Warranty prediction for parts with design changes

• Published in: 2017 Annual Reliability and Maintainability Symposium (RAMS) pp. 1 - 4
• Main Authors: Szidarovszky, Miklos, Guo, Huairui Harry, Szidarovszky, Ferenc, Hijawi, Mohammad
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2017
• Subjects: Maintenance engineering; Mathematical model; Modelling Design Changes; Reliability engineering; Reliability theory; Warranties; Warranty Predictions
• DOI: 10.1109/RAM.2017.7889734

Warranty prediction is a very important task in reliability engineering. It needs to estimate the expected number of failures in any given time period during the length of the warranty contract. Several commercial software packages have been already implemented and used in the industry, including Minitab and Weibull++. The time to failure is usually selected to be a Weibull distribution and no technology improvement in the manufacturing process or in the product design is assumed. This paper introduces a new mathematical model which provides the requested predictions under much more general conditions. It is very common that the design and the manufacturing process of an item will change to fix issues discovered in the field. These changes will result in the change of the failure behavior which is often modeled by a time to failure distribution such as Weibull. In our model we consider a manufacturing plant producing identical items in given numbers during each time period. They are subject to possible failures in any later time period after they are produced and the replacements also can fail later as newly produced items. It is assumed that at a given later time, the technology changes so the time to failure distribution also changes, and all items which are replaced or produced from this time period will follow the new time to failure distribution. In order to plan appropriate inventory strategy it is necessary to predict the expected total number of failures in every time period during the considered warranty time interval. In computing the total number of failures the cumulative effect of the failures of new items as well as those of their possible replacements have to be considered and taken into account. A mathematical model is first introduced, where, for the sake of simplicity, it is assumed that after introducing the new technology the produced or replaced items will no longer fail. The general case can be, however, considered and solved in a similar way. In addition to an analytic solution methodology a simulation study is presented. The Weibull distribution is used in the numerical example, however, it can be replaced with any other distribution type. It is demonstrated that the usual prediction method can be successfully extended into cases when the improvement of the production technology changes the distribution of the time to failure, and therefore the probabilistic properties of all items produced or replaced after this change are also changed. The expectation of the cumulative number of failures in each time period provides important help in finding the most appropriate inventory strategies leading to significant savings in inventory cost as well as in the cost of delayed services.