Quality Control
This presentation is the property of its rightful owner.
Sponsored Links
1 / 24

Quality Control PowerPoint PPT Presentation


  • 113 Views
  • Uploaded on
  • Presentation posted in: General

Quality Control. Agenda. - What is quality? - Approaches in quality control - Accept/Reject testing - Sampling (statistical QC) - Control Charts - Robust design methods. What is ‘Quality’. Performance :. - A product that ‘performs better’ than others at same function Example:

Download Presentation

Quality Control

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Quality control

Quality Control

Agenda

- What is quality?

- Approaches in quality control

- Accept/Reject testing

- Sampling (statistical QC)

- Control Charts

- Robust design methods


Quality control

What is ‘Quality’

Performance:

- A product that ‘performs better’ than others at same function

Example:

Sound quality of Apple iPod vs. iRiver…

- Number of features, user interface

Examples:

Tri-Band mobile phone vs. Dual-Band mobile phone

Notebook cursor control (IBM joystick vs. touchpad)


Quality control

What is ‘Quality’

Reliability:

- A product that needs frequent repair has ‘poor quality’

Example:

Consumer Reports surveyed the owners of > 1 million vehicles. To calculate predicted reliability for 2006 model-year vehicles, the magazine averaged overall reliability scores for the last three model years (two years for newer models)

Best predicted reliability:Sporty cars/Convertibles Coupes

Honda S2000

Mazda MX-5 Miata (2005)

Lexus SC430

Chevrolet Monte Carlo (2005)


Quality control

What is ‘Quality’

Durability:

- A product that has longer expected service life

Nike Air Resolve Plus Mid Men’s Shoe

(no warranty)

Adidas Barricade 3 Men's Shoe

(6-Month outsole warranty)


Quality control

What is ‘Quality’

Aesthetics:

- A product that is ‘better looking’ or ‘more appealing’

Examples?

?

or


Quality control

Defining quality for producers..

Example: [Montgomery]

- Real case study performed in ~1980 for a US car manufacturer

- Two suppliers of transmissions (gear-box) for same car model

Supplier 1: Japanese; Supplier 2: USA

- USA transmissions has 4x service/repair costs than Japan transmissions

Lower variability 

Lower failure rate

Distribution of critical dimensions from transmissions


Quality control

Definitions

Quality is inversely proportional to variability

Quality improvement is the reduction in variability

of products/services.

How to reduce in variability of products/services ?


Quality control

QC Approaches

(1) Accept/Reject testing

(2) Sampling (statistical QC)

(3) Statistical Process Control [Shewhart]

(4) Robust design methods (Design Of Experiments) [Taguchi]


Quality control

Accept/Reject testing

- Find the ‘characteristic’ that defines quality

- Find a reliable, accurate method to measure it

- Measure each item

- All items outside the acceptance limits are scrapped

Lower Specified Limit

Upper Specified Limit

target

Measured characteristic


Quality control

Problem with Accept/Reject testing

(1) May not be possible to measure all data

Examples:

Performance of Air-conditioning system, measure temperature of room

Pressure in soda can at 10°

(2) May be too expensive to measure each sample

Examples:

Service time for customers at McDonalds

Defective surface on small metal screw-heads


Quality control

Problems with Accept/Reject testing

Solution: only measure a subset of all samples

This approach is called: Statistical Quality Control

What is statistics?


Quality control

The standard deviation =s=

=√( s2) ≈ 0.927.

Background: Statistics

Average value (mean) and spread (standard deviation)

Given a list of n numbers, e.g.: 19, 21, 18, 20, 20, 21, 20, 20.

Mean = m =S ai / n = (19+21+18+20+20+21+20+20) / 8 = 19.875

The variance s2 = ≈ 0.8594


Quality control

Background: Statistics..

Example. Air-conditioning system cools the living room and bedroom to 20;

Suppose now I want to know the average temperature in a room:

- Measure the temperature at 5 different locations in each room.

Living Room: 18, 19, 20, 21, 22.

Bedroom: 19, 20, 20, 20, 19.

What is the average temperature in the living room?

m =Sai / n = (18+19+20+21+22) / 5 = 20.

BUT: is m = m ?


Quality control

Background: Statistics...

Example (continued)

m =Sai / n = (18+19+20+21+22) / 5 = 20.

BUT: is m = m ?

If: sample points are selected randomly,

thermometer is accurate, …

then m is an unbiased estimator of m.

- take many samples of 5 data points,

- the mean of the set of m-values will approach m

- how good is the estimate?


Quality control

≈ 1.4142

sn=

The unbiased estimator of stdevof a sample = s =

Background: Statistics....

Example. Air-conditioning system cools the living room and bedroom to 20;

Suppose now I want to know the variation of temperature in a room:

- Measure the temperature at 5 different locations in each room.

Living Room: 18, 19, 20, 21, 22.

BUT: is sn = s?No!


Quality control

Sampling: Example

Soda can production:

Design spec: pressure of a sealed can 50PSI at 10C

Testing: sample few randomly selected cans each hour

Questions:

How many should we test?

Which cans should we select?

To Answer:

We need to know the distribution of pressure among all cans

Problem:

How can we know the distribution of pressure among all cans?


Quality control

Sampling: Example..

How can we know the distribution of pressure among all cans?

Plot a histogram showing %-cans with pressure in different ranges


Quality control

30

40

35

45

55

70

60

65

50

pressure (psi)

Sampling: Example…

Limit (as histogram step-size)  0: probability density function

why?

pdf is (almost) the familiar bell-shaped Gaussian curve!

True Gaussian curve: [-∞ , ∞]; pressure: [0, 95psi]


Quality control

Why is everything normal?

pdf of many natural random variables ~ normal distribution

WHY ?

Central Limit Theorem

Let X random variable, any pdf, mean, m, and variance, s2

Let Sn = sum of n randomly selected values of X;

As n  ∞Sn approaches normal distribution

with mean = nSn, and variance = ns2.


Quality control

-1, with probability 1/3

0, with probability 1/3

1, with probability 1/3

p(S1)

X1 =

S1

1

0

-1

-2, with probability 1/9

-1, with probability 2/9

0, with probability 3/9

1, with probability 2/9

2, with probability 1/9

X1 X2 X1 + X2

-1 -1 -2

-1 0 -1

-1 1 0

0 -1 -1

0 0 0

0 1 1

1 -1 0

1 0 1

1 1 2

X1 + X2 =

p(S2)

S2

1

2

0

-2

-1

-3, with probability 1/27

-2, with probability 3/27

-1, with probability 6/27

0, with probability 7/27

1, with probability 6/27

2, with probability 3/27

3, with probability 1/27

Gaussian curve

Curve joining p(S3)

X1 + X2 + X3 =

p(S3)

3

1

2

S3

0

-2

-1

-3

Central limit theorem..

Example


Quality control

(Weaker) Central Limit Theorem...

Let Sn = X1 + X2 + … + Xn

Different pdf, same m and s

normalized Sn is ~ normally distributed

Another Weak CLT:

Under some constraints, even if Xi are from different pdf’s,

with different m and s, the normalized sum is nearly normal!


Quality control

Central Limit Therem....

Observation: For many physical processes/objects

variation is f( many independent factors)

effect of each individual factor is relatively small

Observation + CLT 

The variation of parameter(s) measuring the

physical phenomenon will follow Gaussian pdf


Quality control

Sampling for QC

Soda Can Problem, recalled:

How can we know the distribution of pressure among all cans?

Answer:

We can assume it is normally distributed

Problem:

But what is the m, s ?

Answer:

We will estimate these values


Quality control

Outline


  • Login