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A study of an ordinary and empirical Bayes approach to reliability estimation in the gamma life testing model
302
WORLD
ABSTRACTS
ON MICROELECTRONICS
effort in economic terms. This paper describes some of the basic relations by which the interaction of reliability with economic parameters can be modelled. Specifically, it is shown how the cost of failure and the cost of failure prevention (reliability improvement) can be expressed in comparable terms, how an economically optimum reliability level can be defined, how the economic benefits of various improvements can be ranked, and how economic criteria can decide whether to spend a limited budget on reliability improvement or in other areas.
Responsive reliability proposals in a tight market. M. B. GREENFIELD, Proe. Ann. Syrup. Reliab., Washington DC, U.S.A. IEEE Cat. No. 71C 2-R. 12-14 January (1971), p. 133. A diversity of forces have been at work for several years to bring about difficult business conditions with which we are presently faced. This paper presents the case for improving industry competitive posture in proposing reliability programs in the existing difficult market environment.
"Weibull" decreasing hazard rate--help or hoax? L. SESSEN,Proc. Ann. Symp. Reliab., Washington DC, U.S.A. IEEE Cat. No. 71C 2-R, 12-14 January (1971), p. 28. Frequently expressed ideas are shown to be fallacious; namely, that hazard rate significantly decreases indefinitely with age, that there exists no such thing as inherent (constant at specific stress) reliability which "uniformed" (non-hip generation) engineers try to predict by calculation, and that the Government should accept equipment with high hazard rate all because some cumulative hazard rates vs. age decrease and are approximated by straight lines (so-called "Weibull") on log-log paper. The Two-Line All-Equipments Test (TAT) and the Aeronautical Systems Division (ASD) reliability testing are analyzed using "Weibull" Monte Carlo simulation. T A T is shown to be more effective than traditional MIL-STD-781B 6 production acceptance testing in preventing the acceptance of infant mortality and precluding the necessity of a Government specified burn-in. ASD testing is shown to, in addition, encourage reliability improvement effort. It is shown that it is not cost effective to waive or adulterate reliability requirements except when unreliability is confined to a small percentage of a weapon system which is not critical to mission success.
A study of an ordinary and empirical Bayes approach to reliability estimation in the g a m m a life testing model. G. C. CANAVOS,Proc. Ann. Symp. Reliab., Washington DC, U.S.A. IEEE Cat No. 71C 2-R. 12-14 January (1971), p. 343. For life-testing procedures, an ordinary, as well as an empirical, Bayesian analysis is developed for a random scale parameter in the gamma distribution. For known shape parameter, ordinary Bayes estimators are derived for the scale parameter and the reliability function; the estimators are based on a
AND RELIABILITY
uniform, an exponential and an inverted gamma prior distribution. The philosophy of empirical Bayes parallels that of ordinary Bayes with the exception that the form of the prior distribution is not assumed known. Instead, empirical Bayes estimators are developed based upon prior experiences whose existence is assumed. A simulation procedure is implemented and a comparison is made between Bayes, empirical Bayes and existing minimum variance unbiased estimators. As expected, the Bayes estimators have the smallest mean squared errors. Moreover, for five or more past experiences empirical Bayes estimators generally have smaller mean squared errors than minimum variance unbiased estimators.
Total confidence limits on observed reliability. H. G. JACKS,Proc. Ann. Syrup. Reliab., Washington DC, U.S.A. IEEE Cat .No. 71C 2-R, 12-14 January (1971), p. 338. Field failure reporting systems are notorious for their inaccuracy, ambiguity and incomplete coverage. For this reason, equipment reliability estimates based on use of field data are subject to errors much greater than those predicted by use of ordinary statistical methods. More realistic bounds on the range of possible error in field reliability estimates are obtained if the analyst's subjective evaluation of the validity of each incident report is combined with total quantity of data in a suitable manner. Techniques for quantifying data validity judgements and for combining the validity estimates with time and number of incidents are presented together with some suggestions for further study.
A facelifting for NASA's reliability requirements. D. S. LIBERMAN,Proc. Ann. Symp. Reliab., Washington DC, U.S.A. IEEE Cat. No. 71C 2-R, 12-14 January (1971), p. 121. In April 1970, NASA issued its secondgeneration reliability requirements publication NHB 5300.4(1A), Reliability Program Provisions for Aeronautical and Space System Contractors. This publication, which supersedes NPC 250-1, represents the latest major step in the evolution of the reliability assurance discipline in NASA and its response to the continuing development of NASA program needs, assurance capabilities and procurement practices. This paper will attempt to review briefly that evolution process and describe the resulting changes in the requirements of NHB 5300.4 (1A) from those of its predecessor.
Applications determine the design, materials, processes and package. G. R. MADLAND, Proc. IEEE Reliab. Phys. Symp., Las Vegas, U.S.A. 31 M a r c h 2 April (1971). For years the system designer has selected rather than designed his semiconductor devices, including microcircuits. Environmental, performance and reliability needs were then approached by modification or merely by additional testing and screening. This paper shows how these needs can be met and a 10:1 reliability improvement realized by proper system, circuit, process and package design especially with M S I or LSI.
WORLD
ABSTRACTS
ON MICROELECTRONICS
effort in economic terms. This paper describes some of the basic relations by which the interaction of reliability with economic parameters can be modelled. Specifically, it is shown how the cost of failure and the cost of failure prevention (reliability improvement) can be expressed in comparable terms, how an economically optimum reliability level can be defined, how the economic benefits of various improvements can be ranked, and how economic criteria can decide whether to spend a limited budget on reliability improvement or in other areas.
Responsive reliability proposals in a tight market. M. B. GREENFIELD, Proe. Ann. Syrup. Reliab., Washington DC, U.S.A. IEEE Cat. No. 71C 2-R. 12-14 January (1971), p. 133. A diversity of forces have been at work for several years to bring about difficult business conditions with which we are presently faced. This paper presents the case for improving industry competitive posture in proposing reliability programs in the existing difficult market environment.
"Weibull" decreasing hazard rate--help or hoax? L. SESSEN,Proc. Ann. Symp. Reliab., Washington DC, U.S.A. IEEE Cat. No. 71C 2-R, 12-14 January (1971), p. 28. Frequently expressed ideas are shown to be fallacious; namely, that hazard rate significantly decreases indefinitely with age, that there exists no such thing as inherent (constant at specific stress) reliability which "uniformed" (non-hip generation) engineers try to predict by calculation, and that the Government should accept equipment with high hazard rate all because some cumulative hazard rates vs. age decrease and are approximated by straight lines (so-called "Weibull") on log-log paper. The Two-Line All-Equipments Test (TAT) and the Aeronautical Systems Division (ASD) reliability testing are analyzed using "Weibull" Monte Carlo simulation. T A T is shown to be more effective than traditional MIL-STD-781B 6 production acceptance testing in preventing the acceptance of infant mortality and precluding the necessity of a Government specified burn-in. ASD testing is shown to, in addition, encourage reliability improvement effort. It is shown that it is not cost effective to waive or adulterate reliability requirements except when unreliability is confined to a small percentage of a weapon system which is not critical to mission success.
A study of an ordinary and empirical Bayes approach to reliability estimation in the g a m m a life testing model. G. C. CANAVOS,Proc. Ann. Symp. Reliab., Washington DC, U.S.A. IEEE Cat No. 71C 2-R. 12-14 January (1971), p. 343. For life-testing procedures, an ordinary, as well as an empirical, Bayesian analysis is developed for a random scale parameter in the gamma distribution. For known shape parameter, ordinary Bayes estimators are derived for the scale parameter and the reliability function; the estimators are based on a
AND RELIABILITY
uniform, an exponential and an inverted gamma prior distribution. The philosophy of empirical Bayes parallels that of ordinary Bayes with the exception that the form of the prior distribution is not assumed known. Instead, empirical Bayes estimators are developed based upon prior experiences whose existence is assumed. A simulation procedure is implemented and a comparison is made between Bayes, empirical Bayes and existing minimum variance unbiased estimators. As expected, the Bayes estimators have the smallest mean squared errors. Moreover, for five or more past experiences empirical Bayes estimators generally have smaller mean squared errors than minimum variance unbiased estimators.
Total confidence limits on observed reliability. H. G. JACKS,Proc. Ann. Syrup. Reliab., Washington DC, U.S.A. IEEE Cat .No. 71C 2-R, 12-14 January (1971), p. 338. Field failure reporting systems are notorious for their inaccuracy, ambiguity and incomplete coverage. For this reason, equipment reliability estimates based on use of field data are subject to errors much greater than those predicted by use of ordinary statistical methods. More realistic bounds on the range of possible error in field reliability estimates are obtained if the analyst's subjective evaluation of the validity of each incident report is combined with total quantity of data in a suitable manner. Techniques for quantifying data validity judgements and for combining the validity estimates with time and number of incidents are presented together with some suggestions for further study.
A facelifting for NASA's reliability requirements. D. S. LIBERMAN,Proc. Ann. Symp. Reliab., Washington DC, U.S.A. IEEE Cat. No. 71C 2-R, 12-14 January (1971), p. 121. In April 1970, NASA issued its secondgeneration reliability requirements publication NHB 5300.4(1A), Reliability Program Provisions for Aeronautical and Space System Contractors. This publication, which supersedes NPC 250-1, represents the latest major step in the evolution of the reliability assurance discipline in NASA and its response to the continuing development of NASA program needs, assurance capabilities and procurement practices. This paper will attempt to review briefly that evolution process and describe the resulting changes in the requirements of NHB 5300.4 (1A) from those of its predecessor.
Applications determine the design, materials, processes and package. G. R. MADLAND, Proc. IEEE Reliab. Phys. Symp., Las Vegas, U.S.A. 31 M a r c h 2 April (1971). For years the system designer has selected rather than designed his semiconductor devices, including microcircuits. Environmental, performance and reliability needs were then approached by modification or merely by additional testing and screening. This paper shows how these needs can be met and a 10:1 reliability improvement realized by proper system, circuit, process and package design especially with M S I or LSI.