Chapter 17 – The Management and Control of Quality
17-42 (Continued)
X Probability, f(x) x*f(x) (x – 0.199991) 2
f(x)
0.1996 0.02 0.003992 0.00000000305762
0.1997 0.05 0.009985 0.00000000423405
0.1998 0.12 0.023976 0.00000000437772
0.1999 0.11 0.021989 0.00000000091091
0.2000 0.45 0.090000 0.00000000003645
0.2001 0.10 0.020010 0.00000000118810
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Chapter 17 – The Management and Control of Quality
17-43 Using Taguchi Function to Determine Tolerance (15 Minutes)
Total quality cost = k(Tolerance),2 where k = cost coefficient, and Tolerance = quality
tolerance allowed
$40.00 = k(0.0001)2
k = $4,000,000,000
The loss function, L(x), is therefore
Note: Tolerance, T, can be calculated using the following four-step process:
Chapter 17 – The Management and Control of Quality
17-44 Taguchi Loss Function [L(x)] Analysis (15 Minutes)
1. a.
L(x) = k(x − T)2
$150 = k (0.0025)2 = k (0.00000625)
b. L(x = 0.1893) = $24,000,000 × (0.1893 − 0.1875)2
2. a. Total quality cost, L(x) = k(Tolerance)2
$6 = $24,000,000(Tolerance)2
b. The specification should therefore be set as:
17-24
Education.
Quality
Revenues/
Costs
Revenues
Costs
Maximum quality level
(e.g., zero defects)
Maximum
Profit
Level
Chapter 17 – The Management and Control of Quality
17-45 Graphical Depiction: Is there an Optimal Level of Spending on Quality, or, Is
Quality “Free”? (40 Minutes)
“Quality is Free” Representation
Interpretation: Under this conceptualization, profit maximization occurs under only
when “total” (i.e., maximum) quality-levels are achieved for the organization’s
outputs. This view is based on a premise that customers seek the highest-quality
products and services and are willing to pay for this level of quality, even if at a
17-25
Education.
Failure
Costs
Prevention &
Appraisal Costs
Total
Cost of
Quality
Chapter 17 – The Management and Control of Quality
17-45 (Continued-1)
Diminishing-Returns Conceptualization
Interpretation: This conceptualization for spending on quality assumes a trade-off
between the costs and financial benefits of improving quality. As compared to the
previous graph, the one above suggests that optimum profits are obtained at a quality
17-26
Cost of
Quality
Revenues & Costs
Total
Costs
Total
Chapter 17 – The Management and Control of Quality
17-45 (Continued-2)
Diminishing Returns Conceptualization: Trading Off Costs and
Benefits for Spending on Quality
Basically, the above representation assumes that after a point, increases in quality spending
do not generate commensurate financial benefits (marginal revenues). The “quality
is free” argument would hold that marginal revenues always exceed marginal costs.
17-27
Education.
17-46 COQ Histograms; Spreadsheet Application (30 minutes)
1. COQ Histogram
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
Genova Company: Cost of Quality as % of Cost of Goods Sold: 2016-2018
2016 2017 2018
2. Cost of Quality (COQ) as Percentage of Costs of Goods Sold (CGS):
2016 2017 2018
Prevention Costs 1.00% 4.00% 2.00%
Appraisal Costs 3.00% 2.50% 1.50%
Internal Failure Costs 27.00% 23.00% 14.00%
the years.
Total COQ as a percentage of CGS decreased from 62.0 percent to 29.5 percent.
17-46 (continued)
17-28
Education.
3. The company can probably expect its total cost of quality to continue declining
provided it maintains adequate level of quality training and other efforts to prevent
poor quality from occurring and to continue emphasis on the importance of quality.
The company was able to see the results within one year of increased efforts in
Chapter 17 – The Management and Control of Quality
17-47 Quality Cost Classification (10 minutes)
1. Internal failure cost
2. Internal failure cost
17-30
Chapter 17 – The Management and Control of Quality
17-48 Cost-of-Quality (COQ) Reporting for Environmental Performance (30 Minutes)
The purpose of this exercise is to get students to think strategically as to how COQ
reporting might be used as part of a comprehensive approach to the management
and control of environmental costs.
1. As global natural resources become more scarce, and therefore subject to
increasing demand, society may demand greater accountability as to the
2. There is no set answer to this part of the assignment, but student samples might
include some of the following elements:
Prevention Costs:
Process design/redesign (to produce environmentally friendly outputs)
Product design/redesign (to consume fewer natural resources, emit fewer
by-products and pollutants, etc.)
Development of environmental performance standards
Internal Failure Costs:
Treating/Disposing of Toxic Materials
Maintaining Pollution-Control Equipment
17-31
Education.