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Failure rate functions from test data
406
WORLD
ABSTRACTS
ON
MICROELECTRONICS
being determined from the ratio of the sample arithmetic mean to the sample geometric mean, requires a complete random sample, yet is independent of the scale parameter. M o m e n t s of a function of the estimator are delineated explicitly; representative distributions associated with the estimator are determined by means of a Monte Carlo analysis. Comparisons, both with the m a x i m u m likelihood estimator and with the estimator based on the method of m o m e n t s for logarithmic transformations of Weibull variates, conclude the paper,
Analysis of early failures in unequal size samples. R. A. HELLER and S. A. HELLER. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January, p. 198. Early failures in unequal size fleets are used to estimate the population distribution function using a combination of analytical and graphical methods. The analysis is based on order statistics and extreme value theory. Failure rate functions from test data. HENRICK V. J. BROBERG, INGER A. M. GUSTAFSON and S. G. FREDRIK SANDIN. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January, p. 109. Presented in this paper is a computerized method for analysis of reported data from operation and testing of components and equipment. The system is based on the hazard plotting technique. When treating the information, consideration i s taken for every tested unit to the following factors: age and test time, failure mode, failure definitions, operational and environmental parameters. As an intermediate result the mean failure rate and confidence limits for times between consecutive observations are given and plotted. Owing to the pattern of the failure rate functions, the operator may choose different statistical distributions for three different intervals of age, so that continuous functions for failure rate and confidence limits can be given. Reliability data plotting using the Pearson curves. FRANCIS J. BREWERTON. Proceedings 1973 IEEE Reliability Maintainability Symposium. 23 25 January, p. 270. One of the basic purposes of failure data collection and analysis is the eventual prediction of failure patterns. Since reliability is defined as the probability that a device will operate satisfactorily for a specified period of time, collection and analysis of failure data play an important role in determining this probability of successful operation. All reliability computations are based either directly or indirectly on an assumed or observed distribution of failures. However, conventional methods of data treatment and description are not always efficient or sufficiently accurate for determination of failure probabilities. Censored sample size selection for life tests. JOHN I. McCOOL. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January, p. 280. The proper choice of the sample size n and the number of failures r in designing a life test is shown to be governed by the use to which the test results will be put. Examples are given of the differences in sample sizes that result when the purposes are:
AND
RELIABILITY
1. The conduct of an acceptance test based on a specific percentile value of the life distribution. 2. The determination of a "historical" value of a percentile. The examples are based on existing results for the exponential distribution and some more recent results for the Weibull distribution.
Modeling the bathtub curve. THOMASW. CALVIN. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January (1973), p. 577. Attempts to model a " b a t h t u b " curve often assume that useful life (the fiat portion of the curve), and wearout (the increasing portion) begin after time zero. The resulting models are called either composite or mixed, depending on the method of model building. Infant mortality, random, and wearout failure modes are relegated to the appropriate portions of the bathtub curve. An approach is suggested in which all models of failure begin at time zero. By looking at the unit (device, component, machine, etc.) as a serial system with respect to failure mechanisms in which any failure results in unit failure, reliability is the product of the reliabilities of the individual mechanisms; equivalently the cumulative hazard is the sum of the individual cumulative hazards. Sampling programs for reliability. GERALD L. LIEBERMAN. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January (1973), p. 275. This paper is concerned with six different types of programs to determine lower confidence bounds on R(to), the reliability at time to, and on the time tR, corresponding to a fixed reliability R. The six plans considered are various combinations of sampling with and without replacement, censored sampling, truncated sampling, and mixed censored-truncated sampling. Complete results are presented when the underlying time to failure distribution is assumed to be exponential, and partial results are given for the Weibull.
Discounting utilization in order to optimise reliability choices on an economic level. J M MOULON Onde Elect. 53, Fasc. 4, April (1973), pp. 117 120. (In French). For comparative purposes on an economic level, choosing an optimum reliability requires expenses incurred at the origin (manufacture) and other expenses incurred later on (failures) to be taken into account. The author establishes very simple relations, based on the discounting method, which enable one to estimate the total cost, allowing for manufacture and failures. The reliability of failure rates. H. G. VAN DIEST. Philips Telecommun. Rev. 31, No. l, January (1973), pp. 1-12. Failure rates of components play an important role in the design of large systems, some of which may have useful lives of 25 to 40 years. Studies over prolonged periods, closely observing and evaluating the failures in a number of systems, resulted in very favourable failure rates. These were obtained by a tight discipline of type approval, quality control and derating. Overstress testing is one way of examining failure mechanisms. Some of these mechanisms are mentioned, of which electromigration is highlighted.
WORLD
ABSTRACTS
ON
MICROELECTRONICS
being determined from the ratio of the sample arithmetic mean to the sample geometric mean, requires a complete random sample, yet is independent of the scale parameter. M o m e n t s of a function of the estimator are delineated explicitly; representative distributions associated with the estimator are determined by means of a Monte Carlo analysis. Comparisons, both with the m a x i m u m likelihood estimator and with the estimator based on the method of m o m e n t s for logarithmic transformations of Weibull variates, conclude the paper,
Analysis of early failures in unequal size samples. R. A. HELLER and S. A. HELLER. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January, p. 198. Early failures in unequal size fleets are used to estimate the population distribution function using a combination of analytical and graphical methods. The analysis is based on order statistics and extreme value theory. Failure rate functions from test data. HENRICK V. J. BROBERG, INGER A. M. GUSTAFSON and S. G. FREDRIK SANDIN. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January, p. 109. Presented in this paper is a computerized method for analysis of reported data from operation and testing of components and equipment. The system is based on the hazard plotting technique. When treating the information, consideration i s taken for every tested unit to the following factors: age and test time, failure mode, failure definitions, operational and environmental parameters. As an intermediate result the mean failure rate and confidence limits for times between consecutive observations are given and plotted. Owing to the pattern of the failure rate functions, the operator may choose different statistical distributions for three different intervals of age, so that continuous functions for failure rate and confidence limits can be given. Reliability data plotting using the Pearson curves. FRANCIS J. BREWERTON. Proceedings 1973 IEEE Reliability Maintainability Symposium. 23 25 January, p. 270. One of the basic purposes of failure data collection and analysis is the eventual prediction of failure patterns. Since reliability is defined as the probability that a device will operate satisfactorily for a specified period of time, collection and analysis of failure data play an important role in determining this probability of successful operation. All reliability computations are based either directly or indirectly on an assumed or observed distribution of failures. However, conventional methods of data treatment and description are not always efficient or sufficiently accurate for determination of failure probabilities. Censored sample size selection for life tests. JOHN I. McCOOL. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January, p. 280. The proper choice of the sample size n and the number of failures r in designing a life test is shown to be governed by the use to which the test results will be put. Examples are given of the differences in sample sizes that result when the purposes are:
AND
RELIABILITY
1. The conduct of an acceptance test based on a specific percentile value of the life distribution. 2. The determination of a "historical" value of a percentile. The examples are based on existing results for the exponential distribution and some more recent results for the Weibull distribution.
Modeling the bathtub curve. THOMASW. CALVIN. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January (1973), p. 577. Attempts to model a " b a t h t u b " curve often assume that useful life (the fiat portion of the curve), and wearout (the increasing portion) begin after time zero. The resulting models are called either composite or mixed, depending on the method of model building. Infant mortality, random, and wearout failure modes are relegated to the appropriate portions of the bathtub curve. An approach is suggested in which all models of failure begin at time zero. By looking at the unit (device, component, machine, etc.) as a serial system with respect to failure mechanisms in which any failure results in unit failure, reliability is the product of the reliabilities of the individual mechanisms; equivalently the cumulative hazard is the sum of the individual cumulative hazards. Sampling programs for reliability. GERALD L. LIEBERMAN. Proceedings 1973 IEEE Annual Reliability Maintainability Symposium. 23-25 January (1973), p. 275. This paper is concerned with six different types of programs to determine lower confidence bounds on R(to), the reliability at time to, and on the time tR, corresponding to a fixed reliability R. The six plans considered are various combinations of sampling with and without replacement, censored sampling, truncated sampling, and mixed censored-truncated sampling. Complete results are presented when the underlying time to failure distribution is assumed to be exponential, and partial results are given for the Weibull.
Discounting utilization in order to optimise reliability choices on an economic level. J M MOULON Onde Elect. 53, Fasc. 4, April (1973), pp. 117 120. (In French). For comparative purposes on an economic level, choosing an optimum reliability requires expenses incurred at the origin (manufacture) and other expenses incurred later on (failures) to be taken into account. The author establishes very simple relations, based on the discounting method, which enable one to estimate the total cost, allowing for manufacture and failures. The reliability of failure rates. H. G. VAN DIEST. Philips Telecommun. Rev. 31, No. l, January (1973), pp. 1-12. Failure rates of components play an important role in the design of large systems, some of which may have useful lives of 25 to 40 years. Studies over prolonged periods, closely observing and evaluating the failures in a number of systems, resulted in very favourable failure rates. These were obtained by a tight discipline of type approval, quality control and derating. Overstress testing is one way of examining failure mechanisms. Some of these mechanisms are mentioned, of which electromigration is highlighted.