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2013 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Stochastic Modeling for Reliability

Shocks, Burn-in and Heterogeneous populations

verfasst von: Maxim Finkelstein, Ji Hwan Cha

Verlag: Springer London

Buchreihe : Springer Series in Reliability Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Focusing on shocks modeling, burn-in and heterogeneous populations, Stochastic Modeling for Reliability naturally combines these three topics in the unified stochastic framework and presents numerous practical examples that illustrate recent theoretical findings of the authors.

The populations of manufactured items in industry are usually heterogeneous. However, the conventional reliability analysis is performed under the implicit assumption of homogeneity, which can result in distortion of the corresponding reliability indices and various misconceptions. Stochastic Modeling for Reliability fills this gap and presents the basics and further developments of reliability theory for heterogeneous populations. Specifically, the authors consider burn-in as a method of elimination of ‘weak’ items from heterogeneous populations. The real life objects are operating in a changing environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stochastic point processes. The basic theory for Poisson shock processes is developed and also shocks as a method of burn-in and of the environmental stress screening for manufactured items are considered.

Stochastic Modeling for Reliability introduces and explores the concept of burn-in in heterogeneous populations and its recent development, providing a sound reference for reliability engineers, applied mathematicians, product managers and manufacturers alike.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
As the title suggests, the book is devoted to stochastic models for reliability. This very wide topic is naturally ‘censored’ by the current research interests of the authors in the field which are: shock models, burn-in and stochastic modeling in heterogeneous populations. At first sight, it seems that these three areas of research are rather ‘independent’. However, it turns out that they can be naturally combined in the unified framework and some of the results of this kind have been already reported in our recent publications. As most of the real-life populations are heterogeneous, taking this property into account in reliability analysis of various problems is only increasing the adequacy of the corresponding modeling. Furthermore, all objects are operating in a changing environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some point process (e.g., the Poisson process or the renewal process). By a ‘shock’ we understand an ‘instantaneous’, potentially harmful event. Depending on its magnitude, a shock can destroy an operating system (failure), leave it unchanged (as good as old), or, e.g., increase its wear (deterioration) on some increment. Numerous shock models were developed and reported in the reliability-related literature during the past 50 years. However, only a few papers (mostly of the authors) deal with shocks in heterogeneous populations and with shocks as a method of burn-in.
Maxim Finkelstein, Ji Hwan Cha
Chapter 2. Basic Stochastics for Reliability Analysis
Abstract
In this introductory chapter, we partially follow, revise, and expand the relevant portions of Chaps. 2 and 4 of Finkelstein [25] and also add other material that should be helpful when reading the rest of this book. Therefore, we will often refer to this chapter in the subsequent parts of the text. It covers the notions and some basic properties of the failure rate, the mean residual lifetime, stochastic point processes, minimal and general repair, multivariate accelerated and proportional hazards models and, finally, the simplest stochastic orders.
Maxim Finkelstein, Ji Hwan Cha
Chapter 3. Shocks and Degradation
Abstract
This chapter is mostly devoted to basic shock models and their simplest applications. Along with discussing some general approaches and results, we want to present the necessary material for describing our recent findings on shocks modeling of the next chapter. As in the other chapters of this book, we do not intend to perform a comprehensive literature review of this topic, but rather concentrate on notions and results that are vital for further presentation.
Maxim Finkelstein, Ji Hwan Cha
Chapter 4. Advanced Theory for Poisson Shock Models
Abstract
In this chapter, we extend and generalize approaches and results of the previous chapter to various reliability related settings of a more complex nature. We relax some assumptions of the traditional models except the one that defines the underlying shock process as the nonhomogeneous Poisson process (NHPP). Only in the last section, we suggest an alternative to the Poisson process to be called the geometric point process. It is remarkable that although the members of the class of geometric processes do not possess the property of independent increments, some shock models can be effectively described without specifying the corresponding dependence structure. Most of the contents of this chapter is based on our recent work [5‐11] and covers various settings that, we believe, are meaningful both from the theoretical and the practical points of view. The chapter is rather technical in nature; however, general descriptions of results are reasonably simple and illustrated by meaningful examples. As the assumption of the NHPP of shocks is adopted, many of the proofs follow the same pattern by using the time-transformation of the NHPP to the HPP (see the derivation of Eq. (2.​31)). This technique will be used often in this chapter. Sometimes the corresponding derivations will be reasonably abridged, whereas other proofs will be presented at full length.
Maxim Finkelstein, Ji Hwan Cha
Chapter 5. Heterogeneous Populations
Abstract
Homogeneity of objects is a unique property that is very rare in nature and in industry. It can be created in the laboratory, but not outside it. Therefore, one can hardly find homogeneous populations in real life; however, most of reliability modeling deals with homogeneous cases. Due to instability of production processes, environmental and other factors, most populations of manufactured items in real life are heterogeneous. Similar considerations are obviously true for biological items (organisms). Neglecting heterogeneity can lead to serious errors in reliability assessment of items and, as a consequence, to crucial economic losses. Stochastic analysis of heterogeneous populations presents a significant challenge to developing mathematical descriptions of the corresponding reliability indices. On the other hand, everything depends on the definition, on what we understand by homogeneous and heterogeneous populations.
Maxim Finkelstein, Ji Hwan Cha
Chapter 6. The Basics of Burn-in
Abstract
In this chapter, we introduce the concept of burn-in and review initial research in this area. Burn-in is a method of ‘elimination’ of initial failures (infant mortality) of components before they are shipped to customers or put into field operation. Usually, to burn-in a component or a system means to subject it to a fixed time period of simulated use prior to the actual operation. That is, before delivery to the customers, the components are exposed to electrical or thermal conditions that approximate the working conditions in field operation. Those components which fail during the burn-in procedure will be scrapped or repaired and only those, which have survived the burn-in procedure will be considered to be of the satisfactory quality. An introduction to this important area of reliability engineering can be found in Jensen and Petersen (1982) and Kuo and Kuo (1983). Surveys of research on different aspects of burn-in can be found in Leemis and Beneke (1990), Block et. al (1997), Liu and Mazzuchi (2008), and Cha (2011).
Maxim Finkelstein, Ji Hwan Cha
Chapter 7. Burn-in for Repairable Systems
Abstract
In the previous chapter, the emphasis was made on the burn-in procedures for non-repairable items. If a non-repairable item fails during burn-in, then, obviously, it is just scraped and discarded. However, an expensive, complex product or device will not be discarded on account of failure of its part, but rather a repair will be performed. Therefore, in this chapter, we deal mostly with repairable items. Note that the contents of this chapter are rather technical and it can be skipped by a less mathematically oriented reader.
Maxim Finkelstein, Ji Hwan Cha
Chapter 8. Burn-in for Heterogeneous Populations
Abstract
In the previous chapters, we discussed the burn-in procedures for homogeneous populations. When the failure rate of a population is decreasing or bathtub-shaped (BT), burn-in can be usually justified. Note that, as mentioned and illustrated earlier, the heterogeneity of populations is often a reason for the decrease in the resulting failure rate, at least, in some time intervals. In this chapter, the optimal burn-in procedures are investigated without assuming that the population failure rate is BT. We consider the mixed population composed of two ordered subpopulations—the subpopulation of strong items (items with ‘normal’ lifetimes) and that of weak items (items with shorter lifetimes). In practice, weak items may be produced along with strong items due to, for example, defective resources and components, human errors, unstable production environment, etc. In the later part of this section, we will also consider the continuous mixtures model.
Maxim Finkelstein, Ji Hwan Cha
Chapter 9. Shocks as Burn-in
Abstract
As described in the previous chapters, in conventional burn-in, the main parameter of the burn-in procedure is its duration. However, in order to shorten the length of this procedure, burn-in is most often performed in an accelerated environment. This indicates that high environmental stress can be more effective in eliminating weak items from a population. In this case, obviously, the larger values of stress should correspond to the shorter duration of burn-in. By letting the stress to increase, we can end up (as some limit) with very short (negligible) durations, in other words, shocks. In practice, the most common types of shocks as a method of burn-in are “thermal shock” and “physical drop”. In these cases, the item is subjected to a very rapid cold-to-hot, or hot-to-cold, instantaneous thermal change or the item is dropped by a “drop tester” which is specifically designed to drop it without any rotational motion, to ensure the most rigorous impact. In this case, the stress level (to be called shock’s severity) can be a controllable parameter for the corresponding optimization, which in a loose sense is an analogue of the burn-in duration in accelerated burn-in.
Maxim Finkelstein, Ji Hwan Cha
Chapter 10. Stochastic Models for Environmental Stress Screening
Abstract
There are different ways of improving reliability characteristics of manufactured items. The most common methodology adopted in industry is burn-in, which is a method of ‘elimination’ of initial failures (infant mortality). As was mentioned previously, the ‘sufficient condition’ for employing the traditional burn-in is the initially decreasing failure rate. For example, when a population of items is heterogeneous, and therefore consists of subpopulations with ordered failure (hazard) rates, it obviously contains weaker (with larger failure rates) subpopulations. As the weakest populations are dying out first, the failure rate of this population is often initially decreasing and burn-in can be effectively applied.
Maxim Finkelstein, Ji Hwan Cha
Backmatter
Metadaten
Titel
Stochastic Modeling for Reliability
verfasst von
Maxim Finkelstein
Ji Hwan Cha
Copyright-Jahr
2013
Verlag
Springer London
Electronic ISBN
978-1-4471-5028-2
Print ISBN
978-1-4471-5027-5
DOI
https://doi.org/10.1007/978-1-4471-5028-2

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