Volume 6, Issue 2

Reliability Edge Home

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 Project Explorer
So where do we start? Let's start with a quick overview of the new Weibull++ interface. Trying to stay true to its roots, the new Weibull++ 7 interface is very similar to and yet more advanced and more flexible than its predecessor. In Version 7, we created an environment where multiple folios and multiple types of folios can be created and saved together as one file. The new format is based on the idea of a "project," which was first introduced in our BlockSim package. Within a project, the analyst can create a variety of data entry forms, use a variety of tools, create a multitude of plots and reports, attach external files such as CAD drawings, Excel files, etc., and save everything together as one file. Figure 1 shows the new interface in which a single project file has multiple folios, plots, special analysis folios, diagrams, reports and attached documents. The user can navigate through these via the Project Explorer panel on the left.

Figure 1: The Weibull++ 7 Interface with Project Explorer

Competing Failure Modes Analysis
Competing Failure Modes (CFM) was a very commonly used analysis type in Weibull++ 6. That option made it easy to analyze data containing multiple failure modes. However, the CFM option had certain limitations. First, it was limited to four failure modes and the same distribution (e.g. Weibull or Lognormal) had to be fitted to all the different modes. Second, the overall reliability was obtained by assuming that all modes are reliability-wise in series. In Weibull++ 7, we took the analysis a step further by allowing the user to create a Reliability Block Diagram (RBD) as part of the project and combine the different failure mode data sets in ANY way to reflect the actual relationships of the modes. The diagram not only calculates the overall reliability based on the RBD, but the uncertainty of the fitted parameters of each data set is also considered in order to calculate confidence bounds on the overall reliability and subsequent metrics. Figure 2 shows the new Diagram utility and one of the available plots for this type of analysis.

Figure 2: Reliability Block Diagram Analysis and Plot

Warranty Analysis
Warranty analysis has been one of the most popular analysis types in Weibull++ 6. When it was introduced, it offered the analyst the means of analyzing data obtained from the field in much less than half the time it would have taken otherwise. The failure distribution and the forecasted failures could be obtained with just a few mouse clicks. In Weibull++ 7, we started the enhancement of this type of analysis by including multiple types of field data entry forms. Specifically, the Warranty Analysis module now includes three different types of data entry forms: the Nevada format, the Times-To-Failure format and the Dates of Failure format. Figure 3 shows the data columns in all three of these forms.

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

Bayesian Analysis
One of the advanced and unique features in Weibull++ 7 is the introduction of Bayesian statistics. Even though this type of analysis represented an almost insignificant amount of requests for enhancement by our customers (less than 0.01% according to our database), we do believe that these methods have many practical applications. All previous versions of Weibull++ explicitly dealt with Classical statistics. With Version 7, we open the door to another school of thought, namely, Bayesian statistics. The whole premise of Bayesian statistics is to incorporate prior knowledge along with a given set of current observations in order to make statistical inferences. Bayesian methods have been incorporated in two ways in Weibull++ 7. First, we have added them as a confidence bounds estimation method, in addition to the existing Fisher Matrix and Likelihood Ratio options. The second application is the Weibull-Bayesian model. As shown in Figure 5, this model considers a distribution and parameters to describe prior knowledge on the beta parameter of the Weibull distribution when it is chosen to be fitted on a given set of data.

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.

Recurrent Events Data Analysis
Another advanced type of analysis included in the new version of Weibull++ is the addition of recurrence data analysis. All previous versions of the Weibull++ software dealt with statistically independent and identically distributed events. In life data analysis, however, there are many cases where events are dependent, not identically distributed (such as data obtained from a repairable system) or where the analyst is interested in modeling the number of occurrences of events over time rather than the length of time prior to the first event (as in a distributional analysis). In Weibull++ 7, non-parametric and parametric approaches are included for analyzing such data. The non-parametric approach is based on the well-known Mean Cumulative Function (MCF) calculation. Our long-time readers may remember the two articles published in the Reliability Edge by Dr. Wayne Nelson on the calculation and applications of MCF.

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

Conclusion
In this article, we have described some of the exciting new features of our Weibull++ 7 software. We hope that you find these features useful, first and foremost, as well as exciting and inspiring. At this point, we would also like to thank you for your continuing support and interest in our products. Your suggestions, comments and ideas over the past years have been an integral part of creating this product. It is a product that is truly designed for reliability engineers by reliability engineers. We hope that it meets and exceeds your expectations. More information is available on the Web at http://www.reliasoft.com/Weibull/version7.htm.