Bayesian-Based Product Life Cycle Reliability Growth Planning Through Dynamic Programming

In the development process for complex engineering systems,the Reliability Growth Planning(RGP)can provide decision makers with critical decision support information in terms of product release time,reliability evaluation and prediction,and development cost estimation.However,the existing RGP methods have the following main limitations:one is that the uncertainty of the reliability parameters is not well taken into account,which is reflected in a common assumption that the reliability parameters are fixed and obtained by expert opinions or evaluated from a small amount of initial/historical sample data.The above methods usually cannot guarantee the accuracy of parameter evaluation.In addition,it also shows that reliability parameters and external conditions may change during the reliability growth process.In other words,the existing reliability growth planning methods lack the dynamic planning capability.The second is the lack of overall planning for product reliability and various costs at the product life cycle level.Therefore,this paper proposes a product life cycle RGP method through dynamic programming based on Bayesian parameter inference.First,this article explores the applicability and calculation methods of Bayesian parameter inference for reliability growth model,and selects the approximate conjugate prior of reliability parameters through fitting analysis method,which improves the updating mechanism.Then,the effectiveness of the proposed method is verified through simulation and comparative analyses.Secondly,based on the established reliability growth model based on Bayesian parameter inference,a product life cycle RGP model is proposed.In order to find the optimal product release time and the best reliability growth resource allocation,the model takes minimizing the product life cycle cost as the objective function,and quantifies the relationship between the resource allocation for reliability growth process and the product reliability,life cycle costs.Product life cycle costs include the reliability growth test cost,early release incentive or delayed release penalty,and after-sales maintenance service cost.The early release incentive or delayed release penalty is a virtual cost,which measure the impact of product release time on RGP,and balance the reliability growth test cost and product after-sales maintenance service cost to obtain the optimal planning.On the other hand,this thesis establishes the mathematical relationship between the cumulative reliability growth test time and the relevant parameters of the product failure rate curve(starting point,shape and scale parameters)to quantify the influence of early reliability growth on the shape of the failure rate curve,which links the cost of the after-sales maintenance service cost to the reliability growth test cost.Numerical examples and comparable methods have been implemented to illustrate that this model can comprehensively consider product reliability growth from the perspective of product life cycle,and obtain the optimal planning solution.Therefore,this model has more advantages than the traditional RGP model.Finally,this paper combines the above two models to propose the dynamic planning method and corresponding model for product life cycle reliability growth based on Bayesian parameter inference.Through numerical examples,it is verified that this method can realize the dynamic RGP of complex engineering systems,which is more suitable for actual engineering applications and has practical value.