A geometric process warranty model using a combination policy

This paper proposes a geometric process warranty model. Assume that a combination policy (W, T) is applied after selling a product, so that a free warranty is offered in [0, W), followed by a pro-rata warranty in [W, T). Assume further the successive operating times (repair times) of the product form a decreasing (increasing) geometric process. The average cost rate of the product to the manufacturer and a consumer can be derived respectively. For exponential distribution case, the explicit formulas of the average cost rate are obtained, and an finite algorithm for determination of an optimal combination policy is suggested.     

Optimum reliability acceptance sampling plans under progressive type-I interval censoring with random removal using a cost model

A reliability acceptance sampling plan (RASP) is a variable sampling plan, which is used for lot sentencing based on the lifetime of the product under consideration. If a good lot is rejected then there is a loss of sales, whereas if a bad lot is accepted then the post sale cost increases and the brand image of the product is affected. Since cost is an important decision-making factor, adopting an economically optimal RASP is indispensable. This work considers the determination of an asymptotically optimum RASP under progressive type-I interval censoring scheme with random removal (PICR-I). We formulate a decision model for lot sentencing and a cost function is proposed that quantifies the losses. The cost function includes the cost of conducting the life test and warranty cost when the lot is accepted, and the cost of batch disposition when it is rejected. The asymptotically optimal RASP is obtained by minimizing the Bayes risk in a set of decision rules based on the maximum likelihood estimator of the mean lifetime of the items in the lot. For numerical illustration, we consider that lifetimes follow exponential or Weibull distributions.     

Two-dimensional Renewal Function Approximation

Two-dimensional renewal functions, which are naturally extensions of one-dimensional renewal functions, have wide applicability in areas where two random variables are needed to characterize the underlying process. These functions satisfy the renewal equation, which is not amenable for analytical solutions. This paper proposes a simple approximation for the computation of the two- dimensional renewal function based only on the first two moments and the correlation coefficient of the variables. The approximation yields exact values of renewal function for bivariate exponential distribution function. Illustrations are presented to compare our approximation with that of Iskandar (1991) who provided a computational procedure which requires the use of the bivariate distribution function of the two variables. A two-dimensional warranty model is used to illustrate the approximation.     

Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.     

Estimating the Cost of a Warranty

The cost of certain types of warranties is closely related to functions that arise in renewal theory. The problem of estimating the warranty cost for a random sample of size n can be reduced to estimating these functions. In an earlier paper, I gave several methods of estimating the expected number of renewals, called the renewal function. This answered an important accounting question of how to arrive at a good approximation of the expected warranty cost. In this article, estimation of the renewal function is reviewed and several extensions are given. In particular, a resampling estimator of the renewal function is introduced. Further, I argue that managers may wish to examine other summary measures of the warranty cost, in particular the variability. To estimate this variability, I introduce estimators, both parametric and nonparametric, of the variance associated with the number of renewals. Several numerical examples are provided.     

Adaptive Sequential Preventive Maintenance Policy and Bayesian Consideration

This article proposes an adaptive sequential preventive maintenance (PM) policy for which an improvement factor is newly introduced to measure the PM effect at each PM. For this model, the PM actions are conducted at different time intervals so that an adaptive method needs to be utilized to determine the optimal PM times minimizing the expected cost rate per unit time. At each PM, the hazard rate is reduced by an amount affected by the improvement factor which depends on the number of PM's preceding the current one. We derive mathematical formulas to evaluate the expected cost rate per unit time by incorporating the PM cost, repair cost, and replacement cost. Assuming that the failure times follow a Weibull distribution, we propose an optimal sequential PM policy by minimizing the expected cost rate. Furthermore, we consider Bayesian aspects for the sequential PM policy to discuss its optimality. The effect of some parameters and the functional forms of improvement factor on the optimal PM policy is measured numerically by sensibility analysis and some numerical examples are presented for illustrative purposes.     

Methods for the estimation of failure distributions and rates from automobile warranty data

We consider the occurrence of warranty claims for automobiles when both age and mileage accumulation may affect failure. The presence of both age and mileage limits on warranties creates interesting problems for the analysis of failures. We propose a family of models that relates failure to time and mileage accumulation. Methods for fitting the models based on warranty data and supplementary information about mileage accumulation are presented and illustrated on some real data. The general problem of modelling failures in equipment when both time and usage are factors is discussed.     

Optimal acceptance sampling policy considering Bayesian risks

In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer's risk and consumer's risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision-makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection, and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy.     

清洁生产、绿色转型与企业产品质量升级

本文基于我国企业微观数据,利用清洁生产行业标准实施这一“准自然实验”,构建多期双重差分模型对清洁生产标准实施后的制造业企业“产品质量效应”进行实证研究。研究发现:清洁生产环境规制尽管在短期内存在“负向挤出效应”,但会通过提升企业生产效率和成本投入效率两大途径在长期显著促进企业产品质量升级,并且政策的影响存在“时间堆积效应”。拓展性分析发现,合规成本规模的差别性、要素密集度的异质性与政策执行的严格性是清洁生产环规规制对企业产品质量产生分化影响的重要原因。进一步通过行业产品质量的动态分解发现,行业产品质量升级的54. 80%源自清洁生产环境规制带来的资源再配置效应。本文对于认识如何通过绿色转型推动我国制造业高质量发展具有重要意义。     

Minimax policies for a two-location/ two-product inventory system

This paper deals with a one period, single-item-twolocation/ two-product inventory distribution problem. A function called the maximum inventory cost, is defined and its expected value is used to derive minimax lot-sizing policies. The resulting policies are shown to avoid shortages as much as possible. Exponential and uniform demand distributions are discussed.     

Setting Policy for On-Line Process Control with Dynamic Characteristics

In this article, we investigate a control policy for the choice of sampling interval and control limit by minimizing the expected quality cost. The study is based on the environment in which (i) the stochastic disturbances are assumed to follow an IMA(1, 1) process, (ii) there is process dynamics between the input series and the output series, (iii) a feedback control scheme is imposed, and (iv) the expected quality cost contains off-target cost, adjustment cost, and inspection cost. Modeling and forecasting for (i), (ii), and (iii) are performed according to the transfer function plus noise model. Minimizing the expected quality cost for (iv) is carried out by a modified pattern search procedure. An example is given to demonstrate the advantage of using the pattern search method over the usual 3-sigma control scheme. The penalty of ignoring the process dynamics and for the case of choosing incorrect value of θ of an IMA(1, 1) disturbance is discussed. The pattern search method is also compared favorably with the modified Taguchi's method in quality cost for the cases considered therein.     

Economic design based on a multivariate Bayesian VSI chart with a dual control limit

In this paper, a multivariate Bayesian variable sampling interval (VSI) control chart for the economic design and optimization of statistical parameters is designed. Based on the VSI sampling strategy of a multivariate Bayesian control chart with dual control limits, the optimal expected cost function is constructed. The proposed model allows the determination of the scheme parameters that minimize the expected cost per time of the process. The effectiveness of the Bayesian VSI chart is estimated through economic comparisons with the Bayesian fixed sampling interval and the Hotelling's T² chart. This study is an in-depth study on a Bayesian multivariate control chart with variable parameter. Furthermore, it is shown that significant cost improvement may be realized through the new model.     

Statistical methods for handling missing data to align with treatment policy strategy

The International Council for Harmonization (ICH) E9(R1) addendum recommends choosing an appropriate estimand based on the study objectives in advance of trial design. One defining attribute of an estimand is the intercurrent event, specifically what is considered an intercurrent event and how it should be handled. The primary objective of a clinical study is usually to assess a product's effectiveness and safety based on the planned treatment regimen instead of the actual treatment received. The estimand using the treatment policy strategy, which collects and analyzes data regardless of the occurrence of intercurrent events, is usually utilized. In this article, we explain how missing data can be handled using the treatment policy strategy from the authors' viewpoint in connection with antihyperglycemic product development programs. The article discusses five statistical methods to impute missing data occurring after intercurrent events. All five methods are applied within the framework of the treatment policy strategy. The article compares the five methods via Markov Chain Monte Carlo simulations and showcases how three of these five methods have been applied to estimate the treatment effects published in the labels for three antihyperglycemic agents currently on the market.     

Models and estimation for systems with recurrent events and usage processes

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to implement maximum likelihood estimation in such cases. Random effects models with linear usage processes and gamma usage processes are considered in some detail. Data on automobile warranty claims are used to illustrate the proposed models and estimation methodology.     

税收激励与企业劳动雇佣——来自薪酬抵税政策的“准自然实验”

在经济下行压力不断加大的形势下,如何“稳就业”成为了各界关注的热点问题。本文以2008 年推行的薪酬抵税政策作为“准自然实验”捕捉企业税负的外生变化,并以2000-2018 年A 股上市公司数据作为研究样本,利用双重差分法考察了税收激励与企业雇佣行为之间的因果关系。实证结果表明:薪酬抵税政策带来了额外的税收优惠,进而促进了企业的雇佣需求,在有效排除共同趋势、预期效应、政策叠加效应以及反向因果问题后,这一结论依然稳健;异质性检验中发现,薪酬抵税政策对企业雇佣的激励效应在民营企业,成本转嫁能力较弱、劳动密集度较高以及处于市场化程度较高区域的企业中表现更加明显,这意味着企业对劳动力成本的变化越敏感,这一政策的作用效果就越好;薪酬抵税政策显著地提升了企业的经营绩效。本文的研究有助于深入理解税收影响企业行为的微观机理,对于政府利用税收政策扩大就业具有重要启示。     

Preventive replacement policies with products update announcements

Abstract

When we consider the improvement of the functional performances that are released by the new updates of the products, it is an interesting problem to revisit the existing replacement policies. For such a viewpoint, four replacement models with product update announcements, i.e., PUA for abbreviation, are given in this paper: Model 1, the unit is replaced at time T or at PUA over time T. Model 2, the unit is replaced at the Kth failure or at PUA over the Kth failure. By considering both time T and failure K, Models 3 and 4 are obtained based on the approaches of replacement first and last. We obtain the expected cost rates for four models and discuss analytically their optimal replacement policies Further, numerical examples are given when the time for PUA has an exponential distribution.     

An optimal age-replacement policy for a simple repairable system with delayed repair

In this article, a simple repairable system (i.e., a repairable system consisting of one component and one repairman) with delayed repair is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, using the geometric process repair model, we consider a replacement policy T based on system age under which the system is replaced when the system age reaches T. Our problem is to determine an optimal replacement policy T*, such that the average cost rate (i.e., the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy T* can be determined by minimizing the average cost rate of the system. Finally, a numerical example is given to illustrate some theoretical results and the model's applicability.     

Considering Taguchi loss function on statistically constrained economic sum of squares exponentially weighted moving average charts

In this paper, Duncan's cost model combined Taguchi's quadratic loss function is applied to develop the economic-statistical design of the sum of squares exponentially weighted moving average (SS-EWMA) chart. The genetic algorithm is applied to search for the optimal decision variables of SS-EWMA chart such that the expected cost is minimized. Sensitivity analysis reveals that the optimal sample size and sampling interval decrease; optimal smoothing constant and control limit increase as the mean and/or variance increases. Moreover, the combination of optimal parameter levels in orthogonal array experiment plays an important guideline for monitoring the process mean and/or variance.     

我国外汇储备的成本—收益分析

 随着我国外汇储备的持续增加,持有外汇储备的成本也在不断上升。文章全面、系统地分析了我国持有外汇储备的各项可量化成本,包括冲销成本、资本损失、债务性储备的成本和机会成本等;分析了我国外汇储备的收益;最后,对我国外汇储备的净收益给出了结论,并提出了相应的政策建议。     

Zero defects: a quality costs approach

Zero Defects has been advocated a s the ultimate target for quality control and assurance.Thispaper conducts an economic analysis of such a concept.The traditional frame work of quality

costs analysis is used to provide the bas is of analysis.A modified quality costs model is formulated to incorporate the revenue effects of quality and the dynamic nature of the manufacturing environment.It is shown that,for the quality cost model specified in this paper,the optimal dynamic strategy for the producer is to continuously improve product quality. Further more,the consumers'perspective and the existence of hidden or unidentifiable defects further reinforce the importance of quality improvement.In this way,a sound economic basis is provided for the Zero Defects concept.