# Open Queuing System

**Question description**

An automotive component has been designed to withstand certain stresses. It is known from past experience that because of variations in loading the stress on the component is normally distributed with a mean of 35000 kPa and a standard deviation of 3000 kPa. The strength of the component is also random because of variations in the material characteristics and the dimensional tolerances. It has been found that the strength is normally distributed with a mean of 40000 KPa and a standard deviation of 4000 kPa. Let x denote the stress on a given component and let y denote the strength of that component. The component does not fail if x is less than y. The Reliability may be expressed as P[X<Y]. Use @Risk to estimate the reliability. One approach is to set up a cell to yield random values of X and another cell to yield random values of Y. Then compute X-Y in a third cell and make it an output cell. From the simulated distribution of X-Y determine the probability that X-Y is less than 0.

A second approach is to compute a binary variable having the value 1 if X<Y and 0 otherwise. The average value of the binary variable will be an estimate of the reliability. Whichever method you choose use 1000 iterations. This problem may be solved analytically but for other distributions than the normal it may not be. The simulation will be valid for any choices of the distributions of stress and strength. The theoretical value for the present case is 84.1%. If you do it correctly your answer should be close to this.

## Tutor Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors