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# Designing a shaft support using decision tree

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Designing a shaft support has two options: using a pair of single row ball (SRB) bearing with a purchasing cost of \$25, or using a pair of cylindrical roller bearing (CRB) with a purchasing cost \$70. If selecting SRB, it will fail (within a specified life) with a probability 25%, and when it fails, it can fail in three forms (failure modes): failure in mode 1 (m1) with a chance of 0.2, in mode 2 (m2) 0.5, and in mode 3 (m3) 0.3. The damaging cost depends on the failure mode: \$40 for failure in m1, \$50 in m2, and \$30 in m3. Assuming that when using CRB, the chance of failure is zero. Develop a decision tree for the problem, calculate the expected cost of each decision option and identify the best option.

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This solution helps design a shaft support using a decision tree. The explanation is given in an Excel spreadsheet along with a diagram.

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• BE, Bangalore University, India
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