LC Technology Manufacturing Systems. Quality Management – Pareto Analysis Pinpoints problems...

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.


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Dry

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Fau

lty

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mp

PC

B f

ault

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.Err

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amag

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Causes of poor soldering

Causes of poor soldering – descending order

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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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Dry J

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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


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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1

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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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6

7

19.7 19.9 20 20.2 20.4

Machine B

Normal Distribution

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120

1.52

5

1.55

1.57

5

1.6

1.62

5

1.65

1.67

5

1.7

1.72

5

1.75

1.77

5

1.8

1.82

5

1.85

1.87

5

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)


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

206

207

215

214

214

210


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216

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220

1 2 3 4 5 6 7

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



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



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1 2 3 4 5 6 7

UCL = 218.27

LCL = 203.72


Interpreting control charts: Process out of control

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1 2 3 4 5 6 7

Last data point is out of control – indicates definite problem to be addressed immediately as defective products are being made.


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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1 2 3 4 5 6 7


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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215

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235

1 2 3 4 5 6 7

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


Morning Midday Evening

210 208 200

212 200 210

215 209 220

216 207 219

220 208 215

210 219 200


2. Calculate the range = highest – lowest reading


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



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


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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


If Cp <1

•Process is NOT capable

•i.e. the natural variation in the process will cause outputs that are outside the acceptable limits.



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

2

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


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


Kanbans – Japanese word for cardOrder form for componentsPassed from one station to anotherInitiates the production or movement of parts

LC Technology Manufacturing Systems. Quality Management – Pareto Analysis Pinpoints problems...

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