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

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

Quality Loss Function

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

Scrap Cost

LSL USLTarget

Cost

Freq.

XTarget USLLSL

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

(Target-oriented)

Sony-US (Conformance-oriented)

Fraction Defective Fallacy

Quality Loss FunctionF

req

uen

cy

Target UpperLower

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

Distribution of Specifications for Products Produced

Conformance-oriented quality keeps products within 3 standard deviations

Lo

ss

High Loss

Low Loss

Unacceptable

Poor

Fair

Good

Best

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

The repair cost for an engine shaft is Rs. 100. The shaft diameter is required to be 101 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 1

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

Quality Loss Function Example 2

Different Quality Loss Functions

i. Smaller-the-better: L(y) = ky2

ii. Larger-the-better: L(y) = k/y2

iii. 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 variationi. External: Variation

in the environment in which the product is used

ii. Unit-to-unit: Variation due to process

iii. Deterioration: Wear and tear due to usage

Process variationi. External: Environment

in which process is carried out

ii. Non-uniformity of the process: Spatial variation in the output

iii. Process drift: Temporal variation in 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

reductioni. Screening out bad productii. Discovering and eliminating the

cause of malfunction (tolerance tightening)

iii. 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

Product / ProcessM

Signal factor

z Noise factors

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-to-unit var.

Drift

Product design

Concept design Y Y YParameter design Y Y YTolerance design Y Y Y

Process design

Concept design N Y NParameter design N Y NTolerance design N Y N

Manufacturing

Detection/ correction N Y NFeed-forward control N Y NScreening N Y N

Usage Warranty / Repair N N N

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