Manufacturing Process A sequence of activities that is

Manufacturing Process A sequence of activities that is intended to achieve a result (Juran. ( • Task Definitions • Validation Definitions • Exit Criteria Task Definitions Validation Definitions Exit Criteria • Entry Criteria Quality of Manufacturing Process depends on 1

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. 2

Allowed tolerance Spec Width? Design tolerance Average? Standard Deviation? Variance? *Allowed tolerance* is not equal to Design tolerance Ideal specification 3

Allowed tolerance Design tolerance Average? Standard Deviation? Variance? *Allowed tolerance* is not equal to Design tolerance 4 Ideal specification

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 5

• 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 6

Data Collection and Plotting points Sampling Distribution Central Limit Theorem Control Limits Randomness 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 7

Variables Charts • X-bar Charts What are Variables Measurement in a process? • R Charts Attributes Charts What are Attributes Measurement in a process? • P Chart • C Chart 8

X-bar Charts To monitor process central tendency based on estimated process mean R Charts To monitor process variability based on estimated process range 9

P Chart To monitor proportion or fraction of process in a category C Chart To monitor count, or number of occurrences 10

UCL CL LC L • • original process a change in process mean a change in process variation a change in both mean & variation Back to 25 11

Sigma* = sigma of sampling distribution X bar, sampling average Upper Control Limit, UCL Center Line, CL Lower Control Limit, LCL Center line, CL = Average of Sample Averages , For 3 -Sigma* limits , Table 14. 4 Control Chart Constants X UCL = X + A 2 R LCL = X - A 2 R 12

Sigma* = sigma of sampling distribution R, sampling range Upper Control Limit, UCL Center Line, CL Lower Control Limit, LCL Center line, CL = Average of Sample Ranges , For 3 -Sigma* limits , Table 14. 4 Control Chart Constants R UCL = RD 4 LCL = R D 3 13

Sample Size (n( A 2 D 3 D 4 3 1. 023 0 2. 575 4 0. 729 0 2. 282 5 0. 577 0 2. 114 0. 308 0. 223 1. 777 … 10 … 14

Sigma* = sigma of sampling distribution Fraction defective, p Upper Control Limit, UCLp Center Line, p bar Lower Control Limit, LCLp Center line, CL = Average of Sample proportion , p For 3 -Sigma* limits , UCL = p + 3 p ( 1 -) p n LCL = p- 3 p ( 1 -) p n 15

Sigma* = sigma of sampling distribution Number of defective, c Upper Control Limit, UCLc Center Line, c bar Lower Control Limit, LCLc Center line, CL = Average number of characteristics , c For 3 -Sigma* limits , UCL = c + 3 c LCL = c- 3 c 16

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Let’s discuss this!! To get Estimated process parameters: X R p c (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? 18

Sampling Basis: Concept of Rational sampling • Homogenous items (Within-Groups and Among-Groups variations( • Time-order Consecutive items • Time-order Distributed items Sample Size : X R-- The most common “n” is 5 p c-- Large enough “n” to detect a defect count 19

Sampling Frequency Depends on the nature of process and Opportunity of assignable variation exposure Initial Number of Samples, m To make sure that we are observing a stable process, practically 20, or 30, 40 of “m” should be located within Control Limits. 20

Easiness • Efforts • Costs Usefulness • Value of obtained information • Company image Then, which one we select , and Why So? 21

Sigma* = sigma of sampling distribution Parameter 2 Sigma* UCL (3 Sigma(* Zone A Zone B 1 Sigma* CL 1 Sigma* Zone B 2 Sigma* Zone A LCL (3 Sigma(* • 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 22

• 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 23

X Red Zone USL Yellow Zone GREEN ZONE Yellow Zone Target, CL LSL Red Zone Initial Set-up: All 5 consecutive items must fall in Green zone Periodically check: 2 items at a time 24

Quiz!? ! To See No. 10 25

• Run Diagram VS Control Charts • Specifications VS Control Limits • Customer spec. Value of information ? • Design spec. • Detection VS Prevention Approach • Points of control • Rapid feedback system • “Quality cannot be inspected into products” 26

• Inspection and Measurement errors • Human Error • Instrument Error: Standard & Calibration • Management & Shop-floor Responsibility 27

In Control Capable Out of Control IDEAL Not Capable 28

• 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 29

Techniques • Failure Mode and Effects Analysis (FMEA( Identification of all the ways in which a failure can occur, its effect 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 increasingly larger losses incurred from variation allowed 30

Management Frameworks • Feigenbaum: SPC & Total Quality Control • Deming and Total Quality Management (TQM( SPC TQC CWQC TQM • ISO 9000 • Six Sigma: Commitment of 3. 4 ppm defect 31