Lecture 1 - Concept Of Quality Engineering

Quality Engineering

Quality • Defined in different terms by different quality Gurus: Deming, Juran, Crosby, Feigenbaum • Western philosophers explained quality in terms of presence of certain characteristics • Taguchi defines quality in terms of loss due to absence of quality • This thinking influenced by Zen philosophy

Quality • Quality is measured in terms of total loss to society due to functional variation and harmful side effects • When the product performance meets the target performance, the loss is zero • Any deviation from the target incurs loss • Greater the deviation, greater the loss • Explained by Taguchi’s Loss Function

Quality Loss Function • The traditional (Western) model for quality losses – No losses when the product is within the specification limits Cost

Scrap Cost LSL

Target

USL

• The Taguchi loss function – Quality loss is zero only if the product achieves target specification

Fraction Defective Fallacy 1. All products within specifications equally good, 2. All products beyond specifications equally bad A study found U.S. consumers preferred Sony TVs made in Japan to those made in the U.S. Both factories used the same designs & specifications. The difference in quality goals made the difference in consumer preferences. Sony-Japan

Freq.

(Target-oriented)

LSL

Target

USL

X

Sony-US (Conformanceoriented)

Quality Loss Function High Loss Unacceptable Loss

Poor Fair Good Best

Low Loss

Frequency

Target-oriented quality yields more product in the "best" category

Conformance-oriented quality keeps products within 3 standard deviations

Lower

Target Distribution of Specifications for Products Produced

Upper

Quality Loss Function • Loss L(y) = k*(y-m)2 • When y=m, Loss = 0 • When functional limits are m±Δ0, and • Loss at y±Δ0 = A0, then • k = A0 /Δ02

Quality Loss Function Example 1 The repair cost for an engine shaft is Rs. 100. The shaft diameter is required to be 10 ±1 mm. On average the produced shafts deviates 0.5 mm from target. Determine the mean quality loss per shaft using the Taguchi QLF. Solution: k = 100/(1)2=100, L(y) = 100*(0.5)2 = Rs. 25

Quality Loss Function Example 2 The specifications for the diameter of a gear are 25.00 ± 0.25 mm. If the diameter is out of specification, the gear must be scrapped at a cost of Rs. 4.0/ unit. What is the unit loss? Solution: k = 4/(0.25)2=64, L(y) = 64*(0.25)2 = Rs. 4

Different Quality Loss Functions • • •

Smaller-the-better: L(y) = ky2 Larger-the-better: L(y) = k/y2 Asymmetric loss function: For example, L(y) = k1*(y-m)2 , when y > m, and = k2*(y-m)2 , when y ≤ m

Causes of Variation - Noise Factors Product variation Process variation ii. External: Variation ii. External: Environment in the environment in in which process is which the product is carried out used iii. Non-uniformity of the iii. Unit-to-unit: process: Spatial Variation due to variation in the output process iv. Process drift: iv. Deterioration: Wear Temporal variation in and tear due to usage the output

Average Quality Loss • Average quality loss Q = k [(μ-m)2+σ2] • Two components – deviation from target, and – variance around mean

• Adjusting mean of the process is easy, but variation reduction is difficult

Variation Reduction •

Three approaches to variation reduction ii. Screening out bad product iii. Discovering and eliminating the cause of malfunction (tolerance tightening) iv. Applying robust design methods (finding and exploring nonlinearity)

Goal of Robust Design • To exploit the nonlinearity of the relationships among the parameters, the noise factors and the quality characteristics • To find a combination of parameter values that result into the smallest variation of the quality characteristic around the target value under nominal noise conditions

Classification of Parameters z

M Signal factor

Noise factors

Product / Process

x Control factors

y Response

Engineering Design Problem i. Concept design ii. Parameter design iii. Tolerance design •

Quality Engineering includes (ii) and (iii)

Stage of product realization

Quality control activity

Ability to reduce effect of External var.

Unit-tounit var.

Drift

Y

Y

Y

Product design Parameter design

Y

Y

Y

Tolerance design

Y

Y

Y

Concept design

N

Y

N

Process design Parameter design

N

Y

N

Tolerance design

N

Y

N

Detection/ correction

N

Y

N

Manufacturing Feed-forward control

N

Y

N

Screening

N

Y

N

Warranty / Repair

N

N

N

Concept design

Usage

Assignment No. 1 • Following measurements were taken on two batches of a machined component for which the tolerance limits were 25.00 ± 0.25 mm. The cost of scrapping a nonconforming unit is Rs.4. Construct a histogram, estimate loss per unit part for each size and calculate total loss and average loss for the two batches. Interpret the results.

Batch 1 25.01

24.89

24.98

25.00

24.97

25.04

24.97

24.98

25.01

25.02

25.04

25.01

24.85

25.00

24.97

24.92

25.03

24.98

24.92

25.05

24.90

25.03

25.03

25.02

24.98

24.91

25.01

24.96

25.01

25.10

24.95

24.96

25.02

24.98

24.99

25.10

24.95

25.04

25.06

25.03

24.96

25.03

25.11

25.00

25.04

25.02

25.12

25.01

25.07

25.02

Batch 2 25.09

24.95

24.91

25.02

24.93

25.06

24.87

25.00

25.19

25.18

24.84

25.18

25.16

25.05

25.04

24.99

25.07

24.88

25.01

24.99

24.92

25.01

25.00

24.95

25.04

25.15

25.12

25.11

25.14

25.29

24.72

24.74

24.81

24.90

25.12

24.96

24.99

25.17

25.14

25.11

25.18

24.92

25.09

24.89

24.91

25.18

25.09

25.23

24.72

25.11