74.011 74.004 3 73.988 74.024 74.021 74.005 74.002 4 74.002 73.996 73.993 74.015 74.009 5 73.992 74.007 74.015 73.989 74.014 6 74.009 73.994 73.997 73.985 73.993 7 73.995 74.006 73.994 74.000 74.005 8 73.985 74.003 73.993 74.015 73.998 9 74.008 73.995 74.009 74.005 74.00410 73.998 74.000 73.990 74.007 73.99511 73.994 73.998 73.994 73.995 73.99012 74.004 74.000 74.007 74.000 73.99613 73.983 74.002 73.998 73.997 74.01214 74.006 73.967 73.994 74.000 73.98415 74.012 74.014 73.998 73.999 74.00716 74.000 73.984 74.005 73.998 73.99617 73.994 74.012 73.986 74.005 74.00718 74.006 74.010 74.018 74.003 74.00019 73.984 74.002 74.003 74.005 73.99720 74.000 74.010 74.013 74.020 74.003

Piston rings for an automotive engine are forged. 20 preliminary samples, each of size 5, were obtained. The inside diameter of these rings are shown here.

Verify if the forging process is in statistical control.

The data are found inSPC Charts.MTW.

46

Basic SPC

MiniTab:Stat Control Charts Xbar-R

Example 1: X-R ChartExample 1: X-R Chart

47

Basic SPC

Example 1: X-R ChartExample 1: X-R Chart

2010Subgroup 0

74.015

74.005

73.995

73.985

Sa

mp

le M

ea

n

Mean=74.00

UCL=74.01

LCL=73.99

0.05

0.04

0.03

0.02

0.01

0.00

Sa

mp

le R

ang

e

R=0.02235

UCL=0.04726

LCL=0

Xbar/R Chart for Inside Diameter of Piston Ring Is process in control?

Why are the 2 distances different in

value?

48

Basic SPC

The X-R chart must be interpreted together as well as separately.

Read the R-chart first to determine if it is in control, i.e. no points out of the control limits or non-random pattern (to be discussed later).

The R-chart is more sensitive to changes in uniformity or consistency. Anything that introduces changes to the process variability, such as poor material or lack of maintenance, will affect the R-chart.

Interpreting X-R Chart Together Interpreting X-R Chart Together

49

Basic SPC

Some assignable causes show up on both the X and R charts. Work on the R-chart first.

Never attempt to interpret the X-chart when the R-chart indicates an out-of-control condition, i.e. when the within-subgroup variability is not stable.

Interpreting X-R Chart Together Interpreting X-R Chart Together

Why?

50

Basic SPC

BREAK

51

Basic SPC

The initial trial control limits should be treated as subject to possible subsequent revision. The control chart should always reflect accurately the present conditions of the process.

A sustained change in the level of either chart, usually for at least 20 points, may call for revision of the control limits to recognize the permanent change.

Some practitioners establish regular periods for review of the control limits, such as every week, month, or every 50 samples, etc.

Revising Control Limits and Revising Control Limits and Center Lines Center Lines

52

Basic SPC

Some users will replace the center line of the X-chart with a target value, such as nominal spec.: If the process mean can be easily adjusted by

manipulating some process inputs, it may be helpful to shift the process mean to the desired value.

If the mean is not easily influenced by a simple process adjustment, such as flatness of a machined part, forcing a target value can result in many points out of the control limits.

Revising Control Limits and Revising Control Limits and Center Lines Center Lines

What about changing the sample size? revise control limit

53

Basic SPC

Indicators of InstabilityIndicators of Instability

Primary Indicators any point outside of a control limit

Secondary Indicators any non-random pattern of points on a control chart

– shift or run– trend– stratification– mixture– periodicity

54

Basic SPC

Primary Indicators of InstabilityPrimary Indicators of Instability

Any point outside a control limit 1 point beyond ±3 limits

Lower Control Limit

Upper Control Limit

Center Line


ple

Qua

lity

Cha

ract

eris

tic

55

Basic SPC

Common Causes

new workers, methods, raw materials or machines

change in inspection methods or standards

change in skill and/or motivation of operators

Primary Indicators of InstabilityPrimary Indicators of Instability

56

Basic SPC

Secondary Indicators of InstabilitySecondary Indicators of InstabilityShift or Run k consecutive points (usually 7, 8 or 9) on the same

side of the center line

4 out of 5 consecutive points beyond 1 (same side)

2 out of 3 consecutive points beyond 2 (same side)

Upper Control Limit

Center Line


ple

Qua

lity

Cha

ract

eris

tic

Lower Control Limit

+ 2+ 1

- 2- 1

57

Basic SPC

Common Causes of “Shift” or “Run”




Secondary Indicators of InstabilitySecondary Indicators of Instability

58

Basic SPC

Trend k consecutive points (usually 5, 6 or 7) moving

in the same direction

Upper Control Limit

Center Line


ple

Qua

lity

Cha

ract

eris

tic

Lower Control Limit

+ 2+ 1

- 2- 1


59

Basic SPC

Common Causes of “Trend”





60

Basic SPC

Stratification points “hugging” the center line, usually within

±1 limits

Upper Control Limit

Center Line


ple

Qua

lity

Cha

ract

eris

tic

Lower Control Limit

+ 2+ 1

- 2- 1


61

Basic SPC

Common Causes of “Stratification”

incorrect calculation of control limits

sampling process collects one or more units from different underlying distributions within each subgroup


Can irrational subgrouping be a cause

of stratification?

62

Basic SPC

Mixture points “hugging” the control limits

Upper Control Limit

Center Line


Sam

ple

Qua

lity

Cha

ract

eris

tic

Lower Control Limit

+ 2+ 1

- 2- 1


63

Basic SPC

Common Causes of “Mixture”

two (or more) overlapping distributions

over-control by operators


64

Basic SPC

Cycle or Periodicity any ongoing, repeating pattern

Upper Control Limit

Center Line


Sam

ple

Qua

lity

Cha

ract

eris

tic

Lower Control Limit

+ 2+ 1

- 2- 1


65

Basic SPC

Common Causes of “Cycle” or “Periodicity”

systematic environmental changes– temperature– operator fatigue– rotation of operators– fluctuation in machine settings

maintenance schedules

tool wear


66

Basic SPC

MiniTab’s Tests for InstabilityMiniTab’s Tests for Instability

Secondary Indicators

Primary Indicator

67

Basic SPC

Shift / Run

Shift / RunShift / Run

Trend

Stratification

Cycle

Mixture

MiniTab’s Tests for InstabilityMiniTab’s Tests for Instability

68

Basic SPC

Tests for InstabilityTests for Instability

CAUTION :CAUTION : Do not apply “tests” blindly

Not every “test” is relevant for all charts

Excessive number of “tests” Increased -error

Nature of application

69

Basic SPC

Relevance of Shut-Down RulesRelevance of Shut-Down Rules

Suitable for all charts

Suitable only for X-Chart

_

70

Basic SPC

X-S ChartsX-S Charts

The Center Line and Control Limits of a X Chart are

The Center Line and Control Limits of a S Chart are

S3

S4

3SSBLCL

SLineCenter

3SSBUCL

_

XX3

X

XX3

σ3μSAXLCL

μXLineCenter

σ3μSAXUCL

_

71

Basic SPC

Shewhart ConstantsShewhart Constantsn A2 A3 d2 c4 B3 B4 D3 D4

2 1.880 2.659 1.128 0.7979 0 3.267 0 3.267

3 1.023 1.954 1.693 0.8862 0 2.568 0 2.575

4 0.729 1.628 2.059 0.9213 0 2.266 0 2.282

5 0.577 1.427 2.326 0.9400 0 2.089 0 2.115

6 0.483 1.287 2.534 0.9515 0.030 1.970 0 2.004

7 0.419 1.182 2.704 0.9594 0.118 1.882 0.076 1.924

8 0.373 1.099 2.847 0.9650 0.185 1.815 0.136 1.864

9 0.337 1.032 2.970 0.9693 0.239 1.761 0.184 1.816

10 0.308 0.975 3.078 0.9727 0.284 1.716 0.223 1.777

11 0.285 0.927 3.173 0.9754 0.321 1.679 0.256 1.744

12 0.266 0.886 3.258 0.9776 0.354 1.646 0.283 1.717

13 0.249 0.850 3.336 0.9794 0.382 1.618 0.307 1.693

14 0.235 0.817 3.407 0.9810 0.406 1.594 0.328 1.672

15 0.223 0.789 3.472 0.9823 0.428 1.572 0.347 1.653

16 0.212 0.763 3.532 0.9835 0.448 1.552 0.363 1.637

17 0.203 0.739 3.588 0.9845 0.466 1.534 0.378 1.622

18 0.194 0.718 3.640 0.9854 0.482 1.518 0.391 1.608

19 0.187 0.698 3.689 0.9862 0.497 1.503 0.403 1.597

20 0.180 0.680 3.735 0.0969 0.510 1.490 0.415 1.585

21 0.173 0.663 3.778 0.9876 0.523 1.477 0.425 1.575

22 0.167 0.647 3.819 0.9882 0.534 1.466 0.434 1.566

23 0.162 0.633 3.858 0.9887 0.545 1.455 0.443 1.557

24 0.157 0.619 3.895 0.9892 0.555 1.445 0.451 1.548

25 0.153 0.606 3.931 0.9896 0.565 1.435 0.459 1.541

1n2c

31B

1n2c

31B

3n4

1n4c

nc

3A

4

4

4

3

4

4

3

For n > 25

72

Basic SPC

Example 2Example 2MiniTab’s Stat Control Charts Xbar-S

73

Basic SPC

R Chart vs S ChartR Chart vs S ChartFor ease of computation, the R Chart is preferred

The S Chart may be used when n is not constant

For large sample size (n 10), the range loses its efficiency as an estimator of

Larger sample size is required when– lower sampling risks are required– greater drift sensitivity is required– quality characteristic is non-normal

Historical Note: When Shewhart developed thest charts in the 1920’s, there was no easy way to calculate the standard deviation. Thus, the range approach became ingrained in SPC application.

74

Basic SPC

Using SPCUsing SPC Place charts only where necessary based on

project scope

Remove charts that are not value-added

Initially, the process outputs may need to be monitored

Goal: Monitor and control process inputs and, over time, eliminate the need for SPC charts

75

Basic SPC

Where to Use SPC ChartsWhere to Use SPC Charts When a mistake-proofing device is not feasible

Identify processes with high RPNs from FMEA

Evaluate the “Current Controls” column to determine “gaps” in the control plan. Does SPC make sense?

Identify critical variables based on DOE

Customer requirements

Management commitments

8

9

10

11

12

13

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

76

Basic SPC

Updating Control LimitsUpdating Control Limits

Control Limits should be updated when: Change in supplier for a critical material Change in process machinery Engineering change orders that affect process

flow Introduction of new operators Change in sample size

77

Basic SPC

Implementing the Control ChartImplementing the Control Chart

1) Preparation of Sampling

2) Data Collection

3) Construct the Control Chart

4) Analysis & Interpretation

5) Use the Control Chart as a Process Monitoring Tool

78

Basic SPC

Preparation of Sampling Choose the quality characteristic to be

measured– measurements taken on the final product– measurements taken on the in-process

product– measurements taken on the process

variables Determine the basis, size and frequency


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Basic SPC

Data Collection Record the data Calculate the relevant statistics: mean, range,

proportion, etc


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Basic SPC

Construct the Control Chart Calculate the trial center line and the trial control

limits Plot the trial center line and the trial control limits Plot the data collected on the chart


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Basic SPC

Analysis & Interpretation: Investigate the chart for lack of control Eliminate out-of-control points if required Recompute control limits if necessary Determine process capability


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Basic SPC

Use the Control Chart as a Process Monitoring Tool

Continue data collection and plotting

Identify out-of-control situations and take

correction action

If a permanent process shift has occurred,

recalculate the new center line and control limits


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Basic SPC

Review Data

Compute Trial Limits

Review Control Charts

Out-Of-ControlPoints?

Compute Production Limits

Real-Time Process Monitoring

ReviseControl Limits?

Yes

No

AssignableCause?

Censor Data?

No

No

Compute Trial LimitsYes

Yes

No

Yes


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Basic SPC

Adequate Discrimination

Inadequate Discrimination


Measurement Variation Affects the Control Chart!

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Basic SPC

Statistical Process ControlStatistical Process Control

A state of statistical control is not a natural state for a manufacturing process. It is an achievement, arrived at by elimination one by one, by determined effort, of special causes of excessive variation.

There is no process capability and no meaningful

specifications, except in statistical control.

- William Edwards Deming

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Basic SPC

End of TopicEnd of TopicWhat question do you have?

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Basic SPC

Reading ReferenceReading Reference

Introduction to Statistical Quality Control,

Douglas C. Montgomery, John Wiley & Sons,

ISBN 0-471-30353-4

variables control charts for subgroups (x-r & x- s charts)

Documents

basic spcquality

basic spcintroduction

basic spcsuccess

basic spcwhat

basic spcproduct control

statistical control

basic spcdr walter

manufacturing process