## Publications

**Selected Published Papers by Nozer D. Singpurwalla:**

(2008) Vague Coherent Systems (with K. Sellers). *The International Statistical Review*. Vol. 76, No. 2, pp. 247-267.

(2008) Probability, Chance, and the Probability of Chance (with A. Wilson). *The IIE Transactions*. Vol. 41, No. 1, pp. 12-22.

(2008) Choosing a Coverage Probability for Prediction Intervals (with J. Landon). *The American Statistician*. Vol. 62, No. 2, pp. 120-124

(2007) Betting on Residual Life: The Caveats of Conditioning. In *Statistics & Probability Letters*. Vol. 77, No. 12, pp. 1354-1361.

(2006) The Hazard Potential: Introduction and Overview. *Journal of American Statistical Association*. Vol. 101, No. 476, pp. 1705-1717.

(2005) A Paradigm for Masking (Camouflaging) Information (with S. McNulty and C. Nakhleh). *International Statistical Review*. Vol. 73, No. 3, pp. 331-349.

(2005) Equitable and Adversarial Pricing for Items Under Warranty (with B. Seung). *Law, Probability, and Risk*. Vol. 4, pp. 51-77.

(2005) Decelerated Testing: A Hierarchical Bayesian Approach. *Technometrics*. Vol. 47, No. 4, pp. 468-477.

(2004) Membership Functions and Probability Measures of Fuzzy Sets (with J. Booker).* Journal of the American Statistical Association* (with discussion by Dempster, Laviolette, Lindley and Zadeh). Vol. 99, No. 467, pp. 867-877.

(2004) Specifying Interdependence in Networked Systems (with C. Kong). *IEEE Transactions in Reliability*. Vol. 53, No. 3, pp. 401-405.

(2003) Knowledge Management and Information Superiority: A Taxonomy. *Journal of Statistical Planning and Inference*. Vol. 115, No. 2, pp. 361-364.

**Publication Topics 1966-2009**

**ACCELERATED LIFE TESTING**

Accelerated life testing describes the process of testing items at stress levels above those usually encountered. This effectively accelerates the time scale, so that failures can be witnessed earlier than would be expected in the field. The technique is much-used and therefore important.

**BAYESIAN STATISTICS**

The Bayesian approach to statistical inference and decision making revolves around the paradigm that probability and its calculus is the only coherent approach for the treatment of uncertainty. Very often, the interpretation of probability is "personal" or "subjective." Bayesian methods have proven to be very useful in engineering applications because they allow for the formal incorporation of scientific knowledge, expertise, and informed judgment into a statistical analysis. The application of such methods to problems in reliability is rapidly growing, and many of the papers given below pertain to these.

**DEGRADATION MODELING**

To engineers degradation is the irreversible accumulation of damage throughout life that leads to failure. The term “damage” is not defined; however it is claimed that damage manifests itself via surrogates such as cracks, corrosion, measured wear, etc. Similarly, in the biosciences, the notion of “ageing” pertains to a unit's position in a state space wherein the probabilities of failure are greater than in a former position. Ageing manifests itself in terms of biomedical and physical difficulties experienced by individuals and other such biomarkers. We conceptualize ageing and degradation as unobservable constructs (or latent variables) that serve to describe a process that results in failure. These constructs can be seen as the cause of observable surrogates like cracks, corrosion, and biomarkers such as CD4 cell counts. The prevailing view is that degradation is an observable phenomenon that reveals itself in the guise of crack length and CD4 cell counts. The item fails when the observable phenomenon hits some threshold whose nature is not specified. Whereas this may be meaningful in some cases, a more general view is to separate the observable and the unobservable and to attribute failure as a consequence of the behavior of the unobservable.

**EXPERT JUDGMENT**

For the Bayesian statistician, it is quite natural to work with subjective opinions. A subject of much interest is how to elicit opinions from experts, how to combine these opinions and how to represent them as prior information in models.

**FORECASTING AND TIME SERIES ANALYSIS**

Time series analysis deals with data that is collected over time, and demonstrates changes overtime. For the Bayesian statistician, the main tool is the dynamic linear model, which can be adapted to many situations to make forecasts about future observations, and to smooth past observations. The Institute has extensive publications in this area.

**FOUNDATIONAL ISSUES**

Foundational issues in reliability pertain to topics that are general and do not pertain to a specific application. As such, these topics are relevant to those interested in reliability, biometry, economics, and finance, subjects wherein the occurrence times to certain events are of interest. The papers described below pertain to issues such as the source of failure models, the interpretation of a failure rate, the meaning of a bath-tub curve, paradoxes in reliability, and the validity of the exponentiation formula.

**PREDICTION INTERVALS**

Coverage probabilities for prediction intervals are germane to filtering, previsions, regression, and time series analysis. It is a common practice to choose the coverage probabilities for such intervals by convention, or astute judgment. We argue that coverage probabilities can be chosen by decision theoretic considerations. But to do so, we need to specify meaningful utility functions.

**QUALITY CONTROL**

Quality Control is the theory behind controlling product quality. It is used extensively on the factory floor, and is possibly the most used of all statistical methods. Control charts are typically used to plot how product quality changes over time, and to warn of changes in quality. Utility based approaches were suggested by Taguchi.

**RELIABILITY MODELS**

One of the most important aspects of reliability theory is the selection of appropriate statistical models for the modelling of failures. The Institute has a number of papers in this area, concerned with the reliability of multiple items, when these items act dependently, either due to a common environment or common shocks.

**RELIABILITY THEORY**

Reliability theory is the theory of failure; when do items fail, how do items fail, what causes items to fail?

**RISK ANALYSIS**

Risk analysis is concerned with estimating risks, and determining courses of action based upon these risks. It is used extensively in decision problems.

**SOFTWARE RELIABILITY**

Software reliability is concerned with the failure of software. A great deal of research has been done in this area, since it is both a very important area and an interesting research area. Most papers concern the modelling of failures during the software testing cycle, where, after a failure is discovered, the code is modified to remove the error

**UTILITY ELICITATION**

Utility theory provides a way to make decisions when faced with uncertain outcomes by maximizing expected utility. Thus in order to apply this approach it is necessary to elicit the utilities that a decision maker ascribes to the possible outcomes.

**WARRANTY ANALYSIS AND DESIGN**

The warranty problem is an important problem. There are many statistical problems associated with the offering of warranties. The calculation of optimal warranty periods is of primary importance, along with the forecasting of warranty claims, and the estimation of warranty reserves.

****To see a list of publications, see members’ websites and resumes.**