Control Charts

Using Minitab

Control charts display the process average (center) and process variability (spread). Process Average is the “expectation” and Process Variability indicates “risk” associated with the expectation.

2

Frequently Used Control Charts

Attribute: Go/no-go Information, sample size of 50 to 100

p-chart (Proportion Defectives)

c-chart (# Defects)

u-chart (Defects/Unit)

Variable: Continuous data, usually measured by the mean and standard deviation, sample size of 2 to 10– X-bar and R-charts– X-bar and s-charts– X-charts for individuals

3

Attribute Charts in Minitab

Stat / Control charts / Attribute Charts

4

p-Chart

Hour SampSizeNon-

conforming

1 75 17

2 75 18

3 75 18

4 75 16

5 75 20

6 75 22

7 75 24

8 75 19

9 75 15

10 75 22

11 75 19

12 75 24

13 75 12

14 75 22

15 75 20

16 75 20

SamplePro

port

ion

252321191715131197531

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

_P=0.2581

UCL=0.4097

LCL=0.1065

P Chart of Nonconforming

P charts are used to study the proportion of defectives in each sample. A “defective” is an attribute that makes something useless.

Data on non-conforming (defective) chips produced at a facility

5

c-Chart

Unit SqFt Blemishes

1 66 2

2 66 2

3 66 0

4 66 0

5 66 1

6 66 4

7 66 0

8 66 0

9 66 2

10 66 3Sample

Sam

ple

Count

464136312621161161

7

6

5

4

3

2

1

0

_C=2.2

UCL=6.650

LCL=0

1

C Chart of Blemishes

C charts are used to display the number of defects in each sample. A defect is a flaw that is undesirable but does not make the product useless.

Data are number of blemishes in 66sqft of painted area

6

U-Chart

Sample

Sam

ple

Count

Per

Unit

464136312621161161

0.12

0.10

0.08

0.06

0.04

0.02

0.00

_U=0.0357

UCL=0.1017

LCL=0

1

U Chart of Blemishes

Tests performed with unequal sample sizes

Unit SqFt Blemishes Rate

1 73 5 0.0685

2 70 4 0.0571

3 60 1 0.0167

4 57 1 0.0175

5 58 0 0.0000

6 57 3 0.0526

7 59 1 0.0169

8 52 4 0.0769

9 55 1 0.0182

10 59 2 0.0339

11 67 0 0.0000

12 55 2 0.0364

13 54 1 0.0185

U charts are used to display the number of defects per unit of measurement. Useful when samples are of different sizes.

Data are number of blemishes in different areas

7

Variable Charts in Minitab

Stat / Control charts / Variable Charts for Subgroups or Individuals

8

XBar-R Charts

Sample Obs1 Obs2 Obs3 Obs4 Obs5

1 11.991 12.001 12.176 12.004 12.030

2 12.065 12.018 12.223 11.955 11.959

3 11.946 11.980 12.089 12.125 12.111

4 12.011 12.069 12.065 12.155 12.197

5 11.783 12.140 12.008 12.076 12.044

6 11.962 12.132 12.149 11.991 12.128

7 12.163 11.961 11.932 12.115 11.870

8 12.053 12.053 11.889 11.975 12.037

9 12.108 11.942 12.102 11.967 12.056

Sample

Sam

ple

Mean

645750433629221581

12.2

12.1

12.0

11.9

__X=12.0457

UCL=12.1832

LCL=11.9082

Sample

Sam

ple

Range

645750433629221581

0.48

0.36

0.24

0.12

0.00

_R=0.2384

UCL=0.5041

LCL=0

Xbar-R Chart of Obs1, ..., Obs5

X-Bar charts are used to plot subgroup means.

R charts are used to plot the range for each subgroup. Data represents actual contents in 12 oz soda cans

9

XBar-S Charts

Sample Obs1 Obs2 Obs3 Obs4 Obs5

1 11.991 12.001 12.176 12.004 12.030

2 12.065 12.018 12.223 11.955 11.959

3 11.946 11.980 12.089 12.125 12.111

4 12.011 12.069 12.065 12.155 12.197

5 11.783 12.140 12.008 12.076 12.044

6 11.962 12.132 12.149 11.991 12.128

7 12.163 11.961 11.932 12.115 11.870

8 12.053 12.053 11.889 11.975 12.037

9 12.108 11.942 12.102 11.967 12.056

Sample

Sam

ple

Mean

645750433629221581

12.2

12.1

12.0

11.9

__X=12.0457

UCL=12.1832

LCL=11.9082

Sample

Sam

ple

StD

ev

645750433629221581

0.20

0.15

0.10

0.05

0.00

_S=0.0963

UCL=0.2013

LCL=0

Xbar-S Chart of Obs1, ..., Obs5

X-Bar charts are used to plot subgroup means.

S charts are used to plot the standard deviation of each subgroup.

10

Is the Process in Control?

Sample

Sa

mp

le M

ea

n

645750433629221581

12.2

12.1

12.0

11.9

__X=12.0457

UCL=12.1832

LCL=11.9082

Sample

Sa

mp

le S

tDe

v

645750433629221581

0.20

0.15

0.10

0.05

0.00

_S=0.0963

UCL=0.2013

LCL=0

Xbar-S Chart of Obs1, ..., Obs5

Observation

Ind

ivid

ua

l V

alu

e

31628124621117614110671361

12.4

12.3

12.2

12.1

12.0

11.9

11.8

11.7

_X=12.0457

UB=12.2

LB=11.9

1

I Chart of SodaCans

XBar-S Chart X (individual) Chart

11

Process Capability

12.312.212.112.011.911.8

LSL USL

Process Data

Sample N 350StDev(Within) 0.102501StDev(Overall) 0.103528

LSL 11.9Target *USL 12.2Sample Mean 12.0457

Potential (Within) Capability

Overall Capability

Pp 0.48PPL 0.47PPU 0.50Ppk 0.47Cpm

Cp

*

0.49CPL 0.47CPU 0.50Cpk 0.47

Observed PerformancePPM < LSL 74285.71PPM > USL 77142.86PPM Total 151428.57

Exp. Within PerformancePPM < LSL 77567.86PPM > USL 66137.55PPM Total 143705.41

Exp. Overall PerformancePPM < LSL 79636.68PPM > USL 68078.20PPM Total 147714.88

WithinOverall

Process Capability of SodaCans

Process capability refers to the ability of a process to produce a defect-free product or service in a controlled manner of production or service environment