Examples provided here are purely for illustrating software features and functionality.

Example R-2 – Reliability Considering Both Failure and Usage Distributions

Software Used: Software Used: ALTA PRO

Download Example File for Version 10 (*.rsgz10) or Version 9 (*.rsr9)

Problem Statement:

Consider the case of a washing machine that can have varied loads:

• Using a 10-pound load, the washing machine fails according to a Weibull distribution with beta = 3 and eta = 2,500 hours.
• Using a 5-pound load, the washing machine fails according to a Weibull distribution with beta = 3 and eta = 10,000 hours.

Assuming that customer loads vary from 2 to 8 pounds, the expected load in the field can be described by a normal distribution with mean = 5 and std = 1 pound.

Objectives

• Estimate the reliability of the washing machine for 2,000 hours of operation in the field.
• Create a plot of the expected reliability vs. time from 1,000 to 10,000 hours (using 1,000 hour increments).
• Generate a data set of times to failure for subsequent life data analysis in Weibull++.

Define the Resources

Let us assume that the effect of load weight on the life of the washing machine is described by an inverse power life-stress relationship:

where L is the life of the machine and V is the load. The constants K and n can be obtained by solving for the equation based on the given conditions: L(V=5) = 10,000 and L(V=10) = 2,500. Therefore, K = 0.000004 and n = 2.

(See also http://reliawiki.org/index.php/Inverse_Power_Law_Relationship for more information about the inverse power law model.)

Create a model to describe the variations in customer loads, as shown next.

Create RENO static functions to describe the life-stress relationship (LSR) and the failure time of the washing machine based on this relationship.

Here, LSR uses the RENO internal function called “rvm” to return a random value based on the UsageLoad model.

FailureTime uses the internal function called “rv_weibull” to return a random time to failure based on the washing machine’s failure distribution. This function returns the inverse of the Weibull cumulative distribution with the specified parameters for the specified probability. In this case, we want the function to return a random value. To do this, we use the predefined function called “rand” as the function’s probability value, and then we enter the following parameters for the distribution: 3 (beta), the variable LSR (eta) and 0 (gamma).

Estimate the Reliability at 2,000 Hours

To estimate the reliability at 2,000 hours, create the flowchart shown below.

In this example, the standard block uses FailureTime to obtain a random time to failure based on customer load.

The conditional block evaluates whether the failure time (obtained from the previous block) occurred before the time of interest (the variable called “Life,” which was set to 2,000).

Create a Plot of the Expected Reliability vs. Time from 1,000 to 10,000 Hours (Using 1,000 Hour Increments)

You can use the sensitivity analysis feature to create a plot that shows how the reliability varies over time.

In the RENO Simulation window, keep the same number of simulations (10,000) and seed (1). Then on the Sensitivity Analysis tab, specify to vary the Life variable from 1,000 to 10,000 hours, with increments of 1,000 hours, as shown below.

With these settings, RENO will perform 10 runs with 10,000 simulations in each run. The first run will calculate the results with the Life variable set at 1,000 hours, the second at 2,000 hours, and so on.

The following picture shows a plot of the reliability from 1,000 to 10,000 hours.

Generate a Data Set of Times to Failure for Subsequent Life Data Analysis in Weibull++

To generate a set of times-to-failure data that can be used for subsequent life data analysis, construct the flowchart shown below.

Here, the result storage block is configured to store an array of the failure times obtained by the standard block, as shown next.

Run 1,000 simulation with a seed of 1 for repeatability. Once the simulation completes, click the Details button in the RENO Simulation window to open the Simulation Results Explorer. Select the result storage block to display the stored values, as shown below.

You can transfer your data from RENO to a Weibull++ standard folio for further life data analysis by selecting the cells that contain the data and then clicking the Send Selection to Weibull++ icon on the Ribbon.