A method for reliability growth analysis combined over multiple stages

Anne Elizabeth McLaren, Purdue University


We propose a reliability growth model that incorporates data from multiple stages of testing and acknowledges fixes implemented at the end of each stage. Competitive pressure and governmental regulations compress the time that can be devoted to product development. Limitations on budgets for testing drive the need for reliability growth models that combine both older and more recent data. Most existing models are single stage, either using data from the immediately preceding test period only or treating the entire development program as one stage. This model extends the projection aspect of existing single stage models and incorporates the author’s contribution to combine all previous stages in order to estimate current and predict next stage failure intensities based on failure and corrective action data. The framework is an iterative process that blends new test results with previous stages, corrects for unseen failure intensity, and incorporates fixes to seen failure modes. Although the research focuses on two- and three-stage cases, the proposed framework could extend for as many stages (r) as there are for testing, plus a prediction for stage r+1, generally referred to as production. Model performance is evaluated by comparing the mean square errors of proposed multistage estimators and predictors of failure intensity to those of existing single stage models. First, analytical calculations are used for tractable estimators and predictors. Later, simulated data are employed for all estimators and predictors. The estimators and predictors are applied to three real-life datasets to prototype this framework and test its practical applicability. Our multistage formulation for estimating the current stage’s failure intensity has a smaller mean square error than the classical single-stage observed estimator. Under practical combinations of design parameter values, the multistage predictor has a smaller mean square error than the next-stage predictor. Comparison among the three proposed multistage alternatives presented in this work indicates that the simplest and most tractable also has the smallest mean square error. Thus, we recommend the McLaren:Ross multistage estimators and predictors. This research has implications for any organization involved in multiple stages of product development testing and improvement.




Wan, Purdue University.

Subject Area

Industrial engineering|Operations research

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