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Bayes' equation, reliability, and multiple hypothesis testing
16
W O R L D A B S T R A C T S ON M I C R O E L E C T R O N I C S
Systematic procedures for fitting priors are shown for Type 1 date (number of failures in fixed time T) and Type 2 data (observed MTBF, number of failures not the same for all equipments) and specific data criteria, in the form of minimum values of n (number of equipments) and K (number of failures) are presented. The inverted-Smm~a prior-distributious were derived from operational failure data obtained from "linker AFB. The equipments are primarily clectrouie, therefore, the timem-failure distribution was assumed to be exponential; however, the methods are generally applicable whatever the form of the conditional distribution. The robustness anal~is shows the affects of errors in cstimatin8 the parametera of the prior on the pmterlor distribution. In general, the effect of errors in estimating parameters of the prior was practically negligible for large values of K. Reliability modzl/ng. Tool of the system smal~mt. H. A. M.Ac~c. M/¢redectron. ~ Rd/ab. 11 (1972), p. 159. "Reliability" is defined differently in related technical areas---and sometimes even within the same area. In the design of switching systems, however, reliability plays an important role at all design levels (system, subsystem, circuit and component). A solid, cost-effective reliability program on a project can benefit everyone involved, from the producer to the ultimate user. This article outlincs some of the concepts, ideas and implementations of reliability in system design. Several reliability topics are touched upon; however, there are many more topics not covered. A review of n e w methods a n d atflmdN in reliability e n l l i n e e ~ e ~ H. S. BLAb-aS.Proc. IRE£, April (1972), p. 121. The paper reviews new attitudes and methods in reliability engineeringshowing, ~ a//a the growing scepticism about, and sophistication of, reliability prediction. The emphasis on rcliabilityphysics and reliability improvement program is discussed, as well as recent work on aceclerated te~:ing, component screening and reliability testing of integrated circuits by means of a standard component. Recently investigated failure mechanisms and tools of analysis are reviewed. The U.K. BS9000 scheme and its status are briefly discussed.
AND RELIABILITY
that are related to electronic equipment. Examples are pres~ted of reliability computations in three of these four classes. FACh of the three specific reliability tasks described was originally undertaken to satisfy an engineering need for reliability deta. The form and interpretation of the print-out of the specific reliability computations is presanted. The justi£cation for the costs of these computations is indicated. The skills of the personnel used to conduct the analyses, the interfaces between the personnel, and the timing of the project is discussed.
l~hlml~ty ~
by p r e c ~ coaerol. W. H.
rout G. A. BROW~. I 0 ~ IEEE .4mull Proceediqs, ~ Phyla 1972, p. 42. It can be argued whether minor process improvements affect the reliability of semiconductor devices which pass extemive ftmctional and reliability tests. On the other hand, the impmvemenmin manufacturingprocesses and reliability testing which will result from the basic understanding and control of key processes ~ have a significant impact on rcliablh'ty and maintenance cost. For instance, a sisnifieant fraction of device failures are due to device parameter changes caused by changes in dopants, impurities, or defects in critical areas superimposed on broad parameter distribut/ous. By identifying how such defects axe introduced and how they affect device performance and reliability, they can be elimirutted or direct screening tests can be established. This paper describes two examples, selected from bipolar and MOS silicon devices, for which oae aspect of device reliability, namely the ~ stab///~, has been improved by co~trollin8 materials and processes. Simplified test structures were sttccemfidly.employed which were theoretically u ~ and permitted computerized data evaluation and interpretation. The analytical techniques included the memuremant of device parameters, ew/uation of calmcitance-voltsse and conductance-voltsge curves, and definition of stress tests. Device and pro,~_~_~rno&~ine efforts led to the propo6ed mechanisms which dominate stability, and allowed correlation of these meah~mltms with fabrication processes. Scmto~, J. G. A ~
Bayes' equation, re~gb/li~, a n d multiple hy-
t~aure physics ~
to XC mlisWUeT.
R. H. FAnROWand G. W. PAma~ M/¢roebetro~ Rd/ab. II (1972), p. 151. Assessment of integrated circuit reliability poses extreme diffacutfies since rarely is there sut]Iclant informstion for meaninllful MTBF estimations. Under such circumstances one may be obliged to adopt the failure physics approach. This approach to rclmbillty is outlined and an extensive list of defects and fidlure mechanisms is given together ~ the e n h a n ~ a ~ n t stresses that will cause the failures to manifcst themselves.
comtmter ~
of device c t r a / t , ~
t
a n d system mlisbtl/ty. D. R. C ~ Y . IRBE Tram. Rd/ab. R-21, No. 2, MJy (1972), p. 84, Asmupinginto four dasscs is proposed for sli reliability computatimm
g e t l m ~ t m t h ~ W. J. MtcF~e.~rD. I ~ E
Trans.
Rd/ab. R-21, No. 3, August (1972), p. 136. The rudiments of Wl~yins Baym' Equation to h y p o t h e ~ concoming reliability are intmduzed in a simple manner. The appllcat/on is a mem~ of o b t e i n ~ pmterior probabilities, for the r ~ hypotheses, which are cormistent with the prior ~ and the avsikble test results. The pmterior distributions, from which decision theory could fonmlly arrive at optimal cstimatm, are greatly ~ t on the prior distr/bu~oDs. Thus, the discussion centers about tim dmired propertim of a prior and its effects m the ~ fi~rvarious a,a~_situations. Formulatiom for both continuous-conjugateand discrete representations of the prior beHds are discussed and conmmtad. Tim usa of diszrete priors offers many a d v a n ~ over the use of eontinuous-conjuffate priors.
W O R L D A B S T R A C T S ON M I C R O E L E C T R O N I C S
Systematic procedures for fitting priors are shown for Type 1 date (number of failures in fixed time T) and Type 2 data (observed MTBF, number of failures not the same for all equipments) and specific data criteria, in the form of minimum values of n (number of equipments) and K (number of failures) are presented. The inverted-Smm~a prior-distributious were derived from operational failure data obtained from "linker AFB. The equipments are primarily clectrouie, therefore, the timem-failure distribution was assumed to be exponential; however, the methods are generally applicable whatever the form of the conditional distribution. The robustness anal~is shows the affects of errors in cstimatin8 the parametera of the prior on the pmterlor distribution. In general, the effect of errors in estimating parameters of the prior was practically negligible for large values of K. Reliability modzl/ng. Tool of the system smal~mt. H. A. M.Ac~c. M/¢redectron. ~ Rd/ab. 11 (1972), p. 159. "Reliability" is defined differently in related technical areas---and sometimes even within the same area. In the design of switching systems, however, reliability plays an important role at all design levels (system, subsystem, circuit and component). A solid, cost-effective reliability program on a project can benefit everyone involved, from the producer to the ultimate user. This article outlincs some of the concepts, ideas and implementations of reliability in system design. Several reliability topics are touched upon; however, there are many more topics not covered. A review of n e w methods a n d atflmdN in reliability e n l l i n e e ~ e ~ H. S. BLAb-aS.Proc. IRE£, April (1972), p. 121. The paper reviews new attitudes and methods in reliability engineeringshowing, ~ a//a the growing scepticism about, and sophistication of, reliability prediction. The emphasis on rcliabilityphysics and reliability improvement program is discussed, as well as recent work on aceclerated te~:ing, component screening and reliability testing of integrated circuits by means of a standard component. Recently investigated failure mechanisms and tools of analysis are reviewed. The U.K. BS9000 scheme and its status are briefly discussed.
AND RELIABILITY
that are related to electronic equipment. Examples are pres~ted of reliability computations in three of these four classes. FACh of the three specific reliability tasks described was originally undertaken to satisfy an engineering need for reliability deta. The form and interpretation of the print-out of the specific reliability computations is presanted. The justi£cation for the costs of these computations is indicated. The skills of the personnel used to conduct the analyses, the interfaces between the personnel, and the timing of the project is discussed.
l~hlml~ty ~
by p r e c ~ coaerol. W. H.
rout G. A. BROW~. I 0 ~ IEEE .4mull Proceediqs, ~ Phyla 1972, p. 42. It can be argued whether minor process improvements affect the reliability of semiconductor devices which pass extemive ftmctional and reliability tests. On the other hand, the impmvemenmin manufacturingprocesses and reliability testing which will result from the basic understanding and control of key processes ~ have a significant impact on rcliablh'ty and maintenance cost. For instance, a sisnifieant fraction of device failures are due to device parameter changes caused by changes in dopants, impurities, or defects in critical areas superimposed on broad parameter distribut/ous. By identifying how such defects axe introduced and how they affect device performance and reliability, they can be elimirutted or direct screening tests can be established. This paper describes two examples, selected from bipolar and MOS silicon devices, for which oae aspect of device reliability, namely the ~ stab///~, has been improved by co~trollin8 materials and processes. Simplified test structures were sttccemfidly.employed which were theoretically u ~ and permitted computerized data evaluation and interpretation. The analytical techniques included the memuremant of device parameters, ew/uation of calmcitance-voltsse and conductance-voltsge curves, and definition of stress tests. Device and pro,~_~_~rno&~ine efforts led to the propo6ed mechanisms which dominate stability, and allowed correlation of these meah~mltms with fabrication processes. Scmto~, J. G. A ~
Bayes' equation, re~gb/li~, a n d multiple hy-
t~aure physics ~
to XC mlisWUeT.
R. H. FAnROWand G. W. PAma~ M/¢roebetro~ Rd/ab. II (1972), p. 151. Assessment of integrated circuit reliability poses extreme diffacutfies since rarely is there sut]Iclant informstion for meaninllful MTBF estimations. Under such circumstances one may be obliged to adopt the failure physics approach. This approach to rclmbillty is outlined and an extensive list of defects and fidlure mechanisms is given together ~ the e n h a n ~ a ~ n t stresses that will cause the failures to manifcst themselves.
comtmter ~
of device c t r a / t , ~
t
a n d system mlisbtl/ty. D. R. C ~ Y . IRBE Tram. Rd/ab. R-21, No. 2, MJy (1972), p. 84, Asmupinginto four dasscs is proposed for sli reliability computatimm
g e t l m ~ t m t h ~ W. J. MtcF~e.~rD. I ~ E
Trans.
Rd/ab. R-21, No. 3, August (1972), p. 136. The rudiments of Wl~yins Baym' Equation to h y p o t h e ~ concoming reliability are intmduzed in a simple manner. The appllcat/on is a mem~ of o b t e i n ~ pmterior probabilities, for the r ~ hypotheses, which are cormistent with the prior ~ and the avsikble test results. The pmterior distributions, from which decision theory could fonmlly arrive at optimal cstimatm, are greatly ~ t on the prior distr/bu~oDs. Thus, the discussion centers about tim dmired propertim of a prior and its effects m the ~ fi~rvarious a,a~_situations. Formulatiom for both continuous-conjugateand discrete representations of the prior beHds are discussed and conmmtad. Tim usa of diszrete priors offers many a d v a n ~ over the use of eontinuous-conjuffate priors.