Reliability analysis : Optimal inspection and maintenance schedules of failing systems

A state-of-the-art survey on system effectiveness models is presented. A variety of system effectiveness models dealing with military and space systems have been developed by the US Air Force, Army, and Navy. Each model has different attributes in its definition of system effectiveness. This survey classifies these attributes and definitions and presents their relationship to system effectiveness. Attributes included are reliability, availability, operational readiness, repairability, maintainability, serviceability, design adequacy, capability, dependability, human performance, and environmental effects. The system effectiveness models and their computer codes are also classified and reviewed.

System Effectiveness Models: An Annotated Bibliography

The measurement of computer performance is of interest to several classes of people associated with computers. Systems analysts, system designers, software designers, and users all have a continuing interest in the most effective techniques for quantifying the performance of the machines they build, program, and use. This bibliography of 440 references covering the period January 1970 to March 1975 was compiled to assist those working in the field.

A Bibliography on System Performance Evaluation

Reliability/availability estimation in the classical sense has been well developed and widely discussed. The parameters in the classical reliability/availability distributions are considered to be unknown constants to be determined. If there is information about these parameters, besides that from some current experiment, it can be used as the basis of Bayesian inference. This paper illustrates procedures for using the Bayesian approach for the study of reliability/availability problems. References on the subject are collected and classified. Specifically, included in this paper are: 1) the statement of the classical estimate and Bayesian estimate, 2) the structure of the prior distribution, 3) the reliability life testing, 4) the empirical Bayes approach in reliability, and 5) Bayesian availability. A Bayesian parameter estimate is generally independent of the sampling stopping rule and has smaller variability than the classical estimate; however, a Bayesian estimate is usually biased and associated with difficulties of choosing a prior. The empirical Bayes approach eliminates some of these difficulties, but frequently at the cost of mathematical tractability. The Bayesian approach to reliability/availability is part of the general trend toward using comprehensive probabilistic methods for dealing with the uncertainties associated with modern engineering problems. This trend should also move toward some system effectiveness measures other than simply reliability or availability. For a large system the Bayesian approach could apply, especially when the test data are scarce and the testing procedure is expensive.

Bayesian Reliability & Availability - A Review

This paper discusses the convenience of predicting, quantitatively, time-dependent reliability and availability levels associated with most building or civil engineering structures. Then, the paper reviews different approaches to these problems and proposes the use of discrete-event simulation as the most realistic way to deal with them, specially during the design stage. The paper also reviews previous work on the use of both Monte Carlo simulation and discrete-event simulation in this area and shows how discrete-event simulation, in particular, could be employed to solve uncertainty in time-dependent structural reliability problems. Finally, a case study is developed to illustrate some of the concepts previously covered in the paper.

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Applications of discrete-event simulation to reliability and availability assessment in civil engineering structures

A number of authors have considered the problem of synthesizing an interval estimate of system reliability from component test data, test time and number of failures. Among those who have treated the topic analytically are Lipow; Springer and Thompson; Lindstrom and Madden; Garner and Vail; Nishime, Conner and Wells; Madansky, Dempskey, and Rubenstein. 1-10 In this brief working paper we present a Monte Carlo simulation procedure which enables synthesis of the probability distributions of reliability parameters where the components are individually exponential. Confidence limits are interpreted as percentiles of the system distribution. The technique permits testing, comparison and verification of the analytical methods cited above.

Monte Carlo simulation of system reliability

The paper applies the theory of learning curves to explain the tendency toward decreasing downtime observed in the maintenance of many systems. Maintainability demonstrations performed under current military specifications assume stationary distributions of maintenance times; that is, the demonstrated times are considered as samples drawn from populations having time-invariant parameters. Statistical evidence, based on observed maintenance actions on military electronic equipments, is presented to contest the validity of these assumptions. The author shows that maintenance times decrease for iterative tasks in accordance with the negative logarithmic relationship, which is the accepted form of the human learning curve, historically applied in manufacturing operations. A s the number of performances of a task increases, the time required for each iteration is progressively reduced in accordance with a constant experience factor. Although the experience factor is, in a strict sense, a unique characteristic of a specific worker at a specific task, it is shown that a satisfactory composite factor may be computed for a maintenance crew or department, and may be employed for prediction of maintainability improvemept . Possible objections to the accepted form of the learning curve stem from the fact that it is empirically based, and from intuitive realization that it can not hold true in the limit, since the function approaches zero asymptotically. Studies are described showing that the accepted form of the function gives excellent correlation coefficients out to the region of x = lo4, and that none of several alternative functions investigated gave better fits. The use of learning curve analysis in maintainability demonstration testing is recommended, and it is argued that present procedures reduce the probability of acceptance of newly developed equipments. Introduction Tests to demonstrate the maintainability @) of newly developed systems are required under current military specifications (MIL-M-26512, MIL-M-23313, MIL-STD-471). The sampling procedures set forth in these documents are predicated on the implicit assumption that maintenance performance time distributions are stationary; that is, the demonstraed times are considered as samples drawn from population distributions having time-invariant parameters. Statistical evidence is presented here to contest the validity of the foregoing assumption, and to support a thesis that maintenance times decrease for iterative tasks in accordance with the accepted form of the human learning curve. By analysis of task times observed during g demonstration testing, the applicable learning curve can be plotted, the rate of learning estimated, and the g to be expected of a system during its service life can be predicted. Confidence statements can also be associated with such predictions. Nature of Learning Curves The validity of the learning curve, particularly in manufacturing operations, has been verified b more than a quarter century of experience. ( 1 , 2 9 3 3 Thus it is one of the few empirical relationships so firmly established by repeated observations that it can be safely extrapolated to predict future behavior. The learning curve describes the human capacity for progressive learning of repetitive tasks. It indicates (Figs. 1 and 2) that as the number of performancesof a task increases, the time required for each performance is progressively reduced in accordance with the relationship log t(x) = log t(1) + m log x (la) log 2 where : x 2 number of performances t(1) = time required for' first performance t(x) = time required for xth performance b = experience factor or, in antilog form The average time also decreases. t(1,x) = Cto X Each time the number of performances is doubled, the time required is reduced to a constant fraction of,the previous time. This fraction by expressed as b = * (3) is called the experience factor and describes the rate of learning. Values of b observed in industrial operations usually lie between .70 and .90. In the strictest sense an experience factor describes only the. behavior of a particular worker learning a specific task. However, a quite satisfactory composite experience factor can often be computed for a department, for workers of a iven grade or skill level, or for an entire plantf3). In many industries such composite factors serve as fundamental indicators for predicting the effects of production run lengths on production costs and, consequently, for establishing price policies. The accepted form of the learning curve, as embodigd in equation (l), could be questioned on the grounds that is is empirically based, and from the realization that it cannot continue to apply

The learning curve in maintenance analysis

Experience with two methods of Bayesian reliability measurement is described. An aerospace subsystem was evaluated assuming continuous gamma-distributed component failure rates. Priors were developed by conventional reliability prediction methods based on handbook data. The ``strength'' of the prior was expressed in terms of variance about a predicted mean. Comparative evaluation was also made by a classical technique during a test program extending over 10 months. The Bayesian method was preferred though problems inherent in the method were apparent. More recently, a complex marine system was evaluated over a one-year period using a Bayesian formulation in which the failure rate is described by a discrete probability distribution with nonuniform cell widths. This technique avoids some of the operational problems of continuous formulations. Experience with Bayesian methods leaves little doubt of their utility as evaluation tools. The philosophical problems, however, remain as intransigent as ever.

Experience with Bayesian Reliability Measurement of Large Systems

The paper reviews the state-of-the-art in space maintenance methods and hardware. Included are sections on the space environment, automatic maintenance, remote handling, space suits, zero-reaction tools, fastening and sealing techniques, and methods of constructing habitable structures in space or on lunar or planetary surfaces. Studies of economic factors in space maintenance, support, and logistics are discussed, and an extensive bibliography of source material is appended.

Myron A. Wilson

Papers

Monte Carlo simulation of system reliability

The learning curve in maintenance analysis

Experience with Bayesian Reliability Measurement of Large Systems

Maintainability in SpaceߞA Survey

Effects of Maintenance and Support Factors on Availability of Systems