Chapter 15 Statistical Process Control

Chapter 15 Statistical Process Control

Statistical Process Control is used to prevent quality problems

MGS3100 Julie Liggett De Jong

Statistical Process Control ….

Take periodic samples from process

How it works.

1

Take periodic samples from process

Take periodic samples from process

Plot sample points on control chart

Plot sample points on control chart

Determine if process is within limits

Determine if process is within acceptable limits

Variation

1 Common Causes 1. 9 Variation inherent in a process 9 Eliminated through system improvements

Variation

2 Special Causes 2. 9 Variation due to identifiable factors 9 Modified through operator or management action

2

Attribute measures

Attribute measures

Product characteristic evaluated with a discrete choice: Good / bad Yes / No Pass / Fail

Product characteristics evaluated with a discrete choice: Good / bad Yes / No Pass / Fail

Attribute measures Product characteristics evaluated with a discrete choice: Good / bad Yes / No Pass / Fail

Variable measures Measurable product characteristic: Length, size Length size, weight, weight height, time, velocity

3

Variable measures

Variable measures

Measurable product characteristics:

Measurable product characteristics

Length, size Length size, weight, weight height, time, velocity

Length, size Length size, weight, weight height, time, velocity

Hospitals Timeliness

SPC Applied to Services

Responsiveness Accuracy of lab tests

4

Grocery Stores Check-out time Stocking Cleanliness

Airlines

Fast Food Restaurants

Internet Orders

Waiting times

Order accuracy Packaging Delivery time Email confirmation Package tracking

Food quality Cleanliness

Luggage handling Waiting times Courtesy

5

Insurance Billing accuracy Timeliness of claims processing Agent g availability y

Control Charts

Response time

Graphs that establish process control limits

Attribute measures: P-Charts C-Charts

6

Variable measures: Mean (x-bar) control charts Range (R) control charts

A Process is in control if:

A Process is in control if:

A Process is in control if:

No sample points are outside control limits

Most points are near process average

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A Process is in control if:

A Process is in control if:

About equal number of points are above & below centerline

Points appear to be randomly distributed

Process Control Chart

To develop Control Charts: Out of control

Upper control li it limit

9Use in-control data 9If non-random causes are present, find them and discard data related to them

Process average

9Correct control chart limits

Lower control limit

1

2

3

4

5

6

7

8

9

10

Sample number Figure 15.1

8

Control Charts Control Charts

Measures

p Chart

Attributes

Calculates percent defectives in sample p

r Chart (range chart) x bar Chart (mean chart)

Variables

Reflects the amount of dispersion in a sample

Variables

Indicates how sample results relate to the process average

Process Capability

Measures the capability p y of a process to meet design specifications

Process Capability

Indicates if the process mean has shifted away from design target

Cp (Process Capability Ratio) Cpk (Process Capability Index)

Control Charts

Description

p-Chart

p = the sample proportion defective; an estimate of the process average

Measures

p Chart

Attributes

Calculates percent defectives in sample p

r Chart (range chart) x bar Chart (mean chart)

Variables

Reflects the amount of dispersion in a sample

Variables

Indicates how sample results relate to the process average

Process Capability

Measures the capability p y of a process to meet design specifications

Process Capability

Indicates if the process mean has shifted away from design target

Cp (Process Capability Ratio) Cpk (Process Capability Index)

Description

p-Chart

UCL = p + zσp LCL = p - zσp where

Control Charts

UCL = p + zσp LCL = p - zσp where p = the sample proportion defective; an estimate of the process average

p=

total defectives total sample observations

9

p-Chart

The Normal Distribution

UCL = p + zσp LCL = p - zσp where p = the sample proportion defective; an estimate of the process average z = the number of standard deviations from the process average

95% 99.74% -3σ

-2σ

-1σ

μ=0

1σ

2σ

3σ

p-Chart

Control Chart Z Values 9 Smaller Z values make more narrow control limits and more sensitive charts 9 Z = 3.00 is standard 9 Compromise between sensitivity and errors

UCL = p + zσp LCL = p - zσp where p = the sample proportion defective; an estimate of the process average z = the number of standard deviations from the process average σp = the standard deviation of the sample proportion

95% 99.74% -3σ

-2σ

-1σ

μ=0

1σ

2σ

3σ

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p-Chart UCL = p + zσp LCL = p - zσp

σp =

p(1 - p) n

total defectives p = total sample observations

p-Chart Example ~ Western Jeans Company p337

p-Chart Example ~ Western Jeans Company

p-Chart Example ~ Western Jeans Company

0.20

20 samples of 100 pairs of jeans (n = 100) SAMPLE

NUMBER OF DEFECTIVES

PROPORTION DEFECTIVE

6 0 4 : : 18 200

.06 .00 .04 : : .18

UCL = 0.190

0.18 0 16 0.16

Proportion defective P

0.14

1 2 3 : : 20

0.12 0.10

p = 0.10

0.08 0.06 0.04 0.02

LCL = 0.010

2

Ex 1, P337

4

6

8 10 Sample number

12

14

16

18

20

Ex 1, P337

11

Control Charts

Range ( R ) Chart

Control Charts

Measures

Description

p Chart

Attributes

Calculates percent defectives in sample

r Chart (range chart)

Variables

Reflects the amount of dispersion in a sample

x bar Chart (mean chart)

Variables

Indicates how sample results relate to the process average

Cp (Process Capability Ratio) Cpk (Process Capability Index)

Process Capability

Measures the capability y of a process to meet design specifications

Process Capability

Indicates if the process mean has shifted away from design target

UCL = D4R R=

LCL = D3R ∑R k

where: R = range of each sample k = number of samples

Factors for R-Chart: D3 & D4 SAMPLE SIZE n

FACTOR FOR x-CHART A2

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.88 1.02 0 73 0.73 0.58 0.48 0.42 0.37 0.44 0.11 0.99 0.77 0.55 0.44 0.22 0.11 0.00 0.99 0.99 0.88

FACTORS FOR R-CHART D3 D4 0.00 0.00 0 00 0.00 0.00 0.00 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 0.38 0.39 0.40 0.41

3.27 2.57 2 28 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.61 1.59 Table 1, P343

R-Chart Example ~ Goliath Tool Company (p345)

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R-Chart Example ~ Goliath Tool Company OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k 1 2 3 4 R 5 6 7 8 9 10

=

1 5.02 5.01 4.99 max5.03 – 4.95 4.97 5.05 5.09 5.14 5.01

2

3

5.01 5.03 5.00 4.91 min 4.92 5.06 5.01 5.10 5.10 4.98

4

5

x

4.94 4.99 4.96 5.07 4.95 4.96 4.93 4.92 4.99 4.89 = 5.01 5.024.98 – 4.94 = 5.03 5.05 5.01 5.06 4.96 5.03 5.10 4.96 4.99 5.00 4.99 5.08 4.99 5.08 5.09 5.08 5.07 4.99 total

R

4.98 5.00 4.97 4.96 0.08 4.99 5.01 5.02 5.05 5.08 5.03

0.08 0.12 0.08 0.14 0.13 0.10 0.14 0.11 0.15 0.10

50.09

1.15

Ex 3, P344

R-Chart Example ~

Factors for R-Chart: D3 & D4 FACTOR FOR x-CHART A2

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.88 1.02 0 73 0.73 0.58 0.48 0.42 0.37 0.44 0.11 0.99 0.77 0.55 0.44 0.22 0.11 0.00 0.99 0.99 0.88

Goliath Tool Company

FACTORS FOR R-CHART D3 D4 0.00 0.00 0 00 0.00 0.00 0.00 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 0.38 0.39 0.40 0.41

3.27 2.57 2 28 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.61 1.59

0.28 – 0.24 –

UCL = 0.243

0.20 – Ra ange

SAMPLE SIZE n

0.16 –

R = 0.115

0.12 – 0.08 – 0.04 – 0–

Table 1, P343

LCL = 0 | | | 1 2 3

| | | | 4 5 6 7 Sample number

| 8

| 9

| 10

Example 15.3

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x-Chart Example ~

x-Chart Calculations = UCL = x + A2R

Goliath Tool Company = LCL = x - A2R

OBSERVATIONS (SLIP-RING DIAMETER, CM) SAMPLE k

x= =

x1 + x2 + ... xk k

where x= = the average of the sample means R bar = the average range values

1 2 3 4 (5.02 5 6 7 8 9 10

1

+

2

3

5.02 5.01 4.94 5.01 5.03 5.07 4.99 5.00 4.93 5.03 4.91 5.01 5.01 + 4.95 + 4.95 4.92 5.03 4.97 5.06 5.06 5.05 5.01 5.10 5.09 5.10 5.00 5.14 5.10 4.99 5.01 4.98 5.08

4 4.99 4.95 4.92 4.98 4.99 5.05 4.96 4.96 4.99 5.08 5.07

5

x

R

4.96 4.98 4.96 5.00 4.99 4.97 4.96 +4.89 4.96)/5 5.01 4.99 5.03 5.01 4.99 5.02 5.08 5.05 5.09 5.08 4.99 5.03

0.08 0.12 0.08 =0.14 4.98 0.13 0.10 0.14 0.11 0.15 0.10

total

1.15

50.09

Ex 4, P345

Factors for R-Chart: D3 & D4 SAMPLE SIZE n

FACTOR FOR x-CHART A2

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.88 1.02 0 73 0.73 0.58 0.48 0.42 0.37 0.44 0.11 0.99 0.77 0.55 0.44 0.22 0.11 0.00 0.99 0.99 0.88

FACTORS FOR R-CHART D3 D4 0.00 0.00 0 00 0.00 0.00 0.00 0.08 0.14 0.18 0.22 0.26 0.28 0.31 0.33 0.35 0.36 0.38 0.39 0.40 0.41

3.27 2.57 2 28 2.28 2.11 2.00 1.92 1.86 1.82 1.78 1.74 1.72 1.69 1.67 1.65 1.64 1.62 1.61 1.61 1.59 Table 1, P343

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x-Chart Example ~ Goliath Tool Company Using x- and R-charts together

5.10 – 5.08 –

UCL = 5.08

5 06 – 5.06

9 Each measures the process differently

Mean

5.04 – 5.02 –

x= = 5.01

9 Both process average (x bar chart) and variability y ((R chart)) must be in control

5.00 – 4.98 – 4.96 – LCL = 4.94

4.94 – 4.92 – | 1

| 2

| 3

| | | | 4 5 6 7 Sample number

| 8

| 9

Example 15.4

Sample Size Determination

9 Attribute control charts (p chart) • 50 to 100 parts in a sample

| 10

Sample Size Determination

9 Variable control charts (R- & x bar- charts) • 2 to 10 parts in a sample

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Process Capability •

•

•

Process Capability

Control limits (the “Voice of the Process” or the “Voice of the Data”): based on natural variations (common causes) Tolerance limits (the “Voice of the Customer”): customer requirements

9 Range of natural variability in process • Measured with control charts.

9 Process cannot meet specifications if natural variability exceeds tolerances 9 3-sigma quality • Specifications equal the process control limits.

Process Capability: A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits

Process Capability

9 6-sigma 6 i quality li • Specifications twice as large as control limits

Process Capability

Design Specifications

Design Specifications (c) Design specifications greater than natural variation; process is capable of always conforming to specifications.

(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time. Process

Process Design Specifications

Design Specifications

(b) Design specifications and natural variation the same; process is capable of meeting specifications most the time.

(d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification. Process

Process Figure 15.5

Figure 15.5

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Process Capability Measures Process Capability Ratio ( Cp )

Process Capability Measures Process Capability Ratio (Cp )

a) Cp < 1.0

Cp =

ttolerance l range process range

Design Specifications Design

c) Cp > 1.0 Specifications

upper specification limit lower specification limit = 6σ

Process

b) Cp = 1.0

Design Specifications S ifi i

Figure 15.5

Process

Process

Process Capability Measures Process Capability Index ( Cpk )

Computing Cp Munchies Snack Food Company Net weight specification = 9.0 oz ± 0.5 oz Process mean = 8 P 8.80 80 oz Process standard deviation = 0.12 oz

Cpk = minimum upper specification limit lower specification limit Cp = 6σ

= x - lower specification limit , 3σ = upper specification limit - x 3σ

D i Design Specifications

9.5 - 8.5 = = 1.39 6(0.12)

Ex 6, P 354

Process

17

Process Capability Measures

Computing Cpk

Process Capability Index ( Cpk )

Munchies Snack Food Company

Cpk > 1.00: 1 00: Process is capable of meeting design specifications Cpk < 1.00: Process mean has moved closer to one of the upper or lower design specifications and will generate defects

Net weight specification = 9.0 oz ± 0.5 oz Process mean = 8.80 oz Process standard deviation = 0.12 oz

Cpk = minimum

Cpk = 1.00: The process mean is centered on the design target. = minimum

= x - lower specification limit , 3σ = upper specification limit - x 3σ 8.80 - 8.50 9.50 - 8.80 , 3(0.12) 3(0.12)

= 0.83

Ex 7, P354

The Process Capability Index

Cpk < 1

Not Capable p

Cpk > 1

Capable at 3σ

Cpk > 1.33

Capable at 4σ

Cpk > 1.67

Capable at 5σ

Cpk > 2

Capable at 6σ

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