By Thabane L.

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**Additional info for A closer look at the distribution of number needed to treat (NNT) a Bayesian approach (2003)(en)(6s)**

**Example text**

For example, we could inspect and then decide whether to sell the product (Exercise 3). This often leads to tolerance settings and is the focus of much of quality control. The general stochastic program provides a framework for uniting design and quality control. Many loss functions can be used to measure performance degradation to help improve designs in their initial stages. These functions may include the stress and performance penalties described earlier, the Taguchi-type quadratic loss, or methods based on reliability characterizations.

0719, x ¯(ξ) ¯ x ¯, ξ) At ﬁrst glance, it appears that this solution obtains a better expected proﬁt than the stochastic problem solution. However, as we shall see in Chapter 9 on approximations, this deterministic problem paints an overly optimistic picture of the actual situation. The deterministic objective is (in the case of concave maximization) always an overestimate of the actual expected proﬁt. 79. 73. In other words, solving the stochastic program yields z ∗ − z(w, an expected proﬁt increase over solving the deterministic problem.

The eight scenarios are represented by the tree in Figure 3. The scenario tree divides into branches corresponding to diﬀerent realizations of the random returns. Because Scenarios 1 to 4, for example, have the same 22 1. Introduction and Examples FIGURE 3. Tree of scenarios for three periods. 2 Financial Planning and Control 23 return for t = 1, they all follow the same ﬁrst branch. Scenarios 1 and 2 then have the same second branch and ﬁnally divide completely in the last period. To show this more explicitly, we may refer to each scenario by the history of returns indexed by st for periods t = 1, 2, 3 as indicated on the tree in Figure 3.