Ziad Zaghati

Two-dimensional reliability modeling from warranty data

The failures of some systems depend on age and amount of accumulated usage. A common example of such systems is the automobile; the life of which is measured by both time in service and mileage. Warranty claims of the systems contain a large amount of information about reliability, such as failure times, usages and failure modes. Using warranty data to model reliability as a function of time and usage provides a more accurate and realistic estimator.This paper describes warranty data structure and censoring mechanism. A sequential regression method is proposed to model mileage accumulation from warranty claim data. The model and mileage failure data are used to evaluate the patterns of failure occurrences at different mileages. The paper then establishes the relationship between reliability and time in service and mileage. The unknown parameters are estimated by maximum likelihood method with time and mileage censoring. The reliability model is used to predict the number of warranty claims, and the number of failed vehicles which do not generate warranty claims due to mileage exceeding warranty limit. In the paper, an example is presented. The example shows that the predicted number of warranty claims has a good agreement with the actual number of claims.

Accelerated life tests at higher usage rates: a case study

The life of some products is measured by usage, e.g., cycles and mileage. Such products are usually operated at a low usage rate in the field. Accelerated life testing of the products often involves the concurrent use of increased usage rate and other stresses. The effects of increasing the usage rate on usage to failure (life) are usually ignored. In fact, increasing the usage rate may shorten or prolong the life. A generic method for accelerated life tests at higher usage rates is described in Ref. 1. Using the method, this paper presents a case study on demonstrating the reliability of a type of compact relays, whose life testing uses increased switching rates. In particular, we develop the component-specific acceleration model, test method, and best compromise plan. Life data analysis using the maximum likelihood method concludes that the compact relays marginally meet the reliability requirement. In addition, this paper evaluates the significance of the switching rate effect and shows that the effect cannot be ignored

A sigmoid process for modeling warranty repairs

This paper proposes a sigmoid process to model the warranty data which graphically illustrate S-shape. In the paper, it is shown that the sigmoid process is the non-homogeneous Poisson process super-imposed by warranty dropout process. The nonparametric estimates of warranty repair rate and mean cumulative function (MCF) are presented. The three parameters of the sigmoid model are estimated by maximum likelihood method. The confidence intervals of the estimates of model parameters and MCF are constructed. Likelihood ratio test is developed to test the hypothesis that the historic values of location parameters are statistically equal. An example is presented to illustrate and validate the sigmoid model.

Robust reliability design of diagnostic systems

Diagnostic systems are software-based built-in-test systems which detect, isolate and indicate the failures of the prime systems. The use of diagnostic systems reduces the losses due to the failures of the prime systems and facilitates subsequent repairs. Thus diagnostic systems have found extensive applications in industry. The algorithms performing operations for diagnosis are important parts of the diagnostic systems. If the algorithms are not adequately designed, the systems will be sensitive to noise sources, and commit type I error (a) and type II error (/spl beta/). This paper is to improve the robustness and reliability of the diagnostic systems through robust design of the algorithms by using reliability as an experimental response. To conduct the design, we define the reliability and robustness of the systems, and propose their metrics. The influences of /spl alpha/ and /spl beta/ errors on reliability are evaluated and discussed. The effects of noise factors on robustness are assessed. The classical P-diagram is modified; a generic P-diagram containing both prime and diagnostic systems is created. Based on the proposed dynamic reliability metric, we describe the steps for robust reliability design and develop a method for experimental data analysis. The robustness and reliability of the diagnostic systems are maximized by choosing optimal levels of algorithm parameters. An automobile example is presented to illustrate how the proposed design method is used. The example shows that the method is efficient in defining, measuring and building robustness and reliability.

Reliability and robustness assessment of diagnostic systems from warranty data

Diagnostic systems are software-intensive built-in-test systems, which detect, isolate and indicate the failures of prime systems. The use of diagnostic systems reduces the losses due to the failures of prime systems and facilitates the subsequent correct repairs. Therefore, they have found extensive applications in industry. Without loss of generality, this paper utilizes the on-board diagnostic systems of automobiles as an illustrative example. A failed diagnostic system generates /spl alpha/ or /spl beta/. /spl alpha/ error incurs unnecessary warranty costs to manufacturers, while /spl beta/ error causes potential losses to customers. Therefore, the reliability and robustness of diagnostic systems are important to both manufacturers and customers. This paper presents a method for assessing the reliability and robustness of the diagnostic systems by using warranty data. We present the definitions of robustness and reliability of the diagnostic systems, and the formulae for estimating /spl alpha/, /spl beta/ and reliability. To utilize warranty data for assessment, we describe the two-dimensional (time-in-service and mileage) warranty censoring mechanism, model the reliability function of the prime systems, and devise warranty data mining strategies. The impact of /spl alpha/ error on warranty cost is evaluated. Fault tree analyses for /spl alpha/ and /spl beta/ errors are performed to identify the ways for reliability and robustness improvement. The method is applied to assess the reliability and robustness of an automobile on-board diagnostic system.