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Assessing the Value of Information for Comparing Multiple, Dependent Design Alternatives

Capser, Shawn Patrick, Capser
http://rave.ohiolink.edu/etdc/view?acc_num=toledo1520689318651851

Abstract Details

2018, Doctor of Philosophy, University of Toledo, Engineering.
Design optimization occurs through a series of decisions that are a standard part of the product development process. Decisions are made anywhere from concept selection to the design of the assembly and manufacturing processes. The effectiveness of these decisions is based on the information available to the decision maker. Decision analysis provides a structured approach for quantifying the value of information that may be obtained in support of the decision-making problem. The presentation of this research and related examples are primarily focused in the area reliability, where the decision maker will be concerned with such metrics as the probability of failure for a simple component or the failure rate of much larger repairable systems. The research set out to demonstrate the approach of determining the value of information for both such cases, allowing the decision maker to use the same fundamental algorithms for addressing a large number decision-making problems based on di erent random variables of interest. This dissertation addresses a critical part of the decision-making problem which is to provide a means for evaluating the value of information, a.k.a. the value of research. and, in turn, help to optimize the decision analysis e ort. It aims at helping the decision maker determines the point of `diminishing return' on their investment in research and determining when obtaining more information will no longer provide value to making the best choice of the alternatives. The research further targets a very speci c situation of the decision making prob- lem, which is the case when the decision alternatives are linearly and statistically dependent. Having dependent alternatives implies that as the decision maker ob- tains information on one alternative, the decision maker can infer some level of per- formance of the other alternative(s). In this case determining the value of information or value of research is viewed as a sample size determination problem. The research presented here addresses the specifi c question of \How many observations must be made in order to maximize the expected utility of our decision? ". Answering the above question becomes a challenge when the decision alternatives cannot be treated as independent, because of a single observation on each of the dif- ferent alternatives does not provide the same level of information as if they were independent. For this reason, if the decision maker were to assume independence, then he/she would overestimate the expected utility of the decision. This research focused on accounting for the level of correlation that exists between the decision alternatives; which allows for a more appropriate estimation in the expected utility of the decision. The situation of evaluating dependent decision alternatives is not typically ad- dressed using a frequentist approach for sample size determination. As such, the research presents an approach that applies a Bayesian probability model that not only accounts for the dependent decision alternatives but also allows the decision- making process to incorporate subjective statements with regards to the behavior of di erent decision alternatives before the start of the data collection e ort. The application of a utility function in conjunction with the Bayesian probability model provides a means for determining the expected utility for varying assumptions in the observations sizes. In doing so, we can produce curves showing the change in the expected utility, i.e. value of information, as a function of increasing observation size. The curve for the expected utility versus observation sizes then provides the decision maker with insight as to the appropriate sample size that can be a orded to maximize the information of the decision and minimize the risk of the decision-making problem. The application of the Bayesian probability model to the value of information problem with correlated alternatives required a means to develop a joint prior density that properly represented the combined density of the random variables with each of the decision alternatives. The dissertation uses a Copula density to de ne the joint prior. The copula is used to \couple" the marginal densities that are the subjective prior for each random variable associated with the decision alternatives. The rst part of the research utilizes a Guassian copula to develop a joint prior for the marginal densities associated with the failure probabilities of the design alternatives. Further into the dissertation, consideration is given to the application of the Archimedean family of copulas. Frank's, Clayton's and Gumbel's copulas are dis- cussed as alternatives describing the statistical dependencies between decision alter- natives. The research presented in this dissertation recognizes the e ort in applying the Bayesian probability model as being computation costly when the number of decision alternative increase beyond 3. To manage these computational costs the use of the Metropolis-Hasting algorithm is introduced and is proven to be a far more ecient means of calculating the posterior densities over that of directly applying numerical integration techniques to the Bayesian probability model. Examples are presented that demonstrate the use of the Metropolis-Hasting's algorithm for cases with 2, 3, and 10 design alternatives. The results demonstrated that the algorithm presented in this research is capable of managing decisions with a large number of dependent alternatives with minimal impact on computational cost. The rst part of the research presented theory and example where the parameter of correlation was taken to be known by the decision-maker for each pair or combination of decision alternatives. The later part of the research focused on the case where the degree of statistical dependency is uncertain. In this case the correlation was taken to be an additional random variable, just as the failure probability or failure rate. In this case, the correlation was given a probability density that became part of the subjective joint prior. An example is presented that addresses the value of information problem when comparing failure rate of two repairable systems when the correlation is uncertain. The research also presents the ability to account for the physical cost of collecting the information, whether through simulation, testing, measurement, etc. The research ends with a more `real-world' example, where the decision-maker takes into account the actual costs of obtaining the information. It is shown that this cost has a direct in uence on the expected utility and the choice of the best sample size. The dissertation presents an algorithm for determining the value of information as a function of the choice of sample size and o ers the decision maker an ecient means for determining the maximum investment needed to minimize the risk of the decisions. This algorithm is developed into an ecient script using R.
Efstratios Nikolaidis (Committee Chair)
Sarit Bhaduri (Committee Member)
Matthew Franchetti (Committee Member)
Nikolaidis Haselgruber (Committee Member)
Vijitashwa Pandey (Committee Member)
179 p.
Engineering
Reliability, Decision Analysis, Bayesian, Utility, Expected Utility, Expected Utility with Perfect Information, Expected Utility with No Information

Recommended Citations

Citations

  • Capser, Capser, S. P. (2018). Assessing the Value of Information for Comparing Multiple, Dependent Design Alternatives [Doctoral dissertation, University of Toledo]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1520689318651851

    APA Style (7th edition)

  • Capser, Capser, Shawn. Assessing the Value of Information for Comparing Multiple, Dependent Design Alternatives. 2018. University of Toledo, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=toledo1520689318651851.

    MLA Style (8th edition)

  • Capser, Capser, Shawn. "Assessing the Value of Information for Comparing Multiple, Dependent Design Alternatives." Doctoral dissertation, University of Toledo, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1520689318651851

    Chicago Manual of Style (17th edition)

toledo1520689318651851
295
© 2018, some rights reserved.Creative Commons License Assessing the Value of Information for Comparing Multiple, Dependent Design Alternatives by Shawn Patrick Capser Capser is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Toledo and OhioLINK.