chap_4__spc

Chapter 4

Statistical Process Control

§ 4.1 Introduction

Weights of the cereal packets:

498 gms, 505 gms, 443 gms, 503 gms, 501 gms

Natural CauseAssignable cause

Possible Factors behind Assignable Causes

• Man – Inexperience, fatigue, personal problem• Machine – Faulty machine, tool wear, aging

machine, broken tool• Materials – Defective raw materials supplied by

new supplier• Method – Work instruction• Measurement – Problem in the measuring

instrument itself• Environment - Temperature, humidity, sudden

power surge

Definition of SPC

Statistical process control is a statistical method of separating variation resulting from special causes from variation resulting from natural causes to eliminate the special causes and to establish and maintain consistency in quality of products/services.

Various SPC Tools• Pareto charts• Flow diagram• Cause and effect diagram• Histogram• Check sheet• Scatter diagram• Run chart

• Control chart

Origin of SPC

Walter Shewhart – Father of SPC

-- The Economic Control of Quality of Manufactured Products (published in 1931)

VariableAttribute

Types of Control Charts

x -b a r ch a rt M e d ia n ch a rt R ch a rt s ch a rt

V a ria b le C h a rts

p ch a rt n p ch a rt c ch a rt u ch a rt

A ttrib u te C h a rts

C o n tro l C h a rts

Overall look of a Control Chart

Sample number

Uppercontrollimit

Centreline

Lowercontrollimit

1 2 3 4 5 6 7

Overall Look of a Control Chart

(Cont’d)

Sample number

Uppercontrollimit

Centreline

Lowercontrollimit

1 2 3 4 5 6 7 8 9 10

О

§4.2Variable Control Charts

Examples of Variables

• Length• Weight• Time• Volume• Temperature• Density• Pressure• Energy• Force• velocity• voltage

Specific Examples of Variables

• Time waiting for service

• Time to process insurance claims

• Time from order receipt to shipment

• Diameter of a piston

• Weight of fertilizer packets

• Volume of shampoo bottles

X-bar and R charts should be used together

R chart

RDUCL

RDLCL

R

R

4

3

For x-bar chart For R-chart

n A2 D3 D4

2 1.880 0 3.267

3 1.023 0 2.574

4 0.729 0 2.282

5 0.577 0 2.114

6 0.483 0 2.004

7 0.419 0.076 1.924

8 0.373 0.136 1.864

9 0.337 0.184 1.816

10 0.308 0.223 1.777

11 0.285 0.256 1.744

12 0.266 0.283 1.717

13 0.249 0.307 1.693

14 0.235 0.328 1.672

15 0.223 0.347 1.653

Example Bukit Battery Corp. has recently been receiving

complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at West’s Austin plant, believes there is no problem because his batteries have had an average life of 50 hours, about 10% longer than competitor’s models. To raise the life time above this level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. He decides to take size-5 samples of 9-volt batteries for each of the next 10 hours to create the standards for control chart limits (see the following table):

Bukit Battery data –Battery Lifetimes (in hours)

Sample

Hour 1 2 3 4 5

1 51 50 49 50 50

2 45 47 70 46 36

3 50 35 48 39 47

4 55 70 50 30 51

5 49 38 64 36 47

6 59 62 40 54 64

7 36 33 49 48 56

8 50 67 53 43 40

9 43 22 36 27 44

10 70 45 50 47 41

Is the manufacturing process under control?

Bukit Battery data –Battery Lifetimes (in hours)

Sample

Hour 1 2 3 4 5 R

1 51 50 49 50 50 2

2 45 47 70 46 36 34

3 50 35 48 39 47 15

4 55 70 50 30 51 40

5 49 38 64 36 47 28

6 59 62 40 54 64 24

7 36 33 49 48 56 23

8 50 67 53 43 40 27

9 30 22 36 27 44 22

10 70 45 50 47 41 29

1 1098765432

24.4

10

20

30

40

51.58

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X-bar Chart

RAxUCL

RAxLCL

x

x

2

2

Bukit Battery data –Battery Lifetimes (in hours)

Sample

Hour 1 2 3 4 5 R

1 51 50 49 50 50 50.0 2

2 45 47 70 46 36 48.8 34

3 50 35 48 39 47 43.8 15

4 55 70 50 30 51 51.2 40

5 49 38 64 36 47 46.8 28

6 59 62 40 54 64 55.8 24

7 36 33 49 48 56 44.4 23

8 50 67 53 43 40 50.6 27

9 30 22 36 27 44 31.8 22

10 70 45 50 47 41 50.6 29

x

1 1098765432

47.38

33.30

40

50

60

61.46

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When can we say that a process is under control?

• There are no sample points that lie outside the control limits.

• Most of the points are clustered around the center line; not too many points close to the control limits.

• Approximately half of the sample points lie above the center line and approximately half of the points lie below the center line.

Properties of Properties of NormalNormalDistributionDistribution

-3 -2 -1 +1 +2 +3Mean

68.26%95.44%99.74%

= Standard deviation

Special cases

Checklist of questions for out-of-control process

(i) Are there any differences in the measurement accuracy of the instruments used?

(ii) Are there differences in the methods used by different operators?

(iii) Does the environment affect the process?(iv) Is the process affected by tool-wear?

Checklist of questions for out-of-control process (Cont’d)

(v) Were any untrained workers involved in the process?

(vi) Has there been any change in the source of the raw materials?

(vii) Is the process affected by operators’ fatigue?

(viii) Did samples come from different shifts, operators, or machines?

• Revised control limit

• Sample size

• Sample number

Few Points for solving real world problems

§4.3 Attribute Control Charts

Defects and Defective

Defects are non-conformities in the products/services

A product or service is said to be defective if it has one or more than one defects.

p chart

n

pppUCL

n

pppLCL

p

p

)1(3

)1(3

Example

A quality engineer takes 20 samples of 100 transistors each from the output of an assembly line. Each transistor is tested and the number of defectives in each sample is recorded which are shown in the next slide.

Draw the p chart and conclude.

Sample No.

Number of defectives

Sample No.

Number of defectives

1 3 11 9

2 2 12 1

3 1 13 3

4 4 14 3

5 0 15 4

6 2 16 5

7 0 17 3

8 5 18 3

9 1 19 1

10 2 20 6

Sample No.

No. of Defectives

Percentage of

defectives

Sample No.

No. of Defectives

Percentage of

defectives

1 3 0.03 11 9 0.09

2 2 0.02 12 1 0.01

3 1 0.01 13 3 0.03

4 4 0.04 14 3 0.03

5 0 0.00 15 4 0.04

6 2 0.02 16 5 0.05

7 0 0.00 17 3 0.03

8 5 0.05 18 3 0.03

9 1 0.01 19 1 0.01

10 2 0.02 20 6 0.06

0.0793

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 1816 2019

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0.029

C chart

ccUCL

ccLCL

c

c

3

3

Example

Coils of synthetic rope are monitored for defects. Each coil contains 1,200 feet of rope. Eighteen rolls have been selected and the number of defects per roll is presented in the next slide. Identify an appropriate control chart and determine the chart’s control limits. Draw the control chart and conclude.

Sample No.

Number of defects

Sample No.

Number of defects

1 1 10 2

2 3 11 1

3 4 12 4

4 2 13 3

5 4 14 0

6 2 15 5

7 0 16 4

8 3 17 2

9 2 18 3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 1816

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5

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7.24

2.5

Start

Collect data. Determine sample size. Select 25 to 30 samples

After tabulating data compute the necessary measures

Compute the center line and control limits for the control chart using the appropriate formulas.

Draw the control chart and plot the sample data on it.

Are any data points outside the

Control limits?

The center line and control limits become permanent, and the control chart is used for monitoring the future behavior of the process.

Special causes are sought for out-of-control conditions and the out-of-control points are removed. New centerline and control limits are computed from the remaining points. The remaining points are plotted ob the new chart.

NoYes

End

Control Chart SelectionQuality Characteristic

variable attribute

n>1?

n>=10 or computer?

x and MRno

yes

x and s

x and Rno

yes

defective defect

constant sample size?

p-chart withvariable samplesize

no

p ornp

yes constantsampling unit?

c u

yes no

§4.4 Applications

Quality Characteristics:

Selected Industries• Hospital: Timeliness and quickness of care, staff

responses to request, accuracy of lab test, cleanliness, checkout time.

• Grocery Store: Waiting time to check out, frequency of stockout items, cleanliness, customer complaints

• Airlines: Flight delays, lost luggage, check-in-time, flight attendant’s courtesy, cabin cleanliness.

• Fast Food Restaurant: Waiting time for service, customer complaints, cleanliness, order accuracy, employee courtesy

1. KFC’s South Central division (Texas and Oklahoma) uses SPC to monitor service times in its drive-through windows. It uses x-bar and R charts.

2. Kurt Manufacturing Company (based in Minneapolis) produces precision machines.

SPC is used by machine operators to monitor their processes by measuring variability, reliability of the machines. SPC charts are displayed on the shop floor so that everybody can see it. If there is any problem in the production, then the operators are empowered to stop production and find out out the cause and remove it.

3. P*I*E* Nationwide is America’s fourth largest trucking company.One part of the company’s quality progrom is to extensive use of SPC.

A p-chart was initially used to monitor the production of daily defective freight bills. This resulted in reduction in the error rate from 10% to 0.8% within one year and the subsequent reduction in inspection time increased productivity by 30%. It is also estimated that use of SPC results savings of $38,000 at a single trucking terminal.

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