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On linear failure rates
314
World Abstract s on M icroelectronics and Reliabilil 3
the parameter of the Poisson process. The time for which the system will work with a given reliability is obtained numerically when the stress and strength distributions are both exponential, gamma, or .~-normal.
An application of Kalman techniques to estimating availability. V. S. SRINIVASAN and K. V. RAMACHANDRA. IEEE Trans. Reliab. R-27, (1) 46 (April 1978). This paper applies Kalman filtering techniques to reliability smoothing. Point availability as a function of time is estimated through Kalman filtering techniques. Approximate determination of the sampling interval and the measurement variance is given. The error variance of the estimate of the steadystate availability and the steady-state Kalman gain are zero. From this, it is found that the estimates of point avaihrbility attain a steady-state. A mathematical approach to reliability evaluation for static generating capacity. THOMAS K. SIU and W. C. CHAN, IEEE Trans. Reliab. R-27, (2) 132 (June 1978). This paper presents a mathematical approach for deriving some important formulas in the reliability evaluation of static generating capacity for electric power systems. The mathematical approach treats the reliability of static generating capacity as the survivor function of a single random variable signifying the difference of the generating capacity and the load. Based on this reliability function various important characteristics for reliability study can be obtained using probability calculus. Cost effective spares. S. J. AMS~tER and R. CE~tNO. IEEE Trans. Reliab. R-27, (2) 124 (June 1978). This paper presents a method for selecting spare modules to support system availability in a cost-effective manner. We apply the method to determine the sparing requirements for a specialized power unit used throughout a telephone transmission system. The method has been extensively used to generate spares complements for large military systems and to perform reliability tradeoffs. Efficiency contours for estimators of reliability in a 2parameter exponential failure model. DANNY DYER and I-LE Lt.. IEEE Trans. Reliab. R-27, (2) 149 (June t978). When several point estimators of some parametric function are available, it is desirable to compare the estimators based on some measure of closeness to the true value. Along these lines, the concept of Pitman-closeness (PC) efficiency is introduced. Essentially, when comparing two estimators, PC efficiency gives the odds in favor of one of the estimators being closer to the true value in a given situation than is the other. The traditional method of comparison, i.e., mean-squared (MS) efficiency is also considered. This paper presents graphical results based on simulation techniques which depict PC & MS efficiencies of the following estimators of the reliability function R(r) of a 2-parameter exponential failure model: (i) the maxim u m likelihood estimator, /~ut.r:(r); (it) the m i n i m u m variance unbiased estimator,/~,u~ t,r:(z); and {iii) a Bayesian/ structural estimator, [~sE(r). Based on the graphs, /~st~(r) is, in general, preferred (in the sense of having the best chance of being closest to the true value of R(z}) except (al when R(zt is very high, in which case R.uL~(z) is preferred, and (b) when R{rl is moderate and the sample size is small to moderate, in which c a s e / ~ , ~ ( r l is preferred. Group reliability predictions. A. B~tHPOHL. IEEE T~'ans. Reliab. R-27, {2) 139 (June 1978). On the basis of an assumed Bayesian model and a set of criteria for judging reliability predictions, it is shown that : 1. Group predictions outperform individual predictions. 2. A weighted average is a satisfactory and perhaps the only satisfactory method of arriving at group predictions.
3. For a series system, group predictions of component reliabilities combined to form a prediction of s~stem reliability are preferred to a group prediction of sys|em reliability. 4. Prior averaging and updating via Bayes" i-ule is sconsistent and seems preferable to averaging posterior individual predictions. The intent of this paper is to provide theoretical guidance to the practical problem of group reliability prediction.
Bayesian lower bounds on reliability for the lognormal model. W. J. PAI)GETT and L. J. WEI. IEEE Tran.v Reliafi. R-27, (2i 161 (June 1978}. Bayesian lower bounds lbr the reliability function are obtained for the lognormal failure model with respect to the s-normal-gamma (conjugatel prior distribution and a vague prior distribution of Jeffreys. The Bayesian lower bound with respect to the vague prior is the same as the uniformly most accurate (UMA) lower s-confidence bound for reliability. All lower bounds are given in terms of the noncentrality parameter of a generalized noncentral t-distribution. A simple approximation for the noncentrality parameter is discussed. Computer simulation rcsults indicate how well the approximation performs and provide a performance comparison between the Bayes lower bounds with respect to the (proper) s-normal-gamma prior and the U M A lower sconfidence bound. Thc two ineasures used in the sinmlations to ewlluate perfnrtnalace of the lower bounds tire (1i the average dilli~rence between the computed lower bound and the true reliability and (2) the fl'action of computed lower bounds which are actually les~, than the true reliability. This Bayes procedure performs very well even though the assumed prior reformation is not exactly correct; and the approximation is used to obtain the lower bounds. Common-cause outages in multiple circuit transmission lines. R. BILL1NTON, T. K. P. MEDICItERLA and M. S. SACHDEV. IEEE Trans. Reliab. R-27, (2) 128 IJune 1978). Reliability evaluation of a power system involving both generation and transmission elements is extremely complex. Outages of these elements are usually considered to be x-independent events. Recent investigations, however, have indicated that common-cause outages of multicircuit transmission configurations can appreciably affect the predicted reliability. Closed R)rm expressions for steady state probabilities in 2- and 3-line cases (including certain c o m m o n cause failures) tire developed. These expressions provide transmission-line state probabilities for composite generation and transmission system reliability studies. The procedure can also be used to develop state probabilities for other line models and for systems with four or more lines on tire same right-of-way. The examples show the influence of the common-cause outage rate on the state probabilities, There is a definite need to includc c o m m o n cause outages in reliability evaluation of transmission systems. This will require a inore comprehensive approach to collecting transmission line outage data than has previously been used by most utilities. On linear failure rates, AN IHONY A. SALVIA. IEEE 7ran.~. Reliub. R-27, {2) 145 (June 19781. This paper considers a reliability model in which the failure rate increases linearly in tiine. Methods of paralneter estimation are discussed, and two applications are given.
A fault tolerant memor~ for duplex systems. W. T. HAI~,rwEt.L, (_'. W. HOH=NER and W. N. To'< If-EE Trams. Reliab. R-2J, (2} 134 (June 1978). A fault-tolerant memory design uses modular bit swapping to achieve high system availability with m i n i m u m redundancy despite high memory-device faihtre rates. The design permits automatic
World Abstract s on M icroelectronics and Reliabilil 3
the parameter of the Poisson process. The time for which the system will work with a given reliability is obtained numerically when the stress and strength distributions are both exponential, gamma, or .~-normal.
An application of Kalman techniques to estimating availability. V. S. SRINIVASAN and K. V. RAMACHANDRA. IEEE Trans. Reliab. R-27, (1) 46 (April 1978). This paper applies Kalman filtering techniques to reliability smoothing. Point availability as a function of time is estimated through Kalman filtering techniques. Approximate determination of the sampling interval and the measurement variance is given. The error variance of the estimate of the steadystate availability and the steady-state Kalman gain are zero. From this, it is found that the estimates of point avaihrbility attain a steady-state. A mathematical approach to reliability evaluation for static generating capacity. THOMAS K. SIU and W. C. CHAN, IEEE Trans. Reliab. R-27, (2) 132 (June 1978). This paper presents a mathematical approach for deriving some important formulas in the reliability evaluation of static generating capacity for electric power systems. The mathematical approach treats the reliability of static generating capacity as the survivor function of a single random variable signifying the difference of the generating capacity and the load. Based on this reliability function various important characteristics for reliability study can be obtained using probability calculus. Cost effective spares. S. J. AMS~tER and R. CE~tNO. IEEE Trans. Reliab. R-27, (2) 124 (June 1978). This paper presents a method for selecting spare modules to support system availability in a cost-effective manner. We apply the method to determine the sparing requirements for a specialized power unit used throughout a telephone transmission system. The method has been extensively used to generate spares complements for large military systems and to perform reliability tradeoffs. Efficiency contours for estimators of reliability in a 2parameter exponential failure model. DANNY DYER and I-LE Lt.. IEEE Trans. Reliab. R-27, (2) 149 (June t978). When several point estimators of some parametric function are available, it is desirable to compare the estimators based on some measure of closeness to the true value. Along these lines, the concept of Pitman-closeness (PC) efficiency is introduced. Essentially, when comparing two estimators, PC efficiency gives the odds in favor of one of the estimators being closer to the true value in a given situation than is the other. The traditional method of comparison, i.e., mean-squared (MS) efficiency is also considered. This paper presents graphical results based on simulation techniques which depict PC & MS efficiencies of the following estimators of the reliability function R(r) of a 2-parameter exponential failure model: (i) the maxim u m likelihood estimator, /~ut.r:(r); (it) the m i n i m u m variance unbiased estimator,/~,u~ t,r:(z); and {iii) a Bayesian/ structural estimator, [~sE(r). Based on the graphs, /~st~(r) is, in general, preferred (in the sense of having the best chance of being closest to the true value of R(z}) except (al when R(zt is very high, in which case R.uL~(z) is preferred, and (b) when R{rl is moderate and the sample size is small to moderate, in which c a s e / ~ , ~ ( r l is preferred. Group reliability predictions. A. B~tHPOHL. IEEE T~'ans. Reliab. R-27, {2) 139 (June 1978). On the basis of an assumed Bayesian model and a set of criteria for judging reliability predictions, it is shown that : 1. Group predictions outperform individual predictions. 2. A weighted average is a satisfactory and perhaps the only satisfactory method of arriving at group predictions.
3. For a series system, group predictions of component reliabilities combined to form a prediction of s~stem reliability are preferred to a group prediction of sys|em reliability. 4. Prior averaging and updating via Bayes" i-ule is sconsistent and seems preferable to averaging posterior individual predictions. The intent of this paper is to provide theoretical guidance to the practical problem of group reliability prediction.
Bayesian lower bounds on reliability for the lognormal model. W. J. PAI)GETT and L. J. WEI. IEEE Tran.v Reliafi. R-27, (2i 161 (June 1978}. Bayesian lower bounds lbr the reliability function are obtained for the lognormal failure model with respect to the s-normal-gamma (conjugatel prior distribution and a vague prior distribution of Jeffreys. The Bayesian lower bound with respect to the vague prior is the same as the uniformly most accurate (UMA) lower s-confidence bound for reliability. All lower bounds are given in terms of the noncentrality parameter of a generalized noncentral t-distribution. A simple approximation for the noncentrality parameter is discussed. Computer simulation rcsults indicate how well the approximation performs and provide a performance comparison between the Bayes lower bounds with respect to the (proper) s-normal-gamma prior and the U M A lower sconfidence bound. Thc two ineasures used in the sinmlations to ewlluate perfnrtnalace of the lower bounds tire (1i the average dilli~rence between the computed lower bound and the true reliability and (2) the fl'action of computed lower bounds which are actually les~, than the true reliability. This Bayes procedure performs very well even though the assumed prior reformation is not exactly correct; and the approximation is used to obtain the lower bounds. Common-cause outages in multiple circuit transmission lines. R. BILL1NTON, T. K. P. MEDICItERLA and M. S. SACHDEV. IEEE Trans. Reliab. R-27, (2) 128 IJune 1978). Reliability evaluation of a power system involving both generation and transmission elements is extremely complex. Outages of these elements are usually considered to be x-independent events. Recent investigations, however, have indicated that common-cause outages of multicircuit transmission configurations can appreciably affect the predicted reliability. Closed R)rm expressions for steady state probabilities in 2- and 3-line cases (including certain c o m m o n cause failures) tire developed. These expressions provide transmission-line state probabilities for composite generation and transmission system reliability studies. The procedure can also be used to develop state probabilities for other line models and for systems with four or more lines on tire same right-of-way. The examples show the influence of the common-cause outage rate on the state probabilities, There is a definite need to includc c o m m o n cause outages in reliability evaluation of transmission systems. This will require a inore comprehensive approach to collecting transmission line outage data than has previously been used by most utilities. On linear failure rates, AN IHONY A. SALVIA. IEEE 7ran.~. Reliub. R-27, {2) 145 (June 19781. This paper considers a reliability model in which the failure rate increases linearly in tiine. Methods of paralneter estimation are discussed, and two applications are given.
A fault tolerant memor~ for duplex systems. W. T. HAI~,rwEt.L, (_'. W. HOH=NER and W. N. To'< If-EE Trams. Reliab. R-2J, (2} 134 (June 1978). A fault-tolerant memory design uses modular bit swapping to achieve high system availability with m i n i m u m redundancy despite high memory-device faihtre rates. The design permits automatic