Using RENO to Analyze Hinge Assembly Variability

ReliaSoft > Software > RENO > Examples > Example G-1

	Visual Stochastic Event SimulatorSM Flowchart and solve the most complex probabilistic problems.
	EXAMPLES

Example G-1 - Hinge Assembly Variability

Software Used:
RENO

Problem Statement:

A hinge is made up of four components. Suppose that the part dimensions vary as follows:

A – Normal distribution with mean = 2 and std = .02
B - Normal distribution with mean = 2 and std = .02
C - Normal distribution with mean = 30 and std = .2
D - Normal distribution with mean = 34.5 and std = .5

Determine the expected times that (A+B+C) will be greater than D.

Hinge Assembly
Diagram courtesy of vertex42.com

RENO Solution:

The following general flowchart shows one way that this problem could be solved using simulation.

Conceptual Flowchart

The first step to define this model in RENO is to create definitions for the Random Variables A, B, C and D, as shown next for A.

Random Variable for Component A

This is equivalent to the first requirement in the general flowchart given above.

Then create a flowchart in RENO to model the problem. It includes three steps executed sequentially from left to right (based on the direction of the arrows), as shown next.

Flowchart in RENO

Step 1: Use a Block to compute A+B+C, as shown next.

Use a block to add three Random Variables

Step 2: Use a Conditional Block to see if A+B+C is greater than D, as shown next.

Conditional Block to check whether A+B+C is greater than D

The input from the “Compute A+B+C” Block is passed to the Conditional Block, which in turn checks against the Random Variable D. If true, then it continues the execution by passing 1 to the next construct (as defined for the “Condition is TRUE” input). Note that there is no requirement to include a false path. If a path is omitted, RENO will terminate the current simulation at that point.

Step 3: Use a Result Storage construct to count the number of times that the condition was true, i.e. that A+B+C was greater than D.

Result Storage construct to store a sum of the results

A Result Storage construct stores values across different simulations. In this case, the construct will hold a sum of all the values passed to it; thus at the end of N simulations, it will hold the number of times, M, that the conditional was true.

Note that it is not necessary to create a loop (i.e. an instruction to repeat the steps for N simulations) because RENO is designed to run multiple simulations of a flowchart by default. The number of simulations is specified via the Simulation Console, as shown next.

RENO Simulation Console

When the simulation completes, the results for the storage variable are displayed in the Simulation Results Explorer and in the flowchart, as shown next.

Flowchart with results displayed

Based on 1,000 simulations (using a fixed seed of 1 for repeatability), 16.2% of the time, A+B+C will exceed D. Note that the original flowchart provides the answer as a count, rather than a percentage. A minor modification can create a model that returns the result as a percentage. One approach is to add a Block called “Normalize” and define it as follows:

Block to normalize results (i.e. convert to percentage)

Instead of adding 1 each time the condition is true, this equation specifies to add (1/Number of Simulations))*100, which produces results as a percentage based on all simulations. Note the use of two reserved keywords in this equation. IN represents the value passed to the Block and SIMS_TOTAL returns the total number of simulations.

The modified flowchart and result (16.2%) is shown next.

Modified flowchart with results displayed

A RENO project with the solution for this example (called "Hinge Assembly.rnp") is shipped with the software and stored in the Examples\General folder in the application directory (e.g. C:\Program Files\ReliaSoft\RENO\Examples\General\Hinge Assembly.rnp).

Questions?