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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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1
2
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4
5
6
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.
Motorola Malaysia Sdn. Bhd.