Georgia-Ann Klutke

A critical look at the bathtub curve

This paper addresses some of the fundamental assumptions underlying the bathtub curve. It is shown to be unlikely that any practical hazard function is decreasing near zero. Great care should be taken in interpreting the hazard function, particularly in applying quality-control practices, such as burn-in or environmental-stress-screening to manufactured products.

A maintenance strategy for systems subjected to deterioration governed by random shocks

The authors examine the time-stationary availability of maintained systems that deteriorate according to a random-shock process. System failures are not self-announcing; hence, failures must be detected via inspection. The approach considers randomly occurring shocks that cumulatively damage the system; shock magnitudes are taken as random. The authors develop an expression for computing system availability when inspections follow a renewal process. This expression leads to a proved proposition showing that, for any specified mean inspection rate, system availability is maximized by choosing deterministic inter-inspection times. >

IMPROVED INSPECTION SCHEMES FOR DETERIORATING EQUIPMENT

In this paper, we introduce and analyze simple, new inspection policies for maintaining deteriorating equipment with non-self-announcing failures. These policies utilize information from the inspection/repair history as well as the system lifetime distribution to schedule future inspections. Numerical results indicate that the policies can significantly outperform standard (periodic) maintenance strategies by providing higher availability for a given inspection rate.

A distribution-free lower bound for availability of quantile-based inspection schemes

This paper develops a lower bound for the availability of quantile-based inspection schemes when device lifetimes are assumed to have an increasing failure rate. The lower bound is useful in designing inspection schemes when lifetime distributions are not explicitly known, but must be estimated from limited failure data.

ON MAINTAINED SYSTEMS OPERATING IN A RANDOM ENVIRONMENT

This paper examines the availability of a maintained system where the rate of deterioration is governed by an exogenous random environment. We provide a qualitative result that exposes the relationship between remaining lifetime, environment, and repairs. This result leads to simple bounds that can be used to choose inspection rates that guarantee a specified level of availability. The principal result requires no specific distributional assumptions, is intuitively appealing and can be directly applied by practitioners. Our development employs techniques from stochastic calculus.

Effects of Risk Aversion on the Value of Information in Two-Action Decision Problems

This paper analyzes the value of information in a two-action decision problem where a decision maker is deciding on whether to accept an uncertain investment. We investigate the effects of the decision makers risk aversion function on the value of information in this setting. We analyze the value of perfect information and the value of partition information where a decision maker with deterministic initial wealth receives information specifying that the outcome lies within a subset of the domain. We show that if two decision makers reject the investment without the information, then the more risk-averse decision maker will value information both perfect and partition, less than the less risk averse one. On the other hand, if both decision makers initially accept the investment, or are indifferent to the investment without the information, then i the more risk-averse decision maker will value perfect information higher than the less risk-averse one, but ii this monotonicity result need not apply for the case of partition information. These results enable us to compare the value of information when decision makers have different risk aversion levels. They also hold when comparison of risk aversion is restricted only to a domain defined by the lottery.

Information and preference reversals in lotteries

Several approaches have been proposed for evaluating information in expected utility theory. Among the most popular approaches are the expected utility increase, the selling price and the buying price. While the expected utility increase and the selling price always agree in ranking information alternatives, Hazen and Sounderpandian [11] have demonstrated that the buying price may not always agree with the other two. That is, in some cases, where the expected utility increase would value information A more highly than information B, the buying price may reverse these preferences. In this paper, we discuss the conditions under which all these approaches agree in a generic decision environment where the decision maker may choose to acquire arbitrary information bundles.

Optimisation of the design of infrastructure components subject to progressive deterioration and extreme loads

The construction of new infrastructure requires solutions that maximise the benefit while meeting acceptable safety levels. The solution to this problem can be obtained through a structural cost-based optimisation. This paper integrates a life-cycle cost optimisation model developed by Rackwitz (2000) with a structural deterioration model that combines the action of progressive degradation (e.g. corrosion, fatigue) and sudden events (e.g. earthquakes). The structural condition at a given time is measured in terms of the systems remaining life, which can be measured in practice through any structural performance indicator (e.g. ductility). It is assumed that sudden events conform to a compound point process with shock sizes and interarrival times that are independent and identically distributed random variables. Deterministic and random progressive deterioration models are also included in the formulation. Randomness in progressive deterioration is modelled as a point process with known arrival times and random shock sizes. Structural reliability is evaluated against prescribed design and operation thresholds that can be used to establish limit states or intervention policies. The entire model is illustrated with an example that compares several life-cycle models showing the importance of taking into account the damage history in evaluating the performance of infrastructure systems.

Buying price of event information in two-action decision problems

Being able to determine in advance whether certain events occur or not enables a decision maker to reduce the uncertainty of a two-action lottery, although the exact outcome of the lottery may still not be known with certainty. This paper studies the á priori value of information in such a decision making environment. Of interest to the decision maker is to compare the value of information about different events in advance of gathering the information. Using buying price as value of information, we show that when information about the occurrence of two different events are offered to a risk neutral decision maker, the event with a greater contribution in absolute value to the expected value of the lottery has higher value in terms of its buying price. For risk averse decision makers, a preference condition needs to be imposed on the set difference of two events to obtain a generic conclusion. We provide several examples that demonstrate the usefulness of these results.

The backlog process in queues with random service speed

This paper examines the backlog (total amount of unfinished work in the system) in a single server queue that works in a ‘random environment’. Specifically, the service speed is described by an exogenous (non-negative) ‘environment’ process. We characterize the time-dependent backlog via a stochastic integral equation and use this equation to compute stationary performance measures. For the M/G/1 queue, our results lead to a generalization of the Pollaczek-Khintchine transform equation for backlog that ‘explains’ why congestion is greater in a queue with random service speed than in an equivalent queue with constant service speed. We provide a numerical example that helps to illustrate our results.