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1 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 Entry Criteria Exit Criteria Validation Definitions Task Definitions

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2 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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3 Average ? Standard Deviation ? Variance? Allowed tolerance Ideal specification *Allowed tolerance* is not equal to Design tolerance Design tolerance Spec Width?

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

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5 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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6 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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7 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

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

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9 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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10 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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11 original process a change in process mean a change in process variation a change in both mean & variation UCL LC L CL Back to 25

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12 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 RX UCL = + A 2 LCL = - A 2 RX Table 14.4 Control Chart Constants

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13 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, R UCL = D 4 LCL = D 3 R R Table 14.4 Control Chart Constants

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14 Sample Size (n) A2A2 D4D4 D3D3 10 3 4 5 2.57501.023 2.28200.729 1.7770.2230.308 2.11400.577 … …

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

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16 Upper Control Limit, UCL c Lower Control Limit, LCL c 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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18 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? XpcR Let’s discuss this !!

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19 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 XR pc

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20 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.

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

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22 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 A 2 Sigma* 1 Sigma*

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23 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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24 GREEN ZONE USL LSL Target, CL X Red 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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25 To See No. 10 Quiz !?!

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26 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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27 Inspection and Measurement errors Human Error Instrument Error: Standard & Calibration Management & Shop-floor Responsibility

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28 In Control Capable Out of Control Not Capable IDEAL

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29 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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30 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

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31 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

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