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Manufacturing Process

A sequence of activities that is intended to achieve a result (Juran).

Quality of Manufacturing Process depends on

• Entry Criteria• Task Definitions• Validation Definitions• Exit Criteria E

ntr

y C

rite

ria

Exi

t Cri

teri

a

Validation Definitions

Task Definitions

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Variation of Process Quality

• Outcomes of the process vary along the process life.

• The variation should follow a Normal Distribution with a

level of acceptable dispersion.

Causes of Variation

• Common Causes (Natural variation)Small, random forces that act continuously on the process.

• Special Causes (Assignable variation)

Extraneous to the process and interfere with the routine operation and normal dynamics of the process.

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Average ?

Standard Deviation ?

Variance?

Allowed tolerance

Allowed tolerance

Ideal specification

*Allowed tolerance* is not equal to

Design tolerance

Design tolerance

Spec Width?

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Average ?

Standard Deviation ?

Variance?

Ideal specification

Allowed tolerance

Allowed tolerance

*Allowed tolerance* is not equal to

Design tolerance

Design tolerance

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Objective

To determine whether a process is staying in control or is

potentially moving out of control at a given point of time --

Process Monitoring

SPC Procedure

• Periodically select a sample of items, inspect and note the

result

• Determine a type of variation cause related to the result

• Take remedy actions, relevant to sources of variation

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• Measures of Central Tendency

• Measures of Dispersion

• Population Distribution

• Sampling Distribution

• Central Limit Theorem

• Normal Distribution (Average, Standard Deviation)

• Standardized Normal Distribution; Z (0,1)

• Level of Confidence Interval

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Data Collection and Plotting points

Sampling Distribution

Central Limit Theorem

Control LimitsRandomness

Positions of Upper and Lower Control Limits

Concept

Calculations

Control Limits Adjustment

Significant change of the process Signals of going “out of control”

Risks of Error: Type I error & Type II error

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Variables Charts

• X-bar Charts

• R Charts

What are Variables Measurement

in a process ?

Attributes Charts

• P Chart

• C Chart

What are AttributesMeasurement

in a process ?

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X-bar Charts

To monitor process central tendency based on estimated process mean

R Charts

To monitor process variability based on estimated process range

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P Chart

To monitor proportion or fraction of process in a category

C Chart

To monitor count, or number of occurrences

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• original process• a change in process mean• a change in process variation• a change in both mean & variation

UCL

LCL

CL

Back to 25

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Center line, CL = Average of Sample Averages,

For 3-Sigma* limits,

Upper Control Limit, UCL

Lower Control Limit, LCL

Center Line, CL

X bar, sampling average

Sigma* = sigma of sampling distribution

X

RXUCL = + A2

LCL = - A2

RXTable 14.4 Control Chart Constants

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Upper Control Limit, UCL

Lower Control Limit, LCL

Center Line, CL

R, sampling range

Sigma* = sigma of sampling distribution

Center line, CL = Average of Sample Ranges,

For 3-Sigma* limits, RUCL = D4

LCL = D3R

R

Table 14.4 Control Chart Constants

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Sample Size(n) A2 D4D3

10

3

4

5

2.57501.023

2.28200.729

1.7770.2230.308

2.11400.577

…

…

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Center Line, p bar

Upper Control Li

mit, UCLp

Lower Control

Limit, LCLp

Fraction defective, p

Center line, CL = Average of Sample proportion,

For 3-Sigma* limits,

p

UCL = + 3 p p (1- )pn

p p (1- )pn

LCL = - 3

Sigma* = sigma of sampling distribution

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Upper Control

Limit, UCLc

Lower Control Li

mit, LCLc

Center Line, c bar

Number of defective, c

Center line, CL = Average number of characteristics,

For 3-Sigma* limits,

c

UCL = + 3 cc LCL = - 3 cc

Sigma* = sigma of sampling distribution

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To get Estimated process parameters :

1) How do we know the estimators are good enough?

2) How many samples should we need, and

How many groups of them?

3) What factors do we consider?

X p cR

Let’s discuss this !!Let’s discuss this !!Let’s discuss this !!Let’s discuss this !!

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Sampling Basis: Concept of Rational sampling

• Homogenous items(Within-Groups and Among-Groups variations)

• Time-order Consecutive items

• Time-order Distributed items

Sample Size:

-- The most common “n” is 5

-- Large enough “n” to detect a defect count

X R

p c

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Sampling Frequency

Depends on the nature of process and Opportunity of a

ssignable variation exposure

Initial Number of Samples, m

To make sure that we are observing a stable process, pr

actically 20, or 30, 40 of “m” should be located within C

ontrol Limits.

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Easiness• Efforts

• Costs

Usefulness• Value of obtained information

• Company image

Then, which one we select, and Why So?

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• A point lies outside the control limits• Any 2 of 3 consecutive points fall in the same A zone• 4 out of 5 consecutive points fall in the same B zone• 8 or more consecutive points lie on the same side of CL• 8 or more consecutive points move continuously in the same

direction either upward or downward

UCL (3 Sigma*)

LCL (3 Sigma*)

CL

Parameter

Sigma* = sigma of sampling distribution

Zone B

Zone B

Zone A

Zone A2 Sigma*

2 Sigma*

1 Sigma*

1 Sigma*

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• Definition of a Stable Process

• Uses of Control Charts

Variable Charts

Attributes Charts

• Control Chart Restructuring: Why & When?

• Pre-Control

• Process Capability Study

• Process Improvement

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GREEN ZONE

USL

LSL

Target, CL

X

Red Zone

Red Zone

Yellow Zone

Yellow Zone

Initial Set-up: All 5 consecutive items must fall in Green zone

Periodically check: 2 items at a time

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To See No. 10

Quiz !?!

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• Run Diagram VS Control Charts

• Specifications VS Control Limits

• Customer spec.

• Design spec.

• Detection VS Prevention Approach

• Points of control

• Rapid feedback system

• “Quality cannot be inspected into products”

Value of information?

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• Inspection and Measurement errors

• Human Error

• Instrument Error: Standard & Calibration

• Management & Shop-floor Responsibility

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In Control

Capable

Out of Control

Not Capable

IDEAL

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• Conformity of outputs

• Process Capability Index

The range over which the natural variation of a process occurs as

determined by the system of common causes, i.e., “what the

process can achieve under stable conditions”

• Quality Assurance and Acceptance Sampling

A method of measuring random samples of lots or batches of

products against predetermined standards

• Risks of Error: Producer’s Risk VS Consumer’s Risk

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Techniques• Failure Mode and Effects Analysis (FMEA)

Identification of all the ways in which a failure can occur, its e

ffect and seriousness estimation as well as corrective actions

recommendation

• Experimental Design or Design of Experiments (DOE)

Further study on Multi-Analysis of Variance (MANOVA)

• Taguchi Loss Function

Tolerance Design: The larger deviation from target the increa

singly larger losses incurred from variation allowed

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Management Frameworks

• Feigenbaum: SPC & Total Quality Control

• Deming and Total Quality Management (TQM)

• ISO 9000

• Six Sigma: Commitment of 3.4 ppm defect

SPC TQC CWQC TQM