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Chapter 9

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Control Chart Decision Tree

Mea

sure

men

ts

Counts

Median, RangeAverage, Range

Average, sigma

Run chart

IX control chart

np control chart

p control chart

c chart

u chart

n = 2 to 9

n = 10 or more

n = 1non-normal data

normal data

n fixed

n varies

n fixed

n varies

Count pieces

or units

Count occurences

Var

iabl

es

Attributes

Mea

sure

men

ts

Counts

Median, RangeAverage, Range

Average, sigma

Run chart

IX control chart

np control chart

p control chart

c chart

u chart

n = 2 to 9

n = 10 or more

n = 1non-normal data

normal data

n fixed

n varies

n fixed

n varies

Count pieces

or units

Count occurences

Var

iabl

es

Attribu

Mea

sure

men

ts

Counts

Median, RangeAverage, Range

Average, sigma

Run chart

IX control chart

np control chart

p control chart

c chart

u chart

n = 2 to 9

n = 10 or more

n = 1non-normal data

normal data

n fixed

n varies

n fixed

n varies

Count pieces

or units

Count occurences

Var

iabl

es

Attributes

Defects

DefectivesDefectives

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An attribute data control chart Used to chart fraction defective

or proportion nonconforming data

The subgroup size can be fixed or it can vary

What is a p chart?

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Used to establish performance control of any process:◦ Pass / fail situations◦ Percent defective per sample◦ Good for any technical or

administrative process

How a p chart is used

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1. Select a process measurement2. Stabilize process and decrease

obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the

points8. Calculate the control limits and

analyze for control9. Calculate the capability and

analyze for capability10. Monitor the process11. Continuous Improvement

11 step procedure for control charts

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7. Chart the points◦ Sets scales for control chart◦ Calculate each subgroup’s

proportion nonconforming◦ Plot the proportion

nonconforming on the chart

8. Calculate control limits and analyze for control

◦ Plot your control limits

p chart control limits

n

pppUCLp

)1(3

n

pppLCLp

)1(3

n

npp

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9. Calculate the capability and analyze for capability

◦ Capability is based on average defective

◦ Is UCL or LCL within your goal value? If UCL > USL or LCL < LSL then

Cpk<1 If UCL < USL or LCL > LSL then

Cpk>1

p chart control limits

n

npp

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Data readily available Helps prioritize problem areas Easy to create with fixed and

variable subgroup sizes

Advantages of a p chart

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Counts failures - not prevention Cannot isolate causes of

process problems Variable control limits may be

confusing on variable subgroup sizes

Limits hard to construct on variable subgroup sizes

Disadvantages of a p chart

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This data represents the number of errors found in purchase orders over a 30 week period.

p Chart Example

1. Complete a p chart.

2. What can you tell from the data?

3. Complete a np chart.

4. What can you tell from the data?

5. How are these charts different?

# of P.O's ErrorsWeek 1 54 7Week 2 34 5Week 3 54 6Week 4 47 9Week 5 67 7Week 6 54 6Week 7 39 13Week 8 36 2Week 9 46 15Week 10 56 11Week 11 55 12Week 12 47 9Week 13 39 6Week 14 60 8Week 15 48 4Week 16 43 14Week 17 47 5Week 18 52 9Week 19 57 5Week 20 43 4Week 21 49 6Week 22 67 3Week 23 55 2Week 24 45 1Week 25 49 2Week 26 67 3Week 27 56 4Week 28 45 0Week 29 55 1Week 30 67 0

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p chart exercise notes

PAR

T #

FEA

TUR

E

ATT

RIB

UTE

CO

NTR

OL

CH

AR

T

Order # & DateO

PE

RA

TIO

N

CH

AR

T TY

PE

: P

(P

erce

nt D

efec

tive)

Sub

Gro

up #

Sam

ple

Siz

e

No.

of

Def

ectiv

es

Pro

port

ion

Def

ectiv

e

UC

L

LCL

Proportion Defective Units

.0.10

.20

.30

.40

.50

.60

110

98

76

54

32

1116

1514

1312

2322

2120

1918

1730

2928

2726

2524

3635

3433

3231

37