Appendix 2: Product Upgrades Based on Minimum Expected Quality Loss 339
increase in their losses about the point m (Figure A2.4). Therefore, the
resultant quality loss function only has a minimum value when Paretoefficiency is achieved. The range of possible curves (Figure A2.4) can be
determined by applying Bayes’ framework to predict the Pareto-efficient
solution either if the true distribution of past observations is known or if one
computes a universal distribution, defined as the weighted sum of distributions based on the complexity (Hutter 2001). Hutter goes on to prove that by
using a universal probability distribution where lower weights are assigned
to more complex distributions, the universal distribution is nearly as good as
using the unknown true distribution. By applying Hutter’s approach, the
Pareto-efficient solution can be defined.
Outline of the General Quality Loss Function (Choi and
Langford 2008)
Quality Characteristics
To achieve the desired level of quality and to determine the period for
upgrading a product, stakeholders pose the following question—how much
loss can I incur for various upgrade periods? This question can be answered
by considering the results of an analysis based on a general quality loss function. We introduce a shape parameter that governs the amount of losses as a
function of the periodicity, m, for the product upgrade. Since the product
upgrade has competing interests between the user and the developer whose
product is to be upgraded, we present a function which covers nominal-thebetter (NTB).
Traditionally, quality is viewed as a step function that signifies a good
product from a bad product. A good product is distinguishable by achieving
its performance with fewer losses than that of a bad product. This view
assumes that product quality is uniformly good between the lower specification and the upper specification. Sometimes traditional decision makers and
those using Taguchi’s loss function will make the same judgments if both the
positions of the average and the variance as well as the averages are equal
and/or the variances are equal. Both the average performance and variation
from a target value are measures of quality (Taguchi et al. 1989).
The principle of Taguchi quality is based on the observation that customers become increasingly dissatisfied as performance falls further away
from a specified target value. His work with industry over the last 35 years
suggests that a quadratic curve best represents this customer’s dissatisfaction with a product’s performance. When the target value is set to zero, the
first derivative of a Taylor series expansion taken about the target value is
of quadratic form. The best achievable performance at the curve’s minimum is centered on the target value. However, identifying the appropriate
increase in their losses about the point m (Figure A2.4). Therefore, the
resultant quality loss function only has a minimum value when Paretoefficiency is achieved. The range of possible curves (Figure A2.4) can be
determined by applying Bayes’ framework to predict the Pareto-efficient
solution either if the true distribution of past observations is known or if one
computes a universal distribution, defined as the weighted sum of distributions based on the complexity (Hutter 2001). Hutter goes on to prove that by
using a universal probability distribution where lower weights are assigned
to more complex distributions, the universal distribution is nearly as good as
using the unknown true distribution. By applying Hutter’s approach, the
Pareto-efficient solution can be defined.
Outline of the General Quality Loss Function (Choi and
Langford 2008)
Quality Characteristics
To achieve the desired level of quality and to determine the period for
upgrading a product, stakeholders pose the following question—how much
loss can I incur for various upgrade periods? This question can be answered
by considering the results of an analysis based on a general quality loss function. We introduce a shape parameter that governs the amount of losses as a
function of the periodicity, m, for the product upgrade. Since the product
upgrade has competing interests between the user and the developer whose
product is to be upgraded, we present a function which covers nominal-thebetter (NTB).
Traditionally, quality is viewed as a step function that signifies a good
product from a bad product. A good product is distinguishable by achieving
its performance with fewer losses than that of a bad product. This view
assumes that product quality is uniformly good between the lower specification and the upper specification. Sometimes traditional decision makers and
those using Taguchi’s loss function will make the same judgments if both the
positions of the average and the variance as well as the averages are equal
and/or the variances are equal. Both the average performance and variation
from a target value are measures of quality (Taguchi et al. 1989).
The principle of Taguchi quality is based on the observation that customers become increasingly dissatisfied as performance falls further away
from a specified target value. His work with industry over the last 35 years
suggests that a quadratic curve best represents this customer’s dissatisfaction with a product’s performance. When the target value is set to zero, the
first derivative of a Taylor series expansion taken about the target value is
of quadratic form. The best achievable performance at the curve’s minimum is centered on the target value. However, identifying the appropriate