Quality Control

Prof. R. S. RengasamyDepartment of Textile Technolgoy

Indian Institute of Technology Delhi

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Quality & Standard

• Quality is a measure of how closely a good or service conforms to specified standard.

• Quality Standard may be any one or combination of attributes/ variables of product.

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AttributesAttributes (discrete data, binary) (Accept or reject; using Go/NoGo gauges)

• Performance• Reliability• Appearance• Commitment to delivery time etc

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VariablesVariables (continuous data; measurable)Some measurement like • Length, Width, Height, Diameter• Surface roughness, Count, Strength• Work of rupture, Elongation, Tear strength , Rate of

moisture vapour transport, Rate of wicking• Air permeability, Bursting strength, etc.

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Results of ‘No quality control’

• No yardstick for comparing quality of goods/ services

• Difficulty in maintaining consistency in quality• Dissatisfied customers due to increased

maintenance & operating costs• Increased rework cost • Reduced life time of products/services• Reduced flexibility for use of standard spares

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Strategic areas of QC program in manufacturing

• Supplier quality• Incoming raw material quality• Process quality• Final inspection• Customer quality

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Basic components of product quality• Careful consideration of product design specifications• Adequate inspection procedures for products• Acceptance procedures for purchased materials &

parts• Control practices to maintain quality levels in

process-stage• Commitment from top to bottom of enterprise

towards quality• Formulation of quality assurance procedures are

necessary to integrate & coordinate these functions

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Quality control techniquesControl Charts (for in-

process quality)Acceptance Sampling (for quality of materials, semi-

finished, finished products)For

VariablesFor

AttributesFor

VariablesFor

Attributes1) X Chart 1) P chart 1) Plan with α 1) Single

sampling plan2) R Chart 2) C chart 2) Plan with α

and β2) Double sampling plan3) Multiple sampling plan

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Process capability

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Process capability

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Control Charts

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Control Charts for variableNotations =Mean of a sample

= Mean of sample means

R = Range of a sample observation = mean range of samplesA, B, & C are factors for different sample size (n)

obtained from published tableK = number of samples

X

X

R

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Control Charts for variableControl limits for chart

Upper control limit,

Lower control limit,

Control limits for R chart

Upper control limit,

Lower control limit,

RAXUCLx

X

RAXLCLx

RBUCLR

RCLCLR

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S. NoK = 10

Observations (n = 5)R1 2 3 4 5

1 10 12 13 8 9 10.4 52 7 10 8 11 9 9.0 43 11 12 9 12 10 10.8 34 10 9 8 13 11 10.2 55 8 11 11 7 7 8.8 46 11 8 8 11 10 9.6 37 10 12 13 13 9 11.4 48 10 12 12 10 12 11.2 29 12 13 11 12 10 11.6 3

10 10 13 7 9 12 10.2 6Total 103.2 39

n = 5 A = 0.58 B = 2.11 C = 0 Mean 10.2 3.9

X

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Chart

R Chart

X

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Control Charts for attributes (good or bad etc.)

Percent defective chart (P-chart)•Based on normal distribution

The no. of defectives per sample (C-chart)•Based on Poisson distribution

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Purpose of P-chart

• To discover average proportion of non-conforming parts/articles submitted for inspection over a period of time

• To bring to the management attention, if there is any change in average quality level

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P-chart

p = percentage defective in a sample = Process mean percent defective n = Sample size k = No. of samples = Standard deviation of percent defective

pP p

n

pppUCL 31

pP p

n

pppLCL 31

p

p

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P-chart

Sample no (k = 5) No. Of defective, n = 50 % of defective rolls

1 10 0.20

2 10 0.20

3 9 0.18

4 10 0.20

5 4 0.08

6 6 0.12

7 2 0.04

8 3 0.06

9 9 0.18

10 4 0.08

11 8 0.16

12 11 0.22

13 8 0.16

14 10 0.20

15 9 0.18

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P-chart

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C-chart• Applies to the no. of nonconformities in each

samplePurpose• To control the no. of defects in final assemblies

ccUCLc 3 ccLCLc 3

Sample No.

1 2 3 4 5 6 7 8 9 10 Mean

Missing items (c )

14 13 26 20 9 25 15 11 14 13 16

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C-chart

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Why acceptance sampling?

100% inspection on lots is not possible due to

High cost of inspectionDestructive method of test results in spoilageLong time for testingImpossible & impracticable, if population is

too large

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PossibilitiesProduct Accept Reject

Good product

Desired Not desired.Rejecting a good product.Producer’s risk(Error I)

Bad product

Accepting a bad product.Consumer’s risk(Error II)

Not Desired.

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Operative Characteristic (OC-Curve

Sample size = nPercentage defective = p (5% means 0.05)Acceptance number = cAQL = Acceptance Quality Level

= percentage defective, p1LTPD = Lot Tolerance Percent Defectives = p2p2 > p1 (n) and (c ) must be decided based on AQL and

LTPD

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O. C. Curve

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O. C. CurveProbability of acceptance of lot is pa

Solution is based on Chi-square distribution,

where (c+1) is degrees of freedom & c can be found out

11pppAQL a

cr

r

rnrr ppnc

0 11 1

cr

r

rnrr ppnc

0 22 1 2pppLTPD a

2

1

122

122

,

1,

p

p

c

c

2

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O. C. Curve for different n and c

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Six SigmaOrigin• Management standard in product variation

(later service) coined by Motorola Engineer Bill Smith during 1920’s

• Standards such as defects in thousands of opportunities did not provide depth of information

• Decided to measure defects per million opportunities

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What is Six Sigma?• It is a disciplined data driven approach and methodology for

eliminating defects which amounts to driving towards six-standard deviation between the mean and the nearest specification

• Six Sigma level indicates that we are 99.99966% confident that the product/service delivered by us is defect free

• 3.4 defects per million opportunities (DPMO)

• A process is said to be at 6-Sigma level provided that the process is not producing more than 3.4 defects per million opportunities

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Objectives & concepts in 6-SigmaObjectives– Process improvement & reduction of variation

Concepts• Attributes which are most important to customers are

critical• Focus on process more specifically what it can deliver• Consistent & predictable processes to improve quality is

utmost expectation of customer• Employing systematic methodology, utilizing tools,

training & measurements to produce at Six Sigma level

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Approaches for Six SigmaDMAIC: Define, Measure, Analyze, Improve, &

Control• For improving existing process falling below

specification and looking for incremental improvements

DMADV: Define, Measure, Analyze, Define, & Verify• To develop new processes/products at Six Sigma

level

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Execution of Six Sigma• DMAIC & DMADA are executed by Six Sigma

Green Belts and Six Sigma Black Belts and these are overseen by Six Sigma Master Black Belts.

Six Sigma Green Belt Team• Team leaders capable of forming & facilitating

Six Sigma teams and managing Six Sigma projects from concept to completion

• 5-days of classroom & practice in Six Sigma projects

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Execution of Six Sigma

Six Sigma Black Belt Team

• Team leaders responsible for measuring, analyzing & improving & controlling key processes that influence customer satisfaction/or productivity growth

• Full time positions

• They focus on 1 to 3 projects

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Benefits of Sig Sigma

• It ensures enhanced product quality• It enables predictable delivery of products• It helps to achieve productivity improvement• It helps to have rapid response to changing

needs of customers• It facilitates the development & introduction

of new products