Optimal Burn-in And Allocation Policies For Heterogeneous Items

In reality,items produced by manufacturers are usually heterogeneous due to environmental,material,mechanical,and human factors.How to burn-in and allocate items to improve the reliability of items and their compose systems has been a hot topic in the field of reliability.However,there are only a few studies that consider the heterogeneity of items in burn-in and allocation problems.This thesis primarily focuses on the burn-in problem of heterogeneous items under a two-dimensional warranty and the allocation problem of heterogeneous items in simple systems.The contents of this thesis are organized as follows:1.We study the failure-based burn-in problem of heterogeneous items and propose two failure-based burn-in models.The failure-based burn-in model screens items based on their failure information during the burn-in to improve the reliability of items passed burn-in.In the first model,we consider that the items have a non-renewing two-dimensional combination warranty and the items are not repairable during burn-in.Then we establish the objective functions considering performance and cost.The second model discusses that the items have a non-renewing two-dimensional free warranty and the failures of items are repaired by the minimal repair during burn-in and warranty.Then we establish an objective function considering cost to reduce the expected total cost per sold item.We analyse the properties of the optimal policies of the two models and derive the sufficient conditions for the optimal burn-in time or the optimal usage rate reaching its upper bound.Furthermore,we conduct a comparative analysis of the optimal burn-in policies across various objective functions for the first model.Additionally,we examine the distinctions between the failure rate function and the strength function.For the second model,we present a Bayesian approach to update the parameters of the model by combining prior knowledge and observed data.And then we will obtain a more accurate and reliable optimal burn-in policy.Finally,numerical examples of the two models are conducted to demonstrate our models and results.2.We investigate the degradation-based burn-in problem of heterogeneous items and propose two degradation-based burn-in models.The degradation-based burn-in model screens items based on the amount of degradation at the end of burn-in to improve the reliability of items passed burn-in.One model considers that the items have a non-renewing twodimensional free warranty and the failures of item during the warranty period are repaired by the minimal repair.Then we establish the objective functions considering performance,cost,and profit,where the degradation of the item is described by the Gamma process.The other model considers that the items have a renewing two-dimensional free warranty.Then we establish an objective function considering cost,where the degradation of the item is described by the inverse Gaussian process.We analyse the properties of the optimal policies of the two models and give the sufficient conditions for the optimal burn-in time or the optimal usage rate reaching its upper bound.Furthermore,we conduct a comparative analysis of the optimal burn-in policies across various objective functions for the first model.For the second model,we propose a Bayesian approach to update the parameters of the model parameters according to prior knowledge and observed data.And then we gain a more accurate and reliable optimal burn-in policy.Finally,numerical examples of the two models are conducted to demonstrate our models and results.3.We study the allocation problem of redundant items in a k-out-of-nsystem and the allocation problem of items in series and parallel systems under random shock environments,where the items come from a heterogeneous population which is composed of different subpopulations.The k-out-of-nsystem with nindependent and differently distributed system components is allocated a certain number of redundant items to enhance the system performance.For series and parallel systems,we consider the allocation problem of system items under extreme and cumulative shock models,where the arrival of shocks is modeled by a nonhomogeneous Poisson process.Initially,the system performance under any two allocation policies is compared using majorization and stochastic order theories.Subsequently the optimal policy for item allocation is determined.Then,the effect of items heterogeneity on the performance indexes(reliability,failure rate,etc)of the systems is analyzed.Finally,some numerical examples are given to illustrate the applicability and necessity of the conditions in the relevant results.