17-42 Taguchi Loss Function (QLF) Analysis (50 Minutes)
1. Value of k, the cost coefficient in the Taguchi Quality Loss Function, L(x):
L(x) = k(x − T)
2
k = $20 ÷ 0.0002
2
= $20 ÷ 0.00000004 = $500,000,000 (rounded to the nearest
whole dollar)
2a & b. Estimated Quality Loss (to two decimal places) for Each Observed
Measurement and Expected (Average) Loss for the Production Process:
3.
a.
Calculations based on Albrecht and Roth, “The Measurement of Quality
Costs: An Alternative Paradigm,” Accounting Horizons (June 1992), pp. 15–27
(see text Exhibit 17.7 and footnote #11 in Chapter 17):
D = square of the deviation of the mean value of x from the targeted value, T
2
The mean value of x,
, is 0.199991 (see table below); T = 0.2 (given)
Therefore:
D = (0.199991 − 0.2)
2
2
= -0.000009
2
= 0.000000000081
b.
(rounded to 12 decimal places)
the variance (σ ) of the observed values of the quality characteristic, x,
around the mean value of x, denoted x-bar
2
from requirement 3(a) above (and the table below), we have the mean value
of x (x-bar) = 0.199991
therefore,
σ = ∑ (x − 0.199991) f(x)
2
2
= 0.000000025419 (rounded to 12 decimal places)
c.
Expected (average) loss per unit = k( + D )
2
2
= $500,000,000 × (0.000000025419 +
0.000000000081)
= $12.75 (rounded to two decimal places)
Calculations for Requirements 3a and 3b
X
Probability, f(x)
x*f(x)
(x − 0.199991) f(x)
2
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
0.2002
0.08
0.016016
0.00000000349448
0.2003
0.05
0.010015
0.00000000477405
0.2004
0.02
0.004008
0.00000000334562
0.199991
0.00000002541900
Note:
x = 0.199991 (rounded to six decimal places)
σ = 0.000000025419 (rounded to 12 decimal places)
2
17-49 Cost-of-Quality (COQ) Report: Environmental Management (30 Minutes)
1. Sample Cost of Environmental Quality Report:
% of Total
Operating
Amounts
Subtotals
Cost
Prevention Costs:
Employee training $100,000
Product design
140,000
Supplier certification 40,000 $280,000 2.8%
Appraisal Costs:
Process inspection
$320,000
3.2%
Internal Failure Costs:
Depreciation—pollutioncontrol equipment $400,000
Maintaining pollutioncontrol equipment 200,000
$600,000 6.0%
External Failure Costs:
Lake clean-up
$500,000
Land restoration
700,000
Property-damage claim 600,000
$1,800,000
18.0%
Totals
$3,000,000 30.0%
2. With only a single year of data, it is difficult to draw any meaningful
conclusions. However, a tentative conclusion is that the company may be
spending far too little in the conformance quality area (i.e., Prevention and
Appraisal Costs) and, therefore, is incurring significant failure costs in the
environmental area.
3. Some qualities (attributes) of an effective (“good”) environmental quality
cost system:

Collect environmental quality-cost data from across the value chain
(i.e., the scope of data collection should be broad).

If possible, utilize activity-based cost (ABC) data, which could be
used to motivate (a) the elimination of non-value-added activities and
(b) improved efficiency in the conduct of value-added activities.

Incorporates baseline data: environmental cost data should be
compared to one or more relevant benchmarks (sales, best-in-class
performance, etc.).

Reflects time-series results (data from a single period are not likely
to be very informative and, in fact, can be misleading; the provision
of time-series data will inform management as to the success in
reducing total spending in the environmental cost area and trade-offs
between and among categories).
17-53 Cost of Quality (COQ) Reporting (40 minutes)
1. Category percentages, rounded to two (2) decimal places:
$ Amount
Prevention Costs:
Quality training
New vendor verification and facilities
inspection
Technical support provided to
vendors
Subtotal
Appraisal Costs:
Field test of new computer
Equipment inspection
Test and inspection of purchased
parts
Subtotal
Internal Failure Costs:
Spoiled work-in-process inventory
disposal
% of
Total
% of
Sales
13.40%
0.98%
41.18%
3.00%
$12,000
25,000
4,000
$41,000
$74,000
20,000
32,000
$126,000
$28,000
Downtime, due to quality problems
Re-inspection
Rework (labor and overhead)
Subtotal
External Failure Costs:
Support of a customer complaint
department
Product liability insurance
Warranty repairs
Subtotal
Total Quality Costs (COQ)
Total Sales
24,000
13,000
8,000
$73,000
23.86%
1.74%
21.57%
100.00%
1.57%
7.29%
$26,000
18,000
22,000
$66,000
$306,000
$4,200,000
100.00%
2. Note that it is dangerous to draw conclusions based on results from just a single
year. Nonetheless, the following observations seem relevant:
a. The company in question may not be spending sufficiently in the area of
prevention costs, while (perhaps) overspending on appraisal costs.
b. In spite of what seems like high spending on appraisal activities, the company
seems to still be experiencing significant failure costs.
c. The mix between conformance costs (prevention plus appraisal) vs.
nonconformance costs (internal failure plus external failure) seems out of
balance; in terms of the latter, 45% of total COQ seems excessive.
d. total spending on quality (i.e., total COQ) of ~7% of sales seems good; some
feel that COQ spending by world-class performers is about 5-10% of sales
dollars; given the above observations, a question might therefore be raised as
to whether there are some measures of COQ that have not been included in
the above report.
Finally, note that benchmarking the results of this company to a relevant standard
would be desirable.
3. There are at least four primary limitations to the COQ report illustrated in the
present exercise: (a) the COQ report provides data for only a single period; timeseries data (multiple observations over time) would be more informative (in part this
is because there is typically a lagged relationship between spending in quality-related
projects and improved COQ performance); (b) the cost data show the results of
quality-related issues but not the underlying causes of poor quality outputs—to
improve future quality requires managerial action and follow-up (put another way,
quality does not improve by the mere process of measuring quality-related costs); (c)
determining trade-offs across categories and an optimum amount of quality-related
costs is partly subjective—as noted above, benchmarking may be helpful in terms of
resolving these issues; and (d) what some would be considered the most important
quality cost (viz., lost sales arising from customers ill will), is usually omitted from
COQ report because this cost is an opportunity cost and therefore difficult to
estimate.