Risk aversion in decision models

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Abstract

Risk aversion has formed an integral part in most applied decision models under uncertainty, where the latter is generated by a probabilistic mechanism. This mechanism is not completely known, so that the environment under which decisions are to be made is random. However, the source of randomness may differ from one application to another, hence the decision-making response may vary. For example, in micro-economic models, consumer’s or producer’s response behavior is analyzed under conditions of price or cost parameter uncertainty and this behavior is compared with the case when there is no uncertainty. In engineering systems having a number of channels, the reliability levels may vary between channels and the noise elements may vary: the decision problem is one of maximizing the system reliability. In quality control, a sample inspection plan seeks to determine an acceptable quality level (AQL) of a product lot by minimizing the cost of making wrong decisions, where the latter involves producer’s risk (α) and consumer’s risk (β). The probability that a sampling plan will reject AQL is called the producer’s risk a i.e. the Type I error, whereas the probability that the plan will accept fraction-defective levels (FDL) is called consumer’s riskβ i.e. the Type II error. Usually, if the lot quality is equal to or better than AQL quality, p a is equal to or greater than (1 — α), where p a denotes the probability of acceptance which is usually 0.95 i.e. α = 0.05. Similarly, if the lot quality is equal to or worse than FDL quality, p a is equal to or less thanβ, the Type II decision error and p a is usually 0.10.