7.Quality Control

02/05/2023 quality control by mesay A------- 1

Engineering Mangement & Industial Economics (MEng

610)

Quality control

02/05/2023quality control by mesay A-------

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What is Quality ?

Quality is a measure of the customer’s experience with the product or service with respect to specifications, requirements and expectations.


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QualityMeeting Customer’s Expectations Through Design and Mfg

ReliabilityEnsuring the Ability to Retain Quality Over a Period of Time

Product SupportProviding Necessary Support to Ensure Reliability

Competitive Edge


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Customer Supplier Sample Insp.

Sample Insp.

Customer Supplier Sample Insp.

Process control

Customer Supplier 100% Insp.

100%Insp.

Customer Supplier

Trends in quality control process


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Process of quality control - Sony produced TV’s in the U.S. and Japan. Sony had significantly

more complaints from the U.S. TV’s even though both factories produced zero defects. The Japanese factory manufactured “on target” using Taguchi techniques.


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A procedure for sentencing incoming batches or lots of items without doing

100% inspection

What is acceptance sampling?


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Why not 100% inspection?

-Very expensive

-Can’t use when product must be destroyed to test

-Handling by inspectors can itself induce defects

-Inspection becomes tedious in order to prevent defective items from slipping through inspection


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Purpose of acceptance sampling?

Assessing the average quality level of an incoming shipment or at the end of production and judge whether quality level is within the level that has been predetermined.


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The general approach

N(Lot) n

Count Number

ConformingAccept orReject Lot

Specify the sampling plan For a lot size N, determine

the sample size (s) n, and Select acceptance criteria for good lots Select rejection criteria bad lots

Accept the lot if acceptance criteria are satisfied Specify course of action if lot is rejected


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What's a good and bad lot ?

• Acceptance quality level (AQL)

The smallest percentage of defectives that will make the lot definitely acceptable. A quality level that is the base line requirement of the customer

• RQL or Lot tolerance percent defective (LTPD)

Impacts discriminating power of plan-


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d Ac ?

Reject lot

YesAccept

lot

Do 100% inspectio

n

Return lot to

supplier

Inspect all items in the sample

Defectives found = d

No

Take a randomized

sample of size n from the lot

N

Example : Single Sampling procedure


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Sampling plans are based on sample statistics and the theory says that since we inspect only a sample and not the whole lot, there is a chance of making an error.


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We need to consider two types of errors that result in wrong decisions

Type 1 Error No Error

No Error Type 2 Error

Reject Accept

Good lot

Bad lot

TRUTH

DECISION


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TYPE I ERROR = P (reject good lot)

or Producer’s risk

5% is common

TYPE II ERROR = P (accept bad lot)

or Consumer’s risk

10% is typical value

Errors and Risks


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-- Consumer’s risk

Receive shipment, assume good quality, actually bad quality

Beta () risk

= Prob (committing Type II error)

= Prob (accepting a lot at RQL quality level)

Producer’s & Consumer’s Risks

CONTROL CHARTS

In Control Process

Lets represent it with

Process Shift

Shift in Avg Shift in Std Dev

Shift in Avg and Std Dev

Detect using a control chart and Restore

If we can understand variation that occurs in any process, then we begin to understand how to control that process by eliminating special causes of variation

For a manufacturing process, this means reducing the variability of the process by using a mechanism for minimizing the number of non-conformances

Process Performance Measures

• Mean• Standard deviation


= ( y) / n Mean


Standard deviation

Data Analysis

10 mm

9.57 9.91 9.45 9.85 9.899.75 9.62 9.71 10.59 10.239.54 10.07 9.77 10.26 9.979.89 10.38 9.36 10.71 9.849.99 10.36 9.83 9.80 10.4010.01 10.52 9.88 10.50 9.979.90 9.34 10.04 9.52 9.7910.66 9.93 9.89 10.16 9.499.48 10.33 9.90 10.27 9.949.78 9.67 9.89 10.58 10.20

Measured sample Averages

Histogram

5 10 150

10

20

Data Points

Histogram

Freq

uenc

y C

ount

9.57 9.91 9.45 9.85 9.899.75 9.62 9.71 10.59 10.239.54 10.07 9.77 10.26 9.979.89 10.38 9.36 10.71 9.849.99 10.36 9.83 9.80 10.4010.01 10.52 9.88 10.50 9.979.90 9.34 10.04 9.52 9.7910.66 9.93 9.89 10.16 9.499.48 10.33 9.90 10.27 9.949.78 9.67 9.89 10.58 10.20

Measured sample Averages

Common Causes Variation inherent in a process Can be eliminated only through improvements in

the system

Special Causes Variation due to identifiable factors Can be modified through operator or management

action

Causes of variation

x xi

i1

n

n

xi x ) 2

n 1

Common Causes

Assignable Causes

Average

Process Tracking

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

14

16

18

.

LCL=0.8236

CL=9.85

UCL=18.88

Data1_A

Individuals (X) Chart

Indi

vidu

als

Subgroup No.

• 1 Sigma = 68.25 % Yield • 2 Sigma = 95.5 % Yield • 3 Sigma = 99.73 % Yield • 6 Sigma = 99.99998 % Yield

Control Charts

UCL

Nominal

LCL

1 2 3Samples

Assignable causes

likely

Sampling distribution

Control Limits and Errors

UCL

LCL

Processaverage


Type I error:Probability of searching for a cause when none exists

UCL

LCL

Processaverage



Shift in process average

UCL

LCL

Processaverage



Type II error:Probability of concludingthat nothing has changed

Shift in process average

UCL

LCL

Processaverage

Type 1 Error No Error

No Error Type 2 Error

Alarm No Alarm

In-Control

Out-of-Control

Calculating Type 1 error

1. Z = (UCL-CL) / ( / n)2. For this z find P( x UCL)3. Find 1 - P( x UCL)4. Multiply by 2 to get two tailed value

Relation between population and sampling distribution

Calculating Type 2 error

1. Z1 = (UCL- shifted CL) / ( / n)2. Z2 = (LCL- shifted CL) / ( / n)3. Find P( x UCL) and P( x LCL) 4. P (type 2 error) = P( x UCL) - P( x LCL)

Example 1 : If CL= 3, = 2, n = 5, find probability of type 1 error corresponding to a UCL of 5.

Example 2 : If CL shifts to 4 for the above process, find the probability of type 2 error.

a CDF a CDF-4.000 0.00003 0.000 0.50000-3.900 0.00005 0.100 0.53983-3.800 0.00007 0.200 0.57926-3.719 0.00010 0.300 0.61791-3.700 0.00011 0.400 0.65542-3.600 0.00016 0.431 0.66667-3.500 0.00023 0.500 0.69146-3.400 0.00034 0.600 0.72575-3.300 0.00048 0.674 0.75000-3.291 0.00050 0.700 0.75804-3.200 0.00069 0.800 0.78814-3.100 0.00097 0.900 0.81594

a CDF a CDF-3.090 0.00100 1.000 0.84134-3.000 0.00135 1.100 0.86433-2.900 0.00187 1.200 0.88493-2.800 0.00256 1.282 0.90000-2.700 0.00347 1.300 0.90320-2.600 0.00466 1.400 0.91924-2.576 0.00500 1.500 0.93319-2.500 0.00621 1.600 0.94520-2.400 0.00820 1.645 0.95000-2.326 0.01000 1.700 0.95543-2.300 0.01072 1.800 0.96407-2.200 0.01390 1.900 0.97128-2.100 0.01786 1.960 0.97500-2.000 0.02275 2.000 0.97725

a CDF a CDF

-1.960 0.02500 2.100 0.98214-1.900 0.02872 2.200 0.98610-1.800 0.03593 2.300 0.98928-1.700 0.04457 2.326 0.99000-1.645 0.05000 2.400 0.99180-1.600 0.05480 2.500 0.99379-1.500 0.06681 2.576 0.99500-1.400 0.08076 2.600 0.99534-1.300 0.09680 2.700 0.99653-1.282 0.10000 2.800 0.99744-1.200 0.11507 2.900 0.99813-1.100 0.13567 3.000 0.99865-1.000 0.15866 3.090 0.99900-0.900 0.18406 3.100 0.99903

a CDF a CDF

-0.800 0.21186 3.200 0.99931-0.700 0.24196 3.291 0.99950-0.674 0.25000 3.300 0.99952-0.600 0.27425 3.400 0.99966-0.500 0.30854 3.500 0.99977-0.431 0.33333 3.600 0.99984-0.400 0.34458 3.700 0.99989-0.300 0.38209 3.719 0.99990-0.200 0.42074 3.800 0.99993-0.100 0.46017 3.900 0.99995

4.000 0.99997

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7.Quality Control