Estimation of the carbon footprint for telecommunications and electronics products has become a key design activity. Improvement in carbon footprint must be demonstrated consistently on all new products. Current methods of providing a useful estimate are laborious and time-consuming. A simplified approach is described, which uses basic statistical methods for estimation and promises significant improvements over existing methods. [DOI: 10.1115/1.4002143]

Numerous papers and texts have been written in the reliability literature regarding the determination of the optimum test duration for a production stress or a burn‐in test. The techniques presented have largely been based on the identification of the change point at which infant mortality has largely been removed from the units. The time‐on‐test is typically the only factor that influences this decision. Few of these models have attempted to integrate the field performance or the influence of warranty costs into this decision. This paper proposes and validates a methodology that integrates the influence of the production test failures and the field performance including their respective costs into a single unified model. The objective is to identify a production test duration that minimizes the overall cost. A Weibull model is initially developed for the production test that incorporates the failure observations in different time segments of the test based on the ability to detect latent defects in the product. A separate Weibull model is then developed for the product's performance in the field that includes the lifetime of the unit. This paper identifies how both these Weibull models can be combined into a single model including both test and field costs with the objective of minimizing the overall cost. The advantage of the proposed technique is that it does not require one to track individual units from production through to the field in order to develop an integrated test and field cost model. Copyright © 2009 John Wiley & Sons, Ltd.

In this article statistical inference for the failure time distribution of a product from "field return data", that records the time between the product being shipped and returned for repair or replacement, is described. The problem that is addressed is that the data are not failure times because they also include the time that it took to ship and install the product and then to return it to the manufacturer for repair or replacement. The inference attempts to infer the distribution of time to failure (that is, from installation to failure) from the data when in addition there are separate data on the times from shipping to installation, and from failure to return. The method is illustrated with data from units installed in a telecommunications network.

This study describes the production sampling environmental stress test (PSEST) process and the offline analysis conducted. Some of the key characteristics and parameters of the test are outlined. The analytical process is based on two types of regression model, each of which links a dependent variable (the log of time to failure in each dwell, or the log of the number failed in each dwell) to independent variables such as temperature and age. These two types of regression are known as Weibull regression1 and Poisson regression.2 Using the estimated regression coefficients, expressions for the probability distribution of a unit under test can be written and used to optimize the test duration.

Accelerated environmental stress tests (EST) are applied during the manufacturing process to improve reliability by precipitating and detecting latent defects. This test represents an in-process manufacturing screen and the objective of performing it is to avoid early field failures that reduce the customer satisfaction level and increase warranty and compensation costs. Temperature cycling during EST is one of the most commonly used test procedures. Although it is an expensive and energy intensive procedure, usually a lengthy test is initially recommended for a new product. Based on the product test performance or a possible manufacturing process modification, the test duration and regime may be changed after some period. Even if the number of test cycles is reduced, EST continues to be an expensive test and a major process bottleneck. This paper uses generalized linear modeling (GLM) to investigate the effects of the production and EST test variables on the population under test. Both the number of units rejected and the time to failure can be modeled as a regression function of covariates representative of the test environment. The field reliability function is written as a product of the unconditional reliability in each segment of the test profile such as dwell, ramp, etc. The next step is to apply the result of the temperature cycle EST GLM to a mathematical cost model. This cost model includes both the test cost and the warranty and compensation costs of the early field failures. The optimum test regime and number of cycles, which minimizes the total cost is determined by combining the GLM and the cost model. In this way the production test regime can be optimized in terms of field reliability/test cost trade-off.

The problem of optimizing accelerated production testing is a pressing one in most electronic manufacturing facilities. Yet, practical models are scarce in the literature, especially for testing high volumes of electronic circuit packs in failure-accelerating environments. In this paper, we develop both a log-linear and linear model, based initially on the Weibull distribution. The models developed are suitable for modeling accelerated production testing data from a temperature-cycled environment. The model is "piecewise" in that the failures in each discrete "piece" of the temperature cycle are modeled as if the testing was in parallel rather than sequential mode. An extra covariate is introduced to indicate age at the start of each piece. The failures in a piece then depend on the stress in the piece itself and the time elapsed to the start of the piece. This last dependence captures the influence of reliability growth and has the result of providing an alternative linear model to the log-linear one. The paper demonstrates a simpler use of Poisson regression. An application, using actual production data, is described. Uses of the Loglogistic, Logistic, Lognormal and Normal distributions are also illustrated.

The Box-Tidwell represents a commonly-used iterative approach in linear or nonlinear regression but is little used in reliability modeling. It provides a power transformation of the regressor variable in order to linearize the model, or (occasionally) defaults to a log transformation. Its main drawback is lack of convergence under certain circumstances which results in it recommending a log transformation inappropriately. The techniques developed in this paper significantly increase the Box-Tidwell's robustness and ensure a power transformation solution is consistently found. Used along with weighted least squares (WLS), the Box-Tidwell transformation represents a real alternative to maximum likelihood or graphical estimation. This paper takes the example of the power-law model used in reliability growth analysis and demonstrates the application and effectiveness of the robust Box-Tidwell. Extensive simulation modelling has shown it generally provides a better fit to the data than the alternative maximum likelihood estimates. It illustrates that maximum likelihood methods do not always provide the 'best' estimator in the sense of one that minimizes a suitable loss function. The comparative analysis was conducted using simulation of 10, 30, and 100 observations for the power-law model. Cross validation was conducted using the predicted residual sum of squares (PRESS) statistic. Contrary to expectation, the PRESS statistics shows that the parameter estimation by this methodology (called BTW) will provide the best fit to the data (in the sense of minimizing the sum of the squared errors), and not estimation by maximum likelihood methods. The BTW will provide the best interpolated predictions compared to the alternatives

Temperature cycling environmental stress testing (EST) of circuit packs is a standard test procedure for the precipitation of latent defects in order to minimize early product lifecycle customer returns. EST is an expensive, energy-intensive bottleneck in the manufacturing process, one that is based on empiricisms that may be out of date. This presents great opportunity for optimization and test cost reduction. This paper describes the characterization of temperature cycling through analysis and modeling of process data in order to optimize the test parameters — ramp rate, temperature extremes, dwell times, and number of cycles. Failure data from circuit packs tested at a Lucent facility is analyzed using a regression technique and graphical inspection. The dwell and ramp periods of the test are considered in a piecewise manner. A cost model is applied based on distributions fitted to the failure data. The analysis yields a methodology for the dynamic, value-based optimization of temperature cycling EST.

The Quality Measurement Plan (QMP) is a Bayesian procedure for estimating the mean of a process. This standardized algorithm, used across Lucent Technologies, is not available to desktop users. This letter describes an Excel VBA version that is at the user-testing stage of its development. © 2003 Lucent Technologies Inc.