It has been five years since the introduction of Weibull++ 6, a software product so advanced and so ahead of its time that it could have easily remained unchanged for another five years. However, with today's ever-changing environment and customer needs, ReliaSoft saw the need to take a great product and make it even better. Over the past five years, we learned a great deal from our customers and listened to their suggestions and requests. Through our technical support, training courses and consulting, we listened and we learned. Based on the tremendous experience we gained by dealing with a variety of everyday reliability engineering problems and our advanced research that has generated numerous new analysis methods and models (found in many different technical publications), we decided to put all this knowledge into the next generation of Weibull++ software. We looked at every aspect of the software and tried to improve it, starting with the user interface and moving into the different types of data and advanced types of analyses. We looked at the problems that our customers are trying to solve and we came up with advanced solutions and automated processes in order to make the job of the analyst easier, and the solution of complex problems possible. We tried to create an environment where a problem can be analyzed and looked at from many different angles. We tried to create an environment where results can be displayed and presented in a variety of ways, making the process of conveying information and ideas as streamlined and efficient as possible. We tried to create an environment that is easy to use, yet can accommodate a variety of different types of data. We created Weibull++ 7.
In this article, we will point out some of the new and enhanced features of Weibull++ 7. Since the list is very long, we will concentrate on some key features and analyses included in the new version. Look for future articles on advanced analyses and examples using Weibull++ 7 either here in the Reliability Edge or in our online eMagazine, Reliability HotWire. Our long-time readers may notice that some of the features described in this article are methods and models that have previously appeared in these publications. The feedback and interest generated by these articles was a big influence on building this latest iteration of our most popular product. Also, we would like to point out that the motivation of this article is not for marketing purposes, but rather to share the sheer excitement of offering a tool which we believe will answer your reliability analysis needs for years to come. At the end of the day, we are reliability engineers, like you, and we wanted to create a product that would also allow us to do all the different analyses that are either too time-consuming or impossible to do with the current tools.
Enhanced Interface with
Figure 1: The Weibull++ 7 Interface with Project Explorer
Competing Failure Modes
Figure 2: Reliability Block Diagram Analysis and Plot
Figure 3: Data Entry Forms for Warranty Analysis: Nevada, Times-to-Failure and Dates of Failure
On the analysis side, the new Warranty Analysis module offers some unique options. First, the analyst has the option to specify Subset IDs for each data point and analyze the data by Subset ID. This allows for the simultaneous analysis and comparison of different design iterations during the production of a product. At the same time, on the forecasting side of the analysis, new features such as Warranty Length, confidence bounds and a variety of plots were added. Let's take a quick look at these features.
First we will look at the Warranty Length feature. Most of the product warranties given are of a certain duration. This can affect the data analysis in two ways. First, it may reduce the number of failures observed in the field, because in many cases companies do not collect failure information beyond the end of the warranty period. This scenario requires special treatment, which is now included in the Warranty Analysis module in Weibull++ 7. A second consideration when it comes to warranty length is in terms of the forecasted failures. In this case, we need to exclude all the predicted failures that fall outside the warranty period. The user now has the option of including or excluding these failures from the forecast.
The next new feature in the Warranty Analysis module is one of the most requested ones. It involves creating a plot of the forecasted failures that also includes confidence bounds. We answered this request by including several such plots. The analyst now has the option of displaying the forecasted failures as failures per month, as cumulative failures, or as a percentage of the total population, all with confidence bounds. Figure 4 shows one of the available plots.
Figure 4: Expected Failures vs. Period Plot with Confidence Bounds
Figure 5: Bayesian Analysis Assuming a Prior Distribution for Beta
There are many practical applications for this model, particularly when dealing with small sample sizes and some prior knowledge for the shape parameter is available. For example, when a test is performed, there is often a good understanding about the behavior of the failure mode under investigation, primarily through historical data. At the same time, most reliability tests are performed on a limited number of samples. Under these conditions, it would be very useful if we could use this prior knowledge with the goal of making more accurate predictions. A common approach for such scenarios is to use the one-parameter Weibull distribution, but this approach is too deterministic, too absolute you may say (and you would be right). The Weibull-Bayesian model in Weibull++ 7 (which is actually a true "WeiBayes" model, unlike the one-parameter Weibull that is commonly referred to as such) offers an alternative to the one-parameter Weibull by including the variation and uncertainty that we might have observed in the past on the shape parameter. Some initial studies that have been performed by the ReliaSoft R&D group show very promising results using this model.
The parametric approach utilizes the General Renewal Process (GRP) model (which was featured in the last issue of the Reliability Edge). This model provides a way to describe the rate of occurrence of events over time such as in the case of data obtained from a repairable system. This is particularly useful in modeling the failure behavior of a specific system and understanding the effects of the repairs on the age of that system. For example, consider a system that is repaired after a failure. In addition, the repair does not bring the system to an As-Good-As-New or an As-Bad-As-Old condition. In other words, the system is partially rejuvenated after the repair. Traditionally, the failure data from such a system would have been modeled using a homogeneous or non-homogeneous Poisson process. On rare occasions, a Weibull distribution has been used as well (i.e., in cases where the system is almost As-Good-As-New after the repair). However, for the intermediate states after the repair, there has not been a commercially available model, even though many models have been proposed in literature. In Weibull++ 7, the GRP model provides the capability of modeling such systems with partial renewal and allows for a variety of predictions such as reliability, expected failures, etc.
Figure 6: System Data and Fitted Model in the Parametric RDA Module
Figure 7: Predicted System Failures with Confidence Bounds