David M. Steinberg, Editor Technometrics

Advances in applied reliability are a primary topic in the May 2010 issue of Technometrics. The first article, by Yili Hong and William Q. Meeker, is on “Field-Failure and Warranty Prediction Based on Auxiliary Use-rate Information.” Traditionally, such predictions have been based on the length of time that a unit is in service. Actual product usage, although often more important than calendar time, is usually not available. New technology is changing that situation.

Sensors and smart chips are being installed in many modern products and can provide feedback to the manufacturer on how the product has been used and the environment in which it was used. Hong and Meeker develop methods that take advantage of the usage data, with a cycles-to-failure model to compute predictions and prediction intervals for the number of warranty returns. The paper was motivated by the need to predict warranty returns for a product with multiple failure modes and cycles-to-failure/use-rate information available for many of the units via connection to a network. The authors present prediction methods for both units connected and units not connected to the network. The ideas are illustrated using this applied problem. Further insight into the benefits of use-rate models is provided by a comparison of asymptotic variances comparing the cycles-to-failure and time-to-failure models.

The article by Hong and Meeker is our featured article in the issue. It can be accessed freely from the journal web site here.

Todd L. Graves, Christine Anderson-Cook, and Michael S. Hamada consider the problem of assessing system reliability when data are available at the system, subsystem and component level. Their article, “Reliability Models for Almost-Series and Almost-Parallel Systems,” considers model forms that allow for the assessment and modeling of possible discrepancies between reliability estimates based on these different levels of data. Understanding the potential conflicts between data permits a more realistic representation of the true uncertainty of the estimates and enhances understanding of inconsistencies that might guide further improvements to the system model. The new methodology is illustrated with several examples.

Massimiliano Giorgio, Maurizio Guida, and Gianpaolo Pulcini use degradation data to assess reliability in their article, “A State-Dependent Wear Model with an Application to Marine Engine Cylinder Liners.” Their work was motivated by an interesting application: the need to describe the wear of cylinder liners of some identical heavy-duty diesel engines for marine propulsion, which are observed via a staggered inspection.
The authors propose a new wear model in which the transition probabilities between process states, unlike models with independent increments, depend on the current system state. A time and state space discretization is introduced to obtain the likelihood function. The model parameters and reliability characteristics of the liners are then estimated and the wear growth during future inspection intervals is predicted. The homogeneity of wear data and the goodness-of-fit of the proposed model are tested. A simplified maintenance scenario is also considered to show the need for accurate modeling of the wear process for planning condition-based maintenance activities. Fortran code and executable programs, as well as the cylinder liner data, are available online as supplemental material.

Our next article, by Xiao Wang and Dihua Xu, also considers the use of degradation data. In “An Inverse Gaussian Process Model for Degradation Data,” they study maximum likelihood estimation when a class of inverse Gaussian processes is used to model degradation. Both intersubject heterogeneity and covariate information can be incorporated into the model in a natural way. The EM algorithm is used to obtain the maximum likelihood estimators of the unknown parameters, and the bootstrap is used to assess the variability of the maximum likelihood estimators. Simulations are used to validate the method. The model is fitted to laser data, and corresponding goodness-of-fit tests are carried out. Failure time distributions in terms of degradation level passages are calculated and illustrated. Macros in R for implementing the analysis are available online as supplemental material.