# Determining the Connection Between Test and Field Reliability

Software Used

→ ALTA

In last month's HotWire, we discussed an application of categorical variables in accelerated life testing and life-stress analysis. In this issue, we provide another application of categorical variables for comparing test data and field data.

One of the most difficult activities for a reliability engineer is making a quantifiable connection between reliability results from in-house testing and the reliability experienced with items in the field. Often, tests will be performed on products in development in order to make an estimate of the reliability in the field. The results of these tests, however, may not match the actual field performance once the product has been released. In this article, we look at a way of using the proportional hazards model to help quantify an acceleration factor that can link lab and field reliability performance.

## The Proportional Hazards Model

The proportional hazards model is a life-stress relationship used in accelerated testing analysis. One of the advantages of this model is its allowance for indicator variables. Indicator variables are discrete variables, as opposed to continuous variables that may be used to represent temperature, relative humidity, etc. Indicator variables are categorical variables that indicate a discrete state, such as the manufacturing lot from which a sample is drawn. Indicator variables only take on a value of 0 or 1. In the following example, the indicator variable will be used to denote whether a data point is from a laboratory test or from the field.

### Example

To illustrate the process, we have a data set from an in-house test that is supposed to reflect the stresses that the product would see in the field. Based on surveys of customer usage, the test is designed to have the same types of stresses that the product will see in the field. The test is generally regarded to be accelerated in that failures on the test occur more quickly than they do in the field. However, the acceleration factor is unknown and attempts to extrapolate field reliability estimates from the results of the test have been haphazard at best.

We assume that the lab and the field exert different stresses on the product, resulting in different failure times. However, we would also like to be fairly certain that the same failure modes are being exercised as well. Obviously, this could be determined by a failure analysis of all of the failed units. This is not practical in all cases, however, particularly for field failures. Fortunately, there are ways of determining that the assumption of similar failure modes is valid, based on the results of the analysis.

In order to determine the acceleration factor between the test and the field, test data and field data from the same model of the product must be compared. For test data, we have the results of a test in which 10 units were run until failure.

 Time (Hours) 47 50 70 92 97 98 102 110 122 144

For field information, 20 units were selected at random and monitored for field performance. During the course of the monitoring period, the following failures were encountered:

 # of Failures Time (Months) 1 8 1 10 1 11 1 13 1 14 1 16 1 17 2 18 0 19

Note that the time units differ between the in-house test and the field data; the test data set is in hours and the field data set is in months. Rather than try to convert one set of data to the other's time units, we will deal with this discrepancy after the data have been analyzed.

The data will be entered in ReliaSoft's ALTA PRO software, with the environment (lab vs. field) for the stress factor. This will be an indicator variable, with 0 denoting field use and 1 denoting lab testing. With the data entered, the analysis can now be performed using the proportional hazards model.

Once the data set has been analyzed, we should check to make sure that assumptions regarding the nature of the relationship between test lab and field use are valid. Basically, if the same failure modes are being attained at different stress levels, the slope of the Weibull probability plot will be the same at the different stresses. This is shown in the following graphic:

As the plot indicates, the data points for both environments conform closely to the calculated beta value of 3.53. Another way of checking this assumption is to compare contour plots for the two environments. This can be done by analyzing the data sets separately in Weibull++ and creating a multiple contour plot.

The contour plot indicates that the values of eta vary between the two environments, but the beta values fall within the same range. This further supports the assumption that the units are undergoing the same failure modes in both the lab and the field.

With the assumptions supported by the data analysis, we can use ALTA's QCP to calculate the acceleration factor. The results are shown in the next figure:

This indicates that the acceleration factor from stress level 0 (field data) to stress level 1 (lab data) is 4.7. In other words, the units in the field fail 4.7 times faster than the units in the test lab.

While this result initially seems counterintuitive, recall that the time units for the two data sets are different: the lab test times were in hours, while the field data points were in months. Keeping this in mind, we can say that 4.7 hours of time for this particular test is equivalent to one month in the field. We have now quantified the acceleration factor1 between the lab testing and the field, and this information can be used in subsequent reliability calculations.

For example, we can analyze the data in order to determine the time at which five percent (5%) of the units would fail in the lab (i.e., stress = 1).

This shows that five percent of the units in the lab will have failed at 44.38 hours. Since we know that 4.7 hours of lab test time is equivalent to one month of field use, we can say that five percent of the units in the field will have failed at 9.44 months (44.38/4.7 = 9.44). This same value can be obtained in the QCP by changing the stress input to zero (0) and recalculating the result.

1In this case, one can consider this to be a conversion factor as well, since the field units are in months and the lab units are in hours.