Field-Failure and Warranty Prediction Based on Auxiliary Use-Rate Information

Assessment of risk due to product failure is important both for purposes of finance (e.g., warranty costs) and safety (e.g., potential loss of human life). In many applications a prediction of the number of future failures is an important input to such an assessment.

Usually the field-data response used to make predictions of future failures is the number of weeks (or another unit of real time) in service. Use-rate information usually is not available (automobile warranty data are an exception, where both weeks in service and number of miles driven are available for units returned for warranty repair). With new technology, however, sensors and smart chips are being installed in many modern products ranging from computers and printers to automobiles and aircraft engines. Thus the coming generations of field data for many products will provide information on how the product was used and the environment in which it was used. This article was motivated by the need to predict warranty returns for a product with multiple failure modes. For this product, cycles-to-failure/use-rate information was available for those units that were connected to the network. We show how to use a cycles-to-failure model to compute predictions and prediction intervals for the number of warranty returns. We also present prediction methods for units not connected to the network. To provide insight into the reasons that use-rate models provide better predictions, we also present a comparison of asymptotic variances comparing the cycles-to-failure and time-to-failure models. This article has supplementary material online.     

Warranty Data Analysis: A Review

Warranty claims and supplementary data contain useful information about product quality and reliability. Analysing such data can therefore be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy and forecasting future warranty claims needed for preparing fiscal plans. In the last two decades, considerable research has been conducted in warranty data analysis (WDA) from several different perspectives. This article attempts to summarise and review the research and developments in WDA with emphasis on models, methods and applications. It concludes with a brief discussion on current practices and possible future trends in WDA. Copyright © 2012 John Wiley & Sons, Ltd.     

Hazard rate estimation from incomplete and unclean warranty data

Warranty data are a rich source of information for feedback on product reliability. However, two-dimensional automobile warranties that include both time and mileage limits, pose two interesting and challenging problems in reliability studies. First, warranty data are restricted only to the reported failures within warranty coverage and such incompleteness can lead to inaccurate estimates of field failure rate or hazard rate. Second, factors such as inexact time/mileage data and vague reported failures in a warranty claim make warranty data unclean that can suppress inherent failure pattern. In this paper we discuss two parameter estimation methods that address the incompleteness issue. We use a simulation-based experiment to study these estimation methods when departure from normality and varying amount of truncation exists. Using a life cycle model of the vehicle, we also highlight and explore issues that lead to warranty data not being very clean. We then propose a five-step methodology to arrive at meaningful component level empirical hazard plots from incomplete and unclean warranty data.     

Field reliability modeling based on two-dimensional warranty data with censoring times

ABSTRACT

Warranty data can be used for estimating product reliability, identifying causes of failure and designing warranty policy. Based on two-dimensional warranty data, we utilize an accelerated failure time model to investigate the effect of usage rate on product degradation. The stochastic expectation-maximization algorithm is proposed to estimate parameters of the reliability model considering both censored data and field data. Extensive simulation studies are used to validate the proposed method and to compare it with the maximum likelihood method. The utilities of the results have been demonstrated through real warranty data collected from an automobile manufacturer in China.     

Modeling and analysis of automobile warranty data in presence of bias due to customer-rush near warranty expiration limit

Automobile users experiencing soft failures, often delay reporting of warranty claims till the coverage is about to expire. This results into a customer-rush near the warranty expiration limit leading to an occurrence of ‘spikes’ in warranty claims towards the end of warranty period and thereby introducing a bias into the dataset. At the same time, an occurrence of manufacturing/assembly defects in addition to the usage related failures, lead to ‘spikes’ in warranty claims near the beginning of the warranty period. When such data are used to capture the field failures for obtaining feedback on product quality/reliability, it may lead product or reliability engineers to potentially obtain a distorted picture of the reality. Although in reliability studies from automobile warranty data, several authors have addressed the well-recognized issues of incomplete and unclean nature of warranty data, the issue of ‘spikes’ has not received much attention. In this article, we address the issue of ‘spikes’ in the presence of the incomplete and unclean nature of warranty data and provide a methodology to arrive at component-level empirical hazard plots from such automobile warranty data.     

Analysis of Field Return Data With Failed-But-Not-Reported Events

Warranty data contain valuable information on product field reliability and customer behaviors. Most previous studies on analysis of warranty data implicitly assume that all failures within the warranty period are reported and recorded. However, the failed-but-not-reported (FBNR) phenomenon is quite common for a product whose price is not very high. Ignorance of the FBNR phenomenon leads to an overestimate of product reliability based on field return data or an overestimate of warranty cost based on lab data or tracking data. Being an indicator of customer satisfaction, the FBNR proportion provides valuable managerial insights. In this study, statistical inference for the FBNR phenomenon as well as field lifetime distribution is described. We first propose a flexible FBNR function to model the time-dependent FBNR behavior. Then, a framework for data analysis is developed. In the framework, both semiparametric and parametric approaches are used to jointly analyze warranty claim data and supplementary tracking data from a follow-up of selected customers. The FBNR problem in the tracking data is minimal and thus the data can be used to effectively decouple the FBNR information from the warranty claim data. The proposed methods are illustrated with an example. Supplementary materials for this article are available online.     

Development of lifetime warranty policies and models for estimating costs

In today's fiercely competitive products market, product warranty has started playing an important role. The warranty period offered by the manufacturer/dealer has been progressively increasing since the beginning of the 20th Century. Currently, a large number of products are being sold with long-term warranty policies in the form of extended warranty, warranty for used products, service contracts and lifetime warranty policies. Lifetime warranties are relatively a new concept. The modelling of failures during the warranty period and the costs for such policies are complex since the lifespan in these policies are not defined well and it is often difficult to tell about life measures for the longer period of coverage due to usage pattern/maintenance activities undertaken and uncertainties of costs over the period. This paper focuses on defining lifetime, developing lifetime warranty policies and models for predicting failures and estimating costs for lifetime warranty policies.     

二维质保管理研究综述与展望

除了低价格、高质量和卓越的性能外,完善的售后服务在刺激购买需求中起到了关键作用。在此背景下,越来越多的制造商开始提供质保服务。对于二维质保产品而言,产品的失效是使用时间和累积使用度共同作用的结果,例如汽车、重型机械等耐用消费品。本文通过对相关文献的整理,分别从产品现场可靠性建模、质保索赔预测和质保政策设计3个方面分别对有关二维质保管理的研究进行综述,并提出了二维质保管理领域进一步研究方向。     

Field Reliability Prediction in Consumer Electronics Using Warranty Data

In innovative fast product development processes, such as consumer electronics, it is necessary to check as quickly as possible, using field data, whether the product reliability is at the right level. In consumer electronics, some major companies use the Warranty Call Rate (WCR) for this purpose. This paper discusses extensively the theoretical and practical drawbacks of the WCR. Subsequently, it is demonstrated, using a Weibull failure distribution, that only a few months after product launch, say three months, the warranty data offer the opportunity to estimate the parameters of the failure distribution. Of course, this requires that the warranty data are available in the quality department. Unfortunately, for some companies the field feedback information process from the repair centres to the quality department causes a delay of several months. These companies have to speed up their field feedback information process before they can fully take advantage of the proposed estimation procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

Using Accelerated Life Tests Results to Predict Product Field Reliability

Accelerated life tests (ALTs) provide timely assessments of the reliability of materials, components, and subsystems. ALTs can be run at any of these levels or at the full-system level. Sometimes ALTs generate multiple failure modes. A frequently asked question near the end of an ALT program is “what do these test results say about field performance?” ALTs are carefully controlled, whereas the field environment is highly variable. For example, products in the field have different average use rates across the product population. With good characterization of field use conditions, it may be possible to use ALT results to predict the failure time distribution in the field. When such information is not available but both life test data and field data (from, e.g., warranty returns) are available, it may be possible to find a model to relate the two data sets. Under a reasonable set of practical assumptions, this model then can be used to predict the failure time distribution for a future component or product operating in the same use environment. This paper describes a model and methods for such situations. The methods are illustrated by an example to predict the failure time distribution of a newly designed product with two failure modes. Supplemental material for this article is available online at the Technometrics website.     

Field Failure Data: an Alternative Proposal for Reliability Estimation

Product reliability is a very important issue for the competitive strategy of industries. In order to estimate a product's reliability, parametric inferential methods are required to evaluate survival test data, which happens to be a fairly expensive data source. Such costly information usually imposes additional compromises in the product development and new challenges to be overcome throughout the product's life cycle. However, manufacturers also keep field failure data for warranty and maintenance purposes, which can be a low‐cost data source for reliability estimation. Field‐failure data are very difficult to evaluate using parametric inferential methods due to their small and highly censored samples, quite often representing mixed modes of failure. In this paper a method for reliability estimation using field failure data is proposed. The proposal is based on the use of non‐parametric inferential methods, associated with resampling techniques to derive confidence intervals for the reliability estimates. Test results show the adequacy of the proposed method to calculate reliability estimates and their confidence interval for different populations, including cases with highly right‐censored failure data. The method is shown to be particularly useful when the sampling distribution is not known, which happens to be the case in a large number of practical reliability evaluations. Copyright © 2006 John Wiley & Sons, Ltd.     

Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts

Offering extended warranty (EW) contracts for products such as automobiles is a good source of revenue for manufactures, insurers and third party companies. However, difficulties in the modeling of product’s failure process and assessing corrective and preventive maintenance actions’ effects on the reliability of product enforce the service providers to propose limited EW contracts with simple “minimal repair at failures” servicing strategy. In this paper for a product sold with a two-dimensional warranty, we model the failure process of product, the effect of imperfect preventive maintenance (PM) and corresponding servicing cost in terms of product’s age and usage. Then, we propose a mathematical optimization model to derive optimal number and degrees of preventive repairs to minimize the EW provider’s servicing cost. We also provide some guidelines to help the EW provider to design flexible EW contracts and determine their corresponding optimal maintenance strategies. To reproduce an illustrative numerical example, we use the failure history of a commercial vehicle produced in a plant in Iran. The provided results reveal that considering proper preventive maintenance strategy during the EW period may effectively reduces the cost of EW servicing.     

Optimal pricing and two-dimensional warranty policies for a new product

For commercial products, pricing and warranty are two crucial marketing strategies, which are used to promote the potential market share. The warranty policy adopted by most of the capital-intensive products, such as machines and automobiles, usually has two dimensions, i.e. warranty age and warranty usage. In this paper, we propose to investigate the profit-maximisation problem, in which the revenue and costs will be affected by the product price and the area of warranty region, for a new product sold under two-dimensional warranty. We assume that the product sales can be captured by a stochastic Bass model based on the nonhomogeneous Poisson process. The product follows a two-dimensional failure process and is covered by a non-renewable free minimal-repair warranty, with age and usage limits. We focus on three revenue/cost components, i.e. sales revenue, warranty cost and production cost, that will significantly affect a firm’s total profit. The profit is maximised by jointly optimising three decision variables, i.e. product price, warranty age limit and warranty usage limit. Numerical experiments are conducted to illustrate the effects of some key parameters, including product reliability, price elasticity, warranty elasticity and learning effect factor, on the optimal settings of the price and warranty region.     

基于故障树映射的产品族保证成本分析

针对当前制造企业的产品通常以产品族而不是单一产品的形式存在的现实,对现有的基于单一产品的保证成本计算模型进行了改进,并指出产品族保证成本计算取决于配置产品的元件的可靠性。通过逆向搜索的方法,元件可靠性可以根据故障树模型向BOM模型映射得到。作者通过一个笔记本电脑的案例说明文中方法的操作过程,并比较了企业采用FRW和PRW两种策略时保证成本的差异。     

On optimal upgrade level for used products under given cost structures

In spite of the growing share of the second-hand market, often customers of used products encounter the following three problems: (a) they are uncertain regarding the durability and performance of these products due to lack of information on the item’s past usage and maintenance history, (b) they are uncertain about the accurate pricing of warranties and the post-warranty repair costs, and (c) sometimes, right after the sale, used items may have high failure rate and could be harmful to their new owner. Due to these problems, the dealers are currently carrying out actions such as overhaul and upgrade of the used products before their release. Reliability improvement, which is closely related to the concept of warranty, for used products is a relatively new concept and has received very limited attention. This paper also develops a stochastic model which results in the derivation of the optimal expected upgrade level under given structures of the profit and failure rate functions. We provide a numerical study to illustrate our results.     

A review of condition-based maintenance: Its prognostic and operational aspects

Condition-based maintenance (CBM) detects early signs of failure and dictates when maintenance should be performed based on the actual condition of a system. In this paper, we first review some of the recent research on CBM under various physical structures and signal data. Then, we summarize several kinds of prognostic models that use monitoring information to estimate the reliability of complex systems or products. Monitoring information also facilitates operational decisions in production planning, spare parts management, reliability improvement, and prognostics and health management. Finally, we suggest some research opportunities for the reliability and operations management communities to fill the research gap between these two fields.     

Total System Reliability: Integrated Model for Growth and Test Termination

Reliability demonstration testing is not the most efficient method of assuring product reliability prior to shipment. It is costly, time consuming and has inherent technical and social limitations. The dilemma facing the reliability and quality engineer is whether to continue demonstration testing and risk shipping a product late or ship the product and risk warranty and field service returns. Either option can cause the company to lose significant market share and profit. This paper sets out to solve this dilemma by meeting both the time to market constraints and the product reliability goals. The weaknesses of existing reliability demonstration techniques are explored and a comprehensive methodology is introduced involving controlled development processes, stress testing, root cause determination and process change feedback mechanisms. All prototype products are manufactured on the final volume process line resulting in the early identification and correction of process‐related problems. Testing commences on the first available prototypes with system stress/robust testing being employed to stimulate failures, determine their root cause and correct them. Reliability growth modelling assesses the ongoing improvements occurring in reliability during the development cycle, while a statistical stopping rule is used to determine the optimal product release time without risking product warranty. The approach is applicable to systems incorporating both hardware and software elements. The methodology has been validated on three development projects of telecommunication systems comprising hardware and software. In addition to enhancing team behaviour and performance, the development times have been reduced by 14% and the ramp‐up time to full worldwide product shipments has been reduced by 50%. Copyright © 2005 John Wiley & Sons, Ltd.     

Feature selection methods for root-cause analysis among top-level product attributes

Manufacturing companies not only strive to deliver flawless products but also monitor product failures in the field to identify potential quality issues. When product failures occur, quality engineers must identify the root cause to improve any affected product and process. This root-cause analysis can be supported by feature selection methods that identify relevant product attributes, such as manufacturing dates with an increased number of product failures. In this paper, we present different methods for feature selection and evaluate their ability to identify relevant product attributes in a root-cause analysis. First, we compile a list of feature selection methods. Then, we summarize the properties of product attributes in warranty case data and discuss these properties regarding the challenges they pose for machine learning algorithms. Next, we simulate datasets of warranty cases, which emulate these product properties. Finally, we compare the feature selection methods based on these simulated datasets. In the end, the univariate filter information gain is determined to be a suitable method for a wide range of applications. The comparison based on simulated data provides a more general result than other publications, which only focus on a single use case. Due to the generic nature of the simulated datasets, the results can be applied to various root-cause analysis processes in different quality management applications and provide a guideline for readers who wish to explore machine learning methods for their analysis of quality data.     

Integration method for reliability assessment with multi-source incomplete accelerated degradation testing data

ABSTRACT

During the product life cycle, the lifetime information will be collected at each stage, mainly from different tests at the R&D phase, field usage, and maintenance. To comprehensively conduct reliability assessments, it generally requires the integration of multi-source datasets, even that from similar products. In this article, we considered the scenario that products have been arranged with several accelerated degradation tests (ADT) under different types of accelerated stresses with dependency. The obtained data is called incomplete ADT dataset with incomplete stress conditions which fails the traditional integration method for reliability assessments. A novel method is proposed to accomplish this task through mutually exclusive set (MES) theory. The probability assignments for each dataset are given through the union set of several MESs. Then, the multi-source ADT datasets are integrated with the assigned weights of probabilities. Finally, a simulation study and a real application are given to illustrate the effectiveness of the proposed methodology.     

Optimal reliability, warranty and price for new products

The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about product reliability. Product warranty is one such tool to signal reliability with a longer warranty period indicating better reliability. Better warranty terms result in increased sales and also higher expected warranty servicing costs. Warranty costs are reduced by improvements in product reliability. Learning effects result in the unit manufacturing cost decreasing with total sales volume and this in turn impacts on the sale price. As such, reliability, price and warranty decisions need to be considered jointly. The paper develops a model to determine the optimal product reliability, price and warranty strategy that achieve the biggest total integrated profit for a general repairable product sold under a free replacement-repair warranty strategy in a market and looks at two scenarios for the pricing and warranty of the product. The model assumes that the sale rate increases as the warranty period increases and decreases as the price increases. The maximum principle method is used to obtain optimal solutions for dynamic price and warranty situations. Finally, numerical examples are given to illustrate the proposed model.