lc technology manufacturing systems. quality management – pareto analysis pinpoints problems...
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LC Technology
Manufacturing Systems
Quality Management – Pareto Analysis
Pinpoints problems through the identification and separation of the ‘vital few’ problems fromthe trivial many.
Vilifredo Pareto: concluded that 80% of the problems with any process are due to 20% of the causes.
Quality Management – Pareto Analysis
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Causes of poor soldering
Causes of poor soldering – descending order
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Quality Management – Pareto Analysis
Cumulative plot is made of all of the causes
80% caused by two problems
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8792
9597.5 99.5 100
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Quality Management – Pareto Analysis
Statistical Process Control
•Statistical procedure to verify quality
•Check manufacturing process is working correctly
→Inspect and measure manufacturing process
→Varying from target – corrective action taken
•Prevents poor quality before it occurs
Statistical Process Control
When? Manufacturing large quantities of items•Euro coins•Computers•Cars etc.
Why?
•Impractical to measure each item made
•Machine/equipment/human error
How?
•Measure a small proportion of the produced items (sample)
•Use X-bar and R Charts to see if process is in control
•Conclude the quality characteristics of the whole process
Laser machine A – cutting 20mm hole
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19.7 19.8 19.9 19.9 20 20.1 20.2 20.3 20.4
Machine A
Normal Distribution
Some measurement < 20mm
Some measurements > 20mmNatural occurrence
Normal Distribution
Machine B making same part as machine A
•Same distribution
•Skewed to right
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19.7 19.9 20 20.2 20.4
Machine B
Normal Distribution
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1.52
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1.55
1.57
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1.6
1.62
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1.65
1.67
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1.7
1.72
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1.75
1.77
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1.8
1.82
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1.85
1.87
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1.5 1.525 1.55 1.575 1.6 1.625 1.65 1.675 1.7 1.725 1.75 1.775 1.8 1.825 1.85
Series1
Histogram:•Statistical information•Column width represents a range of sizes•Shape of histogram is proportional to spread of data
Results of a survey on the heights of a group of pupils in a large schoolColumn width = 25mm
Normal Distribution
Larger survey – population of a townColumn width = 10mm
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1.5 1.511.521.531.541.551.561.571.581.59 1.6 1.611.621.631.641.651.661.671.681.69 1.7 1.711.721.731.741.751.761.771.781.79 1.8 1.811.821.831.841.851.861.87
•Centered about mean•Characteristic ‘Bell’ shape curve•Number of occurrences reduce as they deviate from the mean
Normal Distribution
A very small sample interval approximates a curve as shown
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Normal Distribution
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All measurable attributes show a variation
Spread of Sizes = Normal Distribution
Normal Distribution
•The spread or ‘width’ of the curve has a precise mathematical meaning - Variance
•The greater the variance the wider the curve
•Defined by a parameter called the standard deviation
Normal Distribution
Calculation of standard distribution (sigma)-measured sizes of a sample of parts
N
yyyyyy n22
22
1 )....()()(
y1,y2…etc are the measured values of the sample is the average value N is the number of samples takeny
Normal Distribution
Sharpen 5 pencils to a length of 8 mm
Mean average = 7.54
Sigma = (each value – mean average)² +
number of values
(6.5 - 7.54)² + (8.2 – 7.54)² + (8.5 – 7.54)² + (7.5 – 7.54)² + (7 – 7.54)²
5
SIGMA = 0.73
6.5mm 8.2mm 8.5mm 7.5mm 7.0mm
Normal Distribution
If sigma is known then we know that:
•95% of parts will lie within +/- 2σ of the mean
•99.74% of parts will lie within +/- 3σ of the mean
Control Charts
• Used to establish the control limits for a process
• Used to monitor the process to show when it is out of control
1.X-bar Chart (Mean Charts)
2.R Charts (Range Charts)
Control Charts
Process Mean = Mean of Sample Means
Upper control limit (UCL) = Process mean+3 sigma
Lower control limit (LCL) = Process mean-3 sigma
Control Charts – X-bar Charts
1. Record measurements from a number of samples sets (4 or 5)
Control Charts – X-bar Charts
Oven temperature data
Morning Midday EveningDaily Means
Monday 210 208 200 206
Tuesday 212 200 210 207
Wednesday 215 209 220 215
Thursday 216 207 219 214
Friday 220 208 215 214
Saturday 210 219 200 210
2. Calculate the mean of each sample set
3. Calculate the process mean (mean of sample means)
Degrees2116
210214214215207206
Daily Means
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215
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210
Control Charts – X-bar Charts
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4. Calculate UCL and LCL
UCL = process mean + 3σsample
LCL = process mean - 3σsample
The standard deviation σsample of the sample means
where n is the sample size (3 temperature readings)σ = process standard deviation (4.2 degrees)
σsample =
n
degrees 2.42 3
2.4
Control Charts – X-bar Charts
4. Calculate UCL and LCL
UCL = process mean + 3σsample
LCL = process mean - 3σsample
σsample
UCL = 211 + 3(2.42) = 218.27 degrees
LCL = 211 – 3(2.42) = 203.72 degrees
degrees 2.42 3
2.4
Control Charts – X-bar Charts
Control Charts – X-bar Charts
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UCL = 218.27
LCL = 203.72
Control Charts – X-bar Charts
Interpreting control charts: Process out of control
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Last data point is out of control – indicates definite problem to be addressed immediately as defective products are being made.
Control Charts – X-bar Charts
Interpreting control charts: Process in control
Process still in control but there is a steady increase toward the UCL. There may be a possible problem and it should be investigated.
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Control Charts – X-bar Charts
Interpreting control charts: Process in control
All data points are all above the process mean. This suggests some non-random influence on the process that should be investigated.
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Control Charts – Range Charts
The range is the difference between the largest and smallest values in a sample.
Range is used to measure the process variation
1. Record measurements from a set of samples
Oven temperature data
Morning Midday Evening
210 208 200
212 200 210
215 209 220
216 207 219
220 208 215
210 219 200
Control Charts – Range Charts
2. Calculate the range = highest – lowest reading
Oven temperature data
Morning Midday Evening Range
210 208 200 10
212 200 210 12
215 209 220 11
216 207 219 12
220 208 215 12
210 219 200 19
Control Charts – Range Charts
3. Calculate UCL and LCL
UCL = D4 x Raverage
LCL = D3 x Raverage
Sample size (n) D3 D4
2 0 3.27
3 0 2.57
4 0 2.28
5 0 2.11
6 0 2.00
7 0.08 1.92
8 0.14 1.86
9 0.18 1.82
10 0.22 1.78
11 0.26 1.74
UCL = 2.57 x 13 = 33.41 degrees
LCL = 0 x 13 = 0 degrees
Control Charts – Range Charts
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UCL
LCL
R average
Matches the natural variation in a process to the size requirements (tolerance) imposed by the design
Filling a box with washers:
•exact number not in all boxes
•upper limit set
•lower limit set
Process Capability
Process not capable: a lot of boxes will be over and under filled
Process Not Capable
Normal distribution > specifications
Cannot achieve tolerances all of the time
Process capable: However there will still be a small number of defective parts
Process Capable
Normal distribution is similar to specifications
Tolerances will be met most of the time
Process capable: No defective parts
Process Capable
Normal distribution < specifications
Tolerances will be met all the time
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LimitSizeLowerLimitSizeUpperRangeToleranceC p
If Cp =1
•Process is capable
•i.e. 99.97% of the natural variation of the process will be within the acceptable limits
Process Capability Index
If Cp > 1
•Process is capable.
•i.e. very few defects will be found – less than three per thousand, often much less
Process Capability Index
If Cp <1
•Process is NOT capable
•i.e. the natural variation in the process will cause outputs that are outside the acceptable limits.
Process Capability Index
Statistical Process Control
Is doing things right 99% of the time good enough?
13 major accidents at Heathrow Airport every 2 days
5000 incorrect surgical procedures per week ………………
Pharmaceutical company producing 1 000 000 tablets a week,
99% quality would mean tablets would be defective!10 000
Process of maintaining high quality standards is called :
Quality Assurance
Modern manufacturing companies often aim for a target of only
3 in a million defective parts.
The term six sigma is used to describe quality at this level
Sampling
Size of Sample?
Sufficient to allow accurate assessment of process
•More – does not improve accuracy
•Less – reduced confidence in result
Size of Sample
S = sample size
e = acceptable error - as a proportion of std. deviation
z = number relating to degree of confidence in the result
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e
zs
Confidence Value for z
99% 2.58
95% 1.96
90% 1.64
80% 1.28
Sampling
Example – find mean value for weight of a packet of sugar
•with a confidence of 95%
•acceptable error of 10%
•Weight of packet of sugar = 1000g
•Process standard deviation = 10g
Sampling
z = 1.96 from the tablee = 0.1 (i.e.10%)
Therefore the sample size s = (1.96 / 0.1)2
Therefore s = 384.16
Sample size = 385
Sampling
Assume mean weight = 1005g
Sigma = 10g
Therefore error = 10g + 10% = 11g
Result:95% confident average weight of all
packets of sugar gg 1016 994
Sampling
QC, QA and TQM
Quality Control:• emerged during the 1940s and 1950s • increase profit and reduce cost by the inspection of product
quality. • inspect components after manufacture• reject or rework any defective components
Disadvantages:• just detects non-conforming products• does not prevent defects happening • wastage of material and time on scrapped and reworked
parts inspection process not foolproof • possibility of non-conforming parts being shipped by
mistake
QC, QA and TQM
Quality Assurance
• Set up a quality system • documented approach to all procedures and processes that
affect quality • prevention and inspection is a large part of the process • all aspects of the production process are involved• system accredited using international standards
QC, QA and TQM
Total Quality Management
• International competition during the 1980s and 1990s • Everybody in the organisation is involved • Focussed on needs of the customer through teamwork• The aim is ‘zero defect’ production
Just-In-Time Manufacture
Modern products – shortened life cycle
Manufacturer – pressure for quick response
Quick turnaround - hold inventory of stock
Holding inventory costs money for storage
Inventory items obsolete before use
New approach: Just-In-Time Manufacture
Just-In-Time Manufacture
Underlying concept: Eliminate waste.
Minimum amount:•Materials•Parts•Space•Tools•Time
Suppliers are coordinated with manufacturing company.
Delivery address
Return Container to
Previous process
Next process
Number of components
Just-In-Time Manufacture
Kanbans – Japanese word for cardOrder form for componentsPassed from one station to anotherInitiates the production or movement of parts