- Email: [email protected]
Optimal replacement rate of devices with lognormal failure distributions
416
World Abstracts on Microelectronics and Reliability
chip protection of CMOS/SOS IC gate oxides. For these gate oxides, the dielectric strength of ~ 800 A thick silicon dioxide on SOS was ~ 7 x 106volts/era for I00 nanosecond pulses.
Effects of electrostatic discharge on linear bipolar integrated circuits. R. L. MINEAR and G. A. Dot)soN. 15th 4. Proc. 3. C I R C U I T
AND
SYSTEMS
RELIABILITY,
Decision making in reliability, V. S. SRINIVASAN and K. V. RAMACHANDRA. IEEE Trans. Reliab, R-26, (4) 261 (October 1977). Distribution-free methods are evolved for 4 models of evaluating time-to-failure. Two decision procedures for choosing the better of two equipments are given in models I and II. Decision procedures for whether two equipments have the same availability or reliability are given in models llI and IV; in these models, it is assumed that the mission time is a r.v. in the interval (0, To). The method of model I is superior to existing tests like the Wilcoxon-Rank-Sum test and Mann-Whitney test in a particular case. Model II is based on the time taken to return to the initial state by a Markov chain and is optimum for large sample sizes. In model III, even though the distributions of time to failure and time to repair-completion are negative exponential, the method is general, distribution-free and optimal. Hence the type I error is constant even if the distributions of time to failure and repair-completion differ from the assumed distributions. Model IV is also distribution-flee and optimum.
Time dependent unavailability analysis of nuclear safety systems. W. E. VESELY and F. F. GOLDBERG. IEEE Trans. Reliah. R-26, (4) 257 (October 1977). A method is presented to predict the time-dependent system unavailability, which includes consideration of the detailed effects of different periodic testing schemes. The FRANTIC computer code is described; it has been developed to study applications of the approach.
Queuing models for estimating aircraft fleet availability. V. V. S. SARMA, K. RAMCnAND and A. K. RAO. IEEE Trans. Reliab. R-26, (4) 253 (October 1977). The availability of a small fleet of aircraft in a flying-base, repair-depot combination is modeled and studied. First, a deterministic flow model relates parameters of interest and represents the state-of-the art in the planning of such systems. Second, a cyclic queue model shows the effect of the principal uncertainties in operation and repair and shows the consequent decrease in the availability of aircraft at the flyingbase. Several options such as increasing fleet size, investments in additional repair facilities, or building reliability and maintainability into the individual aircraft during its life-cycle are open for increasing the availability. A lifecycle cost criterion brings out some of these features. NumericM results confirm Rose's prediction that there exists a minimal cost combination of end products and repairdepot capability to achieve a prescribed operational availability.
Reliability growth apportionment. J. K, BYERS and D. J. GALL[. IEEE Trans. Reliab. R-26, (4) 242 (October 1977). A method is presented for apportioning reliability growth to the subsystems that make up a system in order to achieve the required reliability at least cost. Reliability growth apportionment is handled as an s-expected cost minimization problem subject to the constraint of meeting a system reliability requirement. The problem is formulated in terms of Duane's reliability growth model, and is solved using geometric programming. The method can be useful in the early stages of system design to determine subsystem reliability growth that will
Reliab. Phys. IEEE (1977) Nevada. p. 138. Electrostatic discharge (ESD) can easily damage bipolar integrated circuits. "Second breakdown" of N P N transistor emitter-base junctions is a common failure mode. No external emitter connection is needed for this to occur. ESD current paths, physics of ESD failure, and design concepts for improved FSD resistance are discussed.
MAINTENANCE
AND
REDUNDANCY
allow a system reliability requirement to be met, and in the latter stages of system design when reliability has fallen short of the required goal and improvements are necessary.
Cost model for testing program based on nonhomogeneous poisson failure model JoH~ DONELSON m. IEEE Trans. Reliab. R-26, (3) 189 (August 1977). A model for the s-expected cost of a development testing program is presented in this paper. The total cost function consists of two terms, The first term is proportional to the duration of the testing program; the second term is a loss function that assesses additional costs for failure to meet reliability goals during the testing program. The reliability growth model assumes that failures during the program occur according to a nonhomogeneous Poisson process having a power-law rate. An example shows how the duration of the test program can be chosen to minimize s-expected total cost.
System availability and optimum spare units. MASAFUMI SASKI, SHIGERU KABURAKI and SH1GERU YANAGI. IEEE Trans. Reliab. R-26, (3) 182 (August 1977). The steady-state availability of a repairable system with cold standbys and nonzero replacement time is maximized under constraints of total cost and total weight. Likewise the cost can be minimized under constraints of steady-state availability and total weight. A new, more efficient algorithm is used for the constrained optimization. The problem is formulated as a nonlinear integer programming problem. Since the objective functions are monotone, it is easy to obtain optimal solutions. These new algorithms are natural extensions of the Lawler Bell algorithm. Availability is adjusted by the number of spares allowed. Other measures of system goodness are considered, viz. failure rate, weight, price, mean repair time, mean repair cost, mean replacement time, and mean replacement cost of a unit.
Optimal replacement rate of devices with lognormal failure distributions. S. S. CHENG. IEEE Trans. Reliab. R-26, (3) 174 (August 1977). The time dependence of the replacement rate of devices with lognormal failure distributions is studied. The relationship between the peak replacement rate and er, the standard deviation in the corresponding s-normal distribution, is obtained. The study assumes that each device represents a renewal process and the system of devices represents a superimposed renewal process. The peak replacement rate becomes very large for both extreme values of (~. The corresponding replacement rate eventually approaches the conventional asymptotic rate only after many MTTFs (Mean Time To Failure), possibly long after the system becomes obsolete. Ways to cope with this situation are suggested. However, the replacement rate curve becomes almost critically damped with a minimumpeak-factor ~ 1.03 at tr ~ 0.63. The study also reveals that asymptotically the lognormal devices with > << 1 would require fewer replacements than the exponential devices with the same MTTF. The difference is equal to one-half of the population in service. For large a, more replacements are required. The results of this paper apply to a variety of reliability studies and maintenance and inventory strategies for communication systems that employ lognormal devices such as a semiconductor laser, LED, avalanche photo diode,
World Abstracts on Microelectronics and Reliability or IMPATT diode. In particular, the present approach is especially helpful when such a device is the least reliable component in the system.
An optimal decision rule for repair vs replacement. EGINHARD J. MUTH. IEEE Trans. Reliab. R-26, (3) 179 (August 1977). This paper presents a policy for either repairing or replacing a system that has failed. The policy applies to systems whose mean residual life function is decreasing. An optimal policy is developed that minimizes the cost per unit time for repair and replacement. Results are shown graphically for a particular distribution of time to failure and are motivated in terms of an automobile replacement problem. Optimal selection of sequential tests for reliability. J. M. MOGG. IEEE Trans. Reliab. R-26, (2) 116 (June 1977). Reliability test requirements exist whereby truncated sequential test methods offer management the opportunity to minimize the s-expected cost of a test by optimal selection of the blend of resources that will be consumed by the test. The models presented here are useful in the real world design of reliability tests because of the case of arriving at cost estimates and the existing availability of statistical distributional information on truncated sequential tests. The test parameters of sample size, number of spares, and duration of the test are amenable to optimization for reduction in the cost of reliability acceptance testing. When the various costs associated with the test are known, and the pdf and Sf of failures and/or time to test termination are defined, then minimum s-expected test costs are achievable. Constraints and sensitivity analysis can be applied to the models to assist the managerial decision process. Allocation of test effort for minimum variance of reliability. L. DANIEL MAXIM and HARRISON D. WEED. IEEE Trans. Reliab. R-26, (2) 111 (June 1977). This paper is concerned with the problem of determining the optimal allocation of test effort among individual components of a system. Using knowledge of the relationship between component uncertainty and system uncertainty, and component and system test costs, the test allocation is determined so as to minimize the variance of an estimator of overall system reliability. The optimal allocations for a series system and a parallel system are examined as special cases. The sensitivity of the optimal allocation is examined with respect to differences in system configuration. A variance minimization method of reliability design. R. KRISHNAN IYER and T. DOWNS. IEEE Trans. Reliab. R-26, (2) 106 (June 1977). This approach to reliability design seeks to minimize the variance on system lifetime within s-expected life and economic constraints. We consider the case where the parameters of the lifetime distribution are constant and discuss the more general case where the parameters of the lifetime distribution are random variables. The design procedure is illustrated by simple numerical examples which show that for a small increase in cost an appreciable decrease in the variance of the lifetime is obtained. We have restricted our attention to active redundancy but the extension to standby redundancy is straightforward. Maximum reliability route subject to k-improvements in a directed network. S. P. BANSALand S. KUMAR. IEEE Trans. Reliab. R-26, (2) 103 (June 1977). The network consists of links and perfect nodes. Each link has several known reliability numbers associated with it; each reliability number is related to the number of improvements made on that link. The network reliability is to be maximised subject to a constraint on the sum of the number of link improvements, by finding the appropriate route through
417
the network. Dynamic programming is used to solve the problem. A numerical example illustrates the solution.
Role of assurance technologies in M-PRT evaluation. PATRICK R, ESPOSITO. Proc. IEEE Reliab. Maintainab. Syrup., Philadelphia (Jan. 18-20, 1977) p. 472. In evaluating the performance of a transportation system, several performance factors must be considered. Naturally, in this group of factors are the assurance technologies. To evaluate the performance of the M-PRT, a year of testing was initiated in October, 1975. During this year, passenger service was carried out under normal operating conditions. Of course, significant attention was devoted to assessing and evaluating system performance. Included in the evaluation factors were: safety assessment spares usage O & M costs and, of course, the assurance technologies: reliability availability dependability maintainability. This paper deals with the assurance factors applied to the M-PRT. And, in particular, it discusses the application of assurance technologies to a case study of an advance transportation system--the M-PRT. The results of the M-PRT tests will be discussed with general observations on the system and the application of the assurance technologies to transportation systems. RIW with cost sharing. ROBERT M. SPRINGER JR. Proc. IEEE Reliab. Maintainab. Syrup., Philadelphia (Jan. 18-20, 1977) p. 391. This paper considers Reliability Improvement Warranties (RIW) with cost sharing incentive pricing as an alternative to the Fixed Firm Price (FFP) method presently used for RIW. Some contractors are concerned that the F F P method of rigid pricing of RIW contracts often places maximum economic risk on contractors in conditions of cost uncertainty, and have recommended cost sharing incentives as alternative methods of pricing. This analysis indicates that, from the government's interest, traditional cost sharing with shallow share ratios may tend to dilute the contractor's motivation to improve product reliability and control costs. If, despite this apparent disadvantage, cost sharing is used, then target costs, share ratios, and cost ceilings should be selected in such a way as to retain as much contractor cost control and reliability improvement motivation as possible. From the contractor's point of view, RIW with cost sharing involves less economic risk than the F F P RIW. If the contractor is relatively confident of the reliability of his product, either F F P or cost sharing may be desirable for him, depending on his degree of confidence. If the contractor is not confident of pre-production reliability estimates, neither method is desirable since at very low hours mean time between failure (MTBF) the contractor's costs increase exponentially. Combined environment reliability test (CERT). ALAN H. BURKHARD. Proc. IEEE Reliab. Maintainab. Syrup., Philadelphia (Jan. 18-20, 1977) p. 460. This paper outlines the basic philosophy and assumptions that have been used to formulate the environmental test conditions used in the initial test programs conducted to evaluate the merits of the combined environment reliability test (CERT) concept. General observations based upon the results of these initial tests are presented. Impact of the frequency of technician visits on facility failure rate. H. GILBERT MILLER and R. BRAFF. IEEE Trans. Reliab. R-26, (4) 245 (October 1977). A 3-state Markovchain model has been developed to analyze the relationship between the failure rate and the technician visitation
World Abstracts on Microelectronics and Reliability
chip protection of CMOS/SOS IC gate oxides. For these gate oxides, the dielectric strength of ~ 800 A thick silicon dioxide on SOS was ~ 7 x 106volts/era for I00 nanosecond pulses.
Effects of electrostatic discharge on linear bipolar integrated circuits. R. L. MINEAR and G. A. Dot)soN. 15th 4. Proc. 3. C I R C U I T
AND
SYSTEMS
RELIABILITY,
Decision making in reliability, V. S. SRINIVASAN and K. V. RAMACHANDRA. IEEE Trans. Reliab, R-26, (4) 261 (October 1977). Distribution-free methods are evolved for 4 models of evaluating time-to-failure. Two decision procedures for choosing the better of two equipments are given in models I and II. Decision procedures for whether two equipments have the same availability or reliability are given in models llI and IV; in these models, it is assumed that the mission time is a r.v. in the interval (0, To). The method of model I is superior to existing tests like the Wilcoxon-Rank-Sum test and Mann-Whitney test in a particular case. Model II is based on the time taken to return to the initial state by a Markov chain and is optimum for large sample sizes. In model III, even though the distributions of time to failure and time to repair-completion are negative exponential, the method is general, distribution-free and optimal. Hence the type I error is constant even if the distributions of time to failure and repair-completion differ from the assumed distributions. Model IV is also distribution-flee and optimum.
Time dependent unavailability analysis of nuclear safety systems. W. E. VESELY and F. F. GOLDBERG. IEEE Trans. Reliah. R-26, (4) 257 (October 1977). A method is presented to predict the time-dependent system unavailability, which includes consideration of the detailed effects of different periodic testing schemes. The FRANTIC computer code is described; it has been developed to study applications of the approach.
Queuing models for estimating aircraft fleet availability. V. V. S. SARMA, K. RAMCnAND and A. K. RAO. IEEE Trans. Reliab. R-26, (4) 253 (October 1977). The availability of a small fleet of aircraft in a flying-base, repair-depot combination is modeled and studied. First, a deterministic flow model relates parameters of interest and represents the state-of-the art in the planning of such systems. Second, a cyclic queue model shows the effect of the principal uncertainties in operation and repair and shows the consequent decrease in the availability of aircraft at the flyingbase. Several options such as increasing fleet size, investments in additional repair facilities, or building reliability and maintainability into the individual aircraft during its life-cycle are open for increasing the availability. A lifecycle cost criterion brings out some of these features. NumericM results confirm Rose's prediction that there exists a minimal cost combination of end products and repairdepot capability to achieve a prescribed operational availability.
Reliability growth apportionment. J. K, BYERS and D. J. GALL[. IEEE Trans. Reliab. R-26, (4) 242 (October 1977). A method is presented for apportioning reliability growth to the subsystems that make up a system in order to achieve the required reliability at least cost. Reliability growth apportionment is handled as an s-expected cost minimization problem subject to the constraint of meeting a system reliability requirement. The problem is formulated in terms of Duane's reliability growth model, and is solved using geometric programming. The method can be useful in the early stages of system design to determine subsystem reliability growth that will
Reliab. Phys. IEEE (1977) Nevada. p. 138. Electrostatic discharge (ESD) can easily damage bipolar integrated circuits. "Second breakdown" of N P N transistor emitter-base junctions is a common failure mode. No external emitter connection is needed for this to occur. ESD current paths, physics of ESD failure, and design concepts for improved FSD resistance are discussed.
MAINTENANCE
AND
REDUNDANCY
allow a system reliability requirement to be met, and in the latter stages of system design when reliability has fallen short of the required goal and improvements are necessary.
Cost model for testing program based on nonhomogeneous poisson failure model JoH~ DONELSON m. IEEE Trans. Reliab. R-26, (3) 189 (August 1977). A model for the s-expected cost of a development testing program is presented in this paper. The total cost function consists of two terms, The first term is proportional to the duration of the testing program; the second term is a loss function that assesses additional costs for failure to meet reliability goals during the testing program. The reliability growth model assumes that failures during the program occur according to a nonhomogeneous Poisson process having a power-law rate. An example shows how the duration of the test program can be chosen to minimize s-expected total cost.
System availability and optimum spare units. MASAFUMI SASKI, SHIGERU KABURAKI and SH1GERU YANAGI. IEEE Trans. Reliab. R-26, (3) 182 (August 1977). The steady-state availability of a repairable system with cold standbys and nonzero replacement time is maximized under constraints of total cost and total weight. Likewise the cost can be minimized under constraints of steady-state availability and total weight. A new, more efficient algorithm is used for the constrained optimization. The problem is formulated as a nonlinear integer programming problem. Since the objective functions are monotone, it is easy to obtain optimal solutions. These new algorithms are natural extensions of the Lawler Bell algorithm. Availability is adjusted by the number of spares allowed. Other measures of system goodness are considered, viz. failure rate, weight, price, mean repair time, mean repair cost, mean replacement time, and mean replacement cost of a unit.
Optimal replacement rate of devices with lognormal failure distributions. S. S. CHENG. IEEE Trans. Reliab. R-26, (3) 174 (August 1977). The time dependence of the replacement rate of devices with lognormal failure distributions is studied. The relationship between the peak replacement rate and er, the standard deviation in the corresponding s-normal distribution, is obtained. The study assumes that each device represents a renewal process and the system of devices represents a superimposed renewal process. The peak replacement rate becomes very large for both extreme values of (~. The corresponding replacement rate eventually approaches the conventional asymptotic rate only after many MTTFs (Mean Time To Failure), possibly long after the system becomes obsolete. Ways to cope with this situation are suggested. However, the replacement rate curve becomes almost critically damped with a minimumpeak-factor ~ 1.03 at tr ~ 0.63. The study also reveals that asymptotically the lognormal devices with > << 1 would require fewer replacements than the exponential devices with the same MTTF. The difference is equal to one-half of the population in service. For large a, more replacements are required. The results of this paper apply to a variety of reliability studies and maintenance and inventory strategies for communication systems that employ lognormal devices such as a semiconductor laser, LED, avalanche photo diode,
World Abstracts on Microelectronics and Reliability or IMPATT diode. In particular, the present approach is especially helpful when such a device is the least reliable component in the system.
An optimal decision rule for repair vs replacement. EGINHARD J. MUTH. IEEE Trans. Reliab. R-26, (3) 179 (August 1977). This paper presents a policy for either repairing or replacing a system that has failed. The policy applies to systems whose mean residual life function is decreasing. An optimal policy is developed that minimizes the cost per unit time for repair and replacement. Results are shown graphically for a particular distribution of time to failure and are motivated in terms of an automobile replacement problem. Optimal selection of sequential tests for reliability. J. M. MOGG. IEEE Trans. Reliab. R-26, (2) 116 (June 1977). Reliability test requirements exist whereby truncated sequential test methods offer management the opportunity to minimize the s-expected cost of a test by optimal selection of the blend of resources that will be consumed by the test. The models presented here are useful in the real world design of reliability tests because of the case of arriving at cost estimates and the existing availability of statistical distributional information on truncated sequential tests. The test parameters of sample size, number of spares, and duration of the test are amenable to optimization for reduction in the cost of reliability acceptance testing. When the various costs associated with the test are known, and the pdf and Sf of failures and/or time to test termination are defined, then minimum s-expected test costs are achievable. Constraints and sensitivity analysis can be applied to the models to assist the managerial decision process. Allocation of test effort for minimum variance of reliability. L. DANIEL MAXIM and HARRISON D. WEED. IEEE Trans. Reliab. R-26, (2) 111 (June 1977). This paper is concerned with the problem of determining the optimal allocation of test effort among individual components of a system. Using knowledge of the relationship between component uncertainty and system uncertainty, and component and system test costs, the test allocation is determined so as to minimize the variance of an estimator of overall system reliability. The optimal allocations for a series system and a parallel system are examined as special cases. The sensitivity of the optimal allocation is examined with respect to differences in system configuration. A variance minimization method of reliability design. R. KRISHNAN IYER and T. DOWNS. IEEE Trans. Reliab. R-26, (2) 106 (June 1977). This approach to reliability design seeks to minimize the variance on system lifetime within s-expected life and economic constraints. We consider the case where the parameters of the lifetime distribution are constant and discuss the more general case where the parameters of the lifetime distribution are random variables. The design procedure is illustrated by simple numerical examples which show that for a small increase in cost an appreciable decrease in the variance of the lifetime is obtained. We have restricted our attention to active redundancy but the extension to standby redundancy is straightforward. Maximum reliability route subject to k-improvements in a directed network. S. P. BANSALand S. KUMAR. IEEE Trans. Reliab. R-26, (2) 103 (June 1977). The network consists of links and perfect nodes. Each link has several known reliability numbers associated with it; each reliability number is related to the number of improvements made on that link. The network reliability is to be maximised subject to a constraint on the sum of the number of link improvements, by finding the appropriate route through
417
the network. Dynamic programming is used to solve the problem. A numerical example illustrates the solution.
Role of assurance technologies in M-PRT evaluation. PATRICK R, ESPOSITO. Proc. IEEE Reliab. Maintainab. Syrup., Philadelphia (Jan. 18-20, 1977) p. 472. In evaluating the performance of a transportation system, several performance factors must be considered. Naturally, in this group of factors are the assurance technologies. To evaluate the performance of the M-PRT, a year of testing was initiated in October, 1975. During this year, passenger service was carried out under normal operating conditions. Of course, significant attention was devoted to assessing and evaluating system performance. Included in the evaluation factors were: safety assessment spares usage O & M costs and, of course, the assurance technologies: reliability availability dependability maintainability. This paper deals with the assurance factors applied to the M-PRT. And, in particular, it discusses the application of assurance technologies to a case study of an advance transportation system--the M-PRT. The results of the M-PRT tests will be discussed with general observations on the system and the application of the assurance technologies to transportation systems. RIW with cost sharing. ROBERT M. SPRINGER JR. Proc. IEEE Reliab. Maintainab. Syrup., Philadelphia (Jan. 18-20, 1977) p. 391. This paper considers Reliability Improvement Warranties (RIW) with cost sharing incentive pricing as an alternative to the Fixed Firm Price (FFP) method presently used for RIW. Some contractors are concerned that the F F P method of rigid pricing of RIW contracts often places maximum economic risk on contractors in conditions of cost uncertainty, and have recommended cost sharing incentives as alternative methods of pricing. This analysis indicates that, from the government's interest, traditional cost sharing with shallow share ratios may tend to dilute the contractor's motivation to improve product reliability and control costs. If, despite this apparent disadvantage, cost sharing is used, then target costs, share ratios, and cost ceilings should be selected in such a way as to retain as much contractor cost control and reliability improvement motivation as possible. From the contractor's point of view, RIW with cost sharing involves less economic risk than the F F P RIW. If the contractor is relatively confident of the reliability of his product, either F F P or cost sharing may be desirable for him, depending on his degree of confidence. If the contractor is not confident of pre-production reliability estimates, neither method is desirable since at very low hours mean time between failure (MTBF) the contractor's costs increase exponentially. Combined environment reliability test (CERT). ALAN H. BURKHARD. Proc. IEEE Reliab. Maintainab. Syrup., Philadelphia (Jan. 18-20, 1977) p. 460. This paper outlines the basic philosophy and assumptions that have been used to formulate the environmental test conditions used in the initial test programs conducted to evaluate the merits of the combined environment reliability test (CERT) concept. General observations based upon the results of these initial tests are presented. Impact of the frequency of technician visits on facility failure rate. H. GILBERT MILLER and R. BRAFF. IEEE Trans. Reliab. R-26, (4) 245 (October 1977). A 3-state Markovchain model has been developed to analyze the relationship between the failure rate and the technician visitation