## Product Field-Return

This example illustrates how to calculate field-return distribution, given product failure distribution, and customer usage profile. It demonstrates the applications of Profile Node, User Defined CDF , as well as Time-To-First-Failure simulation in AeROS software. Fig.1 Estimate Failure-Return distribution from Product Failure distribution and Usage Profile

Assumed an in-house test of an improved product demonstrates that its reliability follows Weibull distribution with beta=7, eta= 1000 hours. The test is conducted under constant, high usage rate in order to shorten the reliability test time. The usage stress level for the in-house test is arbitrarily set to 10 stress units/day.

The company conducted a field survey to determine the usage rate behavior of their customers for current product version.

The survey data is summarized as follow:

Explanations:

Row 1: 5 users use 100 (10/0.1) times less frequent than in-house test (light-user).

Row 9: 1 user uses 11.1 (10/0.9) times less frequent than in-house test (heavy-user).

The company wishes to determine the field failure distribution for the new product with this usage profile, and hence estimate the warranty returns on the first year for a given batch sold.

This example uses user define discrete CDF to describe the Flowrate (usage) distribution. 200 random failure times (field-return failures) are generated through Time-To-First-Failure simulation in AeROS software. Life Data Analysis is applied to this Time-To-Failure dataset to obtain the field-return distribution. Fig.3 Profile Node "Usage Stress" in series with a Regular Node "Product"

The Product reliability followings Weibull distribution (Beta=7, Eta=1000 hours) at Design Flowrate (usage stress) = 10 units/day.

The Profile Node “Usage Stress” generates random usage level stress (Flowrate) based on usage distribution (to be defined in following section). The Product will fail according to its distribution with the reduced stress level (Flowrate). This process is repeated to generate field-return dataset.

This example assumes that the in-house test was a usage rate accelerated test. A user in the field is expected to use the product at lower usage rate. This means if the Flowrate (usage rate) reduces from 10 to 1 unit (10 times), the product life increased by 10 times.

The first step is to create a discrete user-defined-CDF, and then apply it to the Flowrate Profile of Usage Stress (Profile Node).

A discrete user-defined-CDF is created using the survey data. Fig.4 The Usage Profile is defined as discrete Cumulative Density Function (CDF)

The next step is to create a Flowrate Profile (a property of Profile Node “Usage Stress” node) that contains only one segment which in turn define flowrate distribution and duration.

The Flowrate Profile Editor is used to create Flowrate Profile.

The flowrate profile is made up of N segments (where N > 0). Each segment defines a flowrate distribution (or a fixed value) and a duration. The time unit is defined when you associate this profile to a Profile Node later (See Fig.7).

"UsageCDF" is assigned the first and only segment of this Flowrate Profile

Flowrate Profile Editor displays the flowrate profile. Fig.6 The Flowrate Profile contains only one segment defined by “UsageCDF”

The vertical axis shows the mean flowrate value of each defined segment. In this case, there is only one segment. This segment flowrate mean value is 0.42, and duration is 100 units time (default value, and the time unit is defined at the Profile Node later). After 100 units time, the Flowrate will remain, since Continue option is selected.

Note that the default Profile Name is “Profile1”.

The next step is to create Profile Node “Usage Stress” and assign Flowrate Profile “Profile1” to it.

A Profile Node is added to the schematic with Duration Unit set to Day and renamed it to “Usage Stress”

The Time Unit is set to Day, which means the units for flowrate and segment duration defined in Profile1 are /Day and Day respectively.

A Regular Node “Product” is created and it Reliability is set to Weibull with Beta=7 and Eta=1000 hours. Both its Max. Flowrate and Design Flowrate are set to 10 units/Day.

Usage Stress node is connected to Product node in series as shown in Fig. 3.

A Simulation (Control Panel->Main tab->Simulation button) is run with the following settings. Fig.8 Using simulation to generate 200 data points using “System Time-To-First-Failure” option

The Time-To-First-Failure Plot shows the simulation results.

The red and green lines represent the Time-To-Failures and Suspensions respectively.

Following is the Time-To-Failure/Suspension data in data-grid format.

Copy the dataset and paste it to a Worksheet in Weibull Toolbox software.

The dataset is fitted with Lognormal distribution using MLE analysis.

Followings are the Probability and PDF plots:

The failure rate behavior of the product in the field is estimated with Lognormal (Log-Mean = 1.011/year, Log-Std 0.4655) distribution.

The percentage of failure-returns one year after a batch is sold can be determine as shown: Fig.14 Probability of failure at first year, Q(1 year) = 0.015

Summary:

This example uses Time-To-First-Failure simulation option to generate field failure dataset. Life Data Analysis is then applied to this dataset to obtain field-return distribution.

-End-