Duane L. Dietrich

Time-varying failure rates in the availability and reliability analysis of repairable systems

This paper combines time varying failure rates and Markov chain analysis to obtain a hybrid reliability and availability analysis. However, combining these techniques can, depending on the size of the system, result in solutions of the Markov chain differential matrix equations that are intractable. This paper identifies solutions that are tractable, These form the analytical baseline for the reliability and availability analysis of systems with time varying failure rates. Tractable solutions were found for the 1-component 2-state and the 2-component 4-state configurations. Time varying failure rates were characterized by a general polynomial expression. Constant, linear, and Weibull failure rate functions are special cases of this polynomial. The general polynomial failure rate provides flexibility in modeling the time varying failure rates that occur in practice. >

An alternative degradation reliability modeling approach using maximum likelihood estimation

An alternative degradation reliability modeling approach is presented in this paper. This approach extends the graphical approach used by several authors by considering the natural ordering of performance degradation data using a truncated Weibull distribution. Maximum Likelihood Estimation is used to provide a one-step method to estimate the models parameters. A closed form expression of the likelihood function is derived for a two-parameter truncated Weibull distribution with time-independent shape parameter. A semi-numerical method is presented for the truncated Weibull distribution with a time-dependent shape parameter. Numerical studies of generated data suggest that the proposed approach provides reasonable estimates even for small sample sizes. The analysis of fatigue data shows that the proposed approach yields a good match of the crack length mean value curve obtained using the path curve approach and better results than those obtained using the graphical approach.

A New Nonparametric Growth Model

This paper proposes a new nonparametric reliability growth model for the analysis of the failure rate of a system that is undergoing development test. The only restrictions on the actual, unknown failure distribution for each stage of testing is that it be continuous, have only one unknown parameter ¿, and have an associated unimodal likelihood function. No assumptions regarding the parametric form of the failure rate of the development process are made, only that there is no decay in the reliability of the system during the design changes. The parameters are assumed to be ordered from one test stage to the next such that ¿1 ¿ ¿2 ¿ ... ¿ ¿m. The new model performs very well based on relative error and mean square error. The model is generally superior to the popular AMSAA model, regardless of the actual underlying failure process. In addition, the results indicate a notable bias in the AMSAA model, early in the development process, regardless of the actual underlying failure process.

A Bayes Reliability Growth Model for A Development Testing Program

The problem of estimating the reliability of a system during development is considered. The development process has several stages at each stage binomial test data are obtained by testing a number of such systems on a success/fail basis. Marginal posterior distributions are derived under the assumption that the development process constrains the reliabilities to be nondecreasing and that the prior distribution for reliability at each stage is uniform. Simulation models are designed to facilitate testing for the validity and computation of the Bayesian model with ordered reliabilities as well as to compare results with other reliability growth models.

Optimal Stress Screening strategies formulti‐component systems sold under warranty:The case of phase‐type lifetimes

Environmental Stress Screening (ESS) is employed to reduce, if not eliminate, the occurrence of early field failures. This paper examines the necessary trade‐offs between the reduction in warranty costs and the increase in manufacturing costs associated with optimal stress screening strategies. A multi‐level ESS model is presented for a multi‐component electronic system. Screening can be performed at component, unit, and system levels. Components and connections are assumed to come from good and substandard populations and their time‐to‐failure distributions are modeled by mixed distributions. The majority of ESS models found in the literature assume that the time‐to‐failure distributions are exponential. The exponential distribution is used primarily to take advantage of its mathematical tractability. This paper generalizes previous work by modeling component and connection lifetimes with phase-type distributions. Phase‐type distributions offer the advantage of mathematical tractability as well as versatility in the family of distributions they can represent. To date there is no significant research into the impact that the selection of a lifetime distributions for modeling the failure process has on ESS decisions. In this paper, we evaluate screening strategies for several lifetime distributions. Numerical examples are provided to illustrate the effect of various model parameters on the optimal stress screening strategy.

Bayesian reliability analysis using the Dirichlet prior distribution with emphasis on accelerated life testing run in random order

Abstract This paper examines Bayesian analysis as a tool for predicting both reliability growth and reliability of censored multi-level, multi-stress accelerated life tests. The methodology is examined using the Dirichlet prior distribution in reliability growth applications and in randomly ordered accelerated life tests occurring in designed experiments (DOE). A simulation is used to examine the utility and accuracy of the approach both graphically and statistically. The results are both enlightening and conclusive

Environmental stress screening strategies for complex systems: A 3-level mixed distribution model

Abstract Environmental Stress Screening (ESS) is employed to reduce, if not eliminate, the occurrence of early field failures. In this paper, a three level ESS model is presented for a complex electronic system. Screening is performed at the component, board and system level. Components are screened for a specified duration before being assembled into printed circuit boards (PCBs). Defects introduced during the assembly of the PCBs are screened at the board level, while defects introduced during final assembly are screened at the system level. Components and connections are assumed to come from good and substandard populations and their times-to-failure distributions are modeled by mixed distributions. Mixed exponential distributions are used to model component timesto-failure and mixed Weibull distributions are used to model the times-to failure for board and system level connections. The mixed Weibull distributions are used to model wear-out characteristics at the board and system level. Optimal screen durations in the presence of wear-out are obtained by minimizing the systems life-cycle cost. ESS is shown to be a cost effective strategy when properly implemented. The optimal screening strategies are shown to be relatively robust to the system warranty period.

Availability/reliability engineering analysis of three, four, and five-stage unreliable series transfer lines

Abstract Series transfer lines provide the modern manufacturing facility with an orderly and efficient method of product assembly. Sequential tasks are assigned to specific workstations along the line. Buffers between the workstations provide on-line inventories to regulate product flow along the line. Previous reliability or availability analysis of these lines employed continuous-time Markov chain models. The analysis here focuses on recent developments in discrete-time Markov modeling of lines with unreliable workstations and nonfailing buffers. Specifically, this paper demonstrates a more stable and efficient computation of stationary-state workstation buffer model probabilities for unreliable lines. In addition, a highly efficient algorithm was developed to isolate and remove transient states from the model. Finally, a regression analysis linear model was developed to predict the effects of changing individual workstation availabilities and buffer capacities on overall line availability.

A Moments Compiler for Computing Bayes Intervals for Complex Systems

This paper develops algorithms and computer processable expressions for the practical computation of the moments of system reliability from the moments of the individual components. The linear (de)composition of structures is extended to an hierarchical (de)composition of reliability functions and moments. A computer processable expression of the system structure is presented for defining an arbitrary configuration of any size of multiple series, parallel, complete, and partial k-out-of-n:G modules.