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A bayesian modelling of failure rate
World Abstracts on Microelectronics and Reliability parts and limited life products, as in manpower during all the assessed lifetime of the item. The program allows to compute for two different quality levels: -the capital cost --the support cost according to the maintenance at the first level. --the support cost out of this of the maintenance. --the total life cycle cost. --the support cost according to the maintenance at the second level. The program allows, when using the influence of different parameters, to make the choice between several solutions.
Modelling, estimation and significance testing of reliability growth or burn-in. P. H. MEAD. Proc. C N E T ConJerence on Reliability and Maintainability, Tregastel, France, p. 287 (8-12 September 1980). The processes of reliability growth are shown to be essentially the same whether by simple repair in a burn-in process or by design changes in an improvement programme. However, the latter has the more far reaching effect. In both of these situations there is a need to assess effectiveness and reliability achievement using mathematical models. As well as the Duane reliability growth model the less well known model of IBM and Smith's Industries is presented, and its advantages and more rational basis explained. The methods of assessment using these models are also compared, showing progression from over-simplistic graphical methods to maximum-likelihood (ML) techniques. It is also suggested that the concept of a discrete growth process is more realistic than the continuous process often assumed. ML methods are given for both processes and demonstrated upon real data. The possibility of "extended burn-in" confusing the assessment of reliability improvement is suggested, together with a possible correction method. Finally, a tentative significance test is proposed for comparing growth mode)s and their associated techniques. AFDT~, maintenance software. M. MORGANTI and G. NOVIELLL Proc. C N E T Confi, rence on Reliability and Maintainability, Treqastel, France, p. 434 (8-12 September 1980). The paper outlines the main characteristics and features of the maintenance software developed to ensure to the AFDT z, a PCM SPC fully electronic telephone exchange for voice and data. switching, the attainment of all of its dependability and availability goals. Emphasis has been put on those choices and solutions which better testify to the comprehensiveness and of the originality of the whole approach, and particularly on the use of Petri-nets as an effective instrument for the implementation of recovery strategies in redundant fault-tolerant systems. A Bayesian modelling of failure rate. R. RINGLER. Proc. C N E T Co~!/&ence on Reliability and Maintainability, Treyastel, France, p. 262 (8-12 September 1980). (In French). The classical approach in reliability in which no difference is made between the failure rates of various electronic components making up an assumedly homogenous batch, leads to some formal difficulties which will be demonstrated. A new approach is proposed in which each component in the batch is characterized by its own "'stress resistance capability". This approach leads us to postulate the existence of an individual "lambda'" attached to each component and thus that of a statistical distribution of the "lambdas" at batch level. Taking this distribution as a law a priori, a Bayesian treatment is then applied. The result is a formatization of an inconditional failure rate reflecting the mean failure rate of the batch considered. Choosing a priori a gamma type distribution law (justified by reasons of a
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practical and theorical nature), it will be shown that the inconditional failure rate decreases hyperbolically with time. Consequently, a new "'bath-curve" profile is obtained in which the horizontal line becomes slightly inclined. Lastly, the proposed model reveals a simple relationship between the burn-in time for a batch of components and the inconditional failure rate of the same batch after burn-in.
Suitability of the Iognormal distribution for repair times. PROF. M. B. KLINE. Proc. C N E T Cm!/erence on Reliability and Maintainability, Treyastel, France, p. 338 (8-12 September 1980). The usual mathematical formulation for availability assumes an exponential distribution for failure and repair times. While such an assumption is sometimes correct for reliability, it is not valid for maintainability. This study was conducted to verify that the Iognormal distribution is a suitable descriptor for corrective maintenance repair times and to estimate the error caused in assuming an exponential distribution for availability and maintainability calculations when in fact the distribution is lognormal. Twenty-four sets of existing maintainability demonstration repair time data, from nineteen essentially electronic systems, were analyzed using the methods of probability plotting and statistical goodness-of-fit testing for distributional assumption. The results show that the lognormal distribution assumption cannot be reject in most of the cases, while the exponential distribution is rejected. The error in calculating inherent availability caused when assuming an exponential distribution for MTTR was found to be negligible. Dependability evaluation of computer system with stochastic PETRi nets. G. FLORIN, P, LONG and S. NATK1N. Proc. C N E T Conference on Reliability and Maintainability, Treyastel, France, p. 214 (8-12 September 1980). (In French). A computer system can be considered at a certain level of description as a set of elements, the behaviour of each one can generally be represented by an automaton. The system structure (communication between elements, scheduling of resources, activation, reconfiguration and maintenance policies...) defines the synchronizations between automata. Petri nets have been introduced as a mean of representation of automata synchronizations. The time properties of the random phenomena acting on the system can be added to the timeless Petri Nets modelling, using distribution functions. This leads to a rigorous definition of stochastic Petri Nets where the stochastic process associated to "the marking is a semi-Markov process. A method for the evaluation of complex computer system reliability availability and maintainability is given. We briefly present a CAD tool for computer system evaluation based on stochastic Petri Nets. We show how this tool was used for the analysis of a complex configuration (15 computers) used in the automatic control of Caracas subway. Failure data collecting of DX 100 and DX 200 telephone exchanges. P. HAMALAINEN and T. PURHO. Proc. C N E T Cmference on Reliability and Maintainability, Tregastel, France, p. 391 (8-12 September 1980). The first digital telephone exchanges DX 100 and DX 200 are under installation and operation phase in the network of Finnish PTT. Reliability and maintainability (R&M) performances of these systems have been especially taken into account in the systematic reliability and maintainability program between the'supplier and customer. Failure data collection is very important activity. For these exchanges data collecting system with careful failure data and reliability parameter definition, reliability target definition and reliability test plan have been developed. The information to be supplied by the failure data collection will be utilized in availability performance study of the telephone service, as a feed-back to the design and production as well as for the maintenance support purposes. In this paper the availability performance study is of the main interest.
Modelling, estimation and significance testing of reliability growth or burn-in. P. H. MEAD. Proc. C N E T ConJerence on Reliability and Maintainability, Tregastel, France, p. 287 (8-12 September 1980). The processes of reliability growth are shown to be essentially the same whether by simple repair in a burn-in process or by design changes in an improvement programme. However, the latter has the more far reaching effect. In both of these situations there is a need to assess effectiveness and reliability achievement using mathematical models. As well as the Duane reliability growth model the less well known model of IBM and Smith's Industries is presented, and its advantages and more rational basis explained. The methods of assessment using these models are also compared, showing progression from over-simplistic graphical methods to maximum-likelihood (ML) techniques. It is also suggested that the concept of a discrete growth process is more realistic than the continuous process often assumed. ML methods are given for both processes and demonstrated upon real data. The possibility of "extended burn-in" confusing the assessment of reliability improvement is suggested, together with a possible correction method. Finally, a tentative significance test is proposed for comparing growth mode)s and their associated techniques. AFDT~, maintenance software. M. MORGANTI and G. NOVIELLL Proc. C N E T Confi, rence on Reliability and Maintainability, Treqastel, France, p. 434 (8-12 September 1980). The paper outlines the main characteristics and features of the maintenance software developed to ensure to the AFDT z, a PCM SPC fully electronic telephone exchange for voice and data. switching, the attainment of all of its dependability and availability goals. Emphasis has been put on those choices and solutions which better testify to the comprehensiveness and of the originality of the whole approach, and particularly on the use of Petri-nets as an effective instrument for the implementation of recovery strategies in redundant fault-tolerant systems. A Bayesian modelling of failure rate. R. RINGLER. Proc. C N E T Co~!/&ence on Reliability and Maintainability, Treyastel, France, p. 262 (8-12 September 1980). (In French). The classical approach in reliability in which no difference is made between the failure rates of various electronic components making up an assumedly homogenous batch, leads to some formal difficulties which will be demonstrated. A new approach is proposed in which each component in the batch is characterized by its own "'stress resistance capability". This approach leads us to postulate the existence of an individual "lambda'" attached to each component and thus that of a statistical distribution of the "lambdas" at batch level. Taking this distribution as a law a priori, a Bayesian treatment is then applied. The result is a formatization of an inconditional failure rate reflecting the mean failure rate of the batch considered. Choosing a priori a gamma type distribution law (justified by reasons of a
619
practical and theorical nature), it will be shown that the inconditional failure rate decreases hyperbolically with time. Consequently, a new "'bath-curve" profile is obtained in which the horizontal line becomes slightly inclined. Lastly, the proposed model reveals a simple relationship between the burn-in time for a batch of components and the inconditional failure rate of the same batch after burn-in.
Suitability of the Iognormal distribution for repair times. PROF. M. B. KLINE. Proc. C N E T Cm!/erence on Reliability and Maintainability, Treyastel, France, p. 338 (8-12 September 1980). The usual mathematical formulation for availability assumes an exponential distribution for failure and repair times. While such an assumption is sometimes correct for reliability, it is not valid for maintainability. This study was conducted to verify that the Iognormal distribution is a suitable descriptor for corrective maintenance repair times and to estimate the error caused in assuming an exponential distribution for availability and maintainability calculations when in fact the distribution is lognormal. Twenty-four sets of existing maintainability demonstration repair time data, from nineteen essentially electronic systems, were analyzed using the methods of probability plotting and statistical goodness-of-fit testing for distributional assumption. The results show that the lognormal distribution assumption cannot be reject in most of the cases, while the exponential distribution is rejected. The error in calculating inherent availability caused when assuming an exponential distribution for MTTR was found to be negligible. Dependability evaluation of computer system with stochastic PETRi nets. G. FLORIN, P, LONG and S. NATK1N. Proc. C N E T Conference on Reliability and Maintainability, Treyastel, France, p. 214 (8-12 September 1980). (In French). A computer system can be considered at a certain level of description as a set of elements, the behaviour of each one can generally be represented by an automaton. The system structure (communication between elements, scheduling of resources, activation, reconfiguration and maintenance policies...) defines the synchronizations between automata. Petri nets have been introduced as a mean of representation of automata synchronizations. The time properties of the random phenomena acting on the system can be added to the timeless Petri Nets modelling, using distribution functions. This leads to a rigorous definition of stochastic Petri Nets where the stochastic process associated to "the marking is a semi-Markov process. A method for the evaluation of complex computer system reliability availability and maintainability is given. We briefly present a CAD tool for computer system evaluation based on stochastic Petri Nets. We show how this tool was used for the analysis of a complex configuration (15 computers) used in the automatic control of Caracas subway. Failure data collecting of DX 100 and DX 200 telephone exchanges. P. HAMALAINEN and T. PURHO. Proc. C N E T Cmference on Reliability and Maintainability, Tregastel, France, p. 391 (8-12 September 1980). The first digital telephone exchanges DX 100 and DX 200 are under installation and operation phase in the network of Finnish PTT. Reliability and maintainability (R&M) performances of these systems have been especially taken into account in the systematic reliability and maintainability program between the'supplier and customer. Failure data collection is very important activity. For these exchanges data collecting system with careful failure data and reliability parameter definition, reliability target definition and reliability test plan have been developed. The information to be supplied by the failure data collection will be utilized in availability performance study of the telephone service, as a feed-back to the design and production as well as for the maintenance support purposes. In this paper the availability performance study is of the main interest.