SYSTEM EFFECTIVENESS MODELS VIA RENEWAL THEORY AND BAYESIAN INFERENCE

System effectiveness, the probability that a system can successfully meet an operational demand within a given time when operated under specified conditions, is a performance measure of a system. The objectives of this study are: (i) to develop a practical system effectiveness model which can handle various situations and include the important factors such as the environmental effect and operator effect; (ii) to introduce the model as a useful tool for consistent system evaluation and optimal test design; (iii) to approach availability and system effectiveness using renewal theory and develop a simulation approach to the solutions of performance whenever empirical data are given; (iv) to estimate availability by the Bayesian approach when the sample size is small; and (v) to discuss the distribution functions of system performances such as reliability, availability, and the developed system effectiveness model of (i).; The rationale is that this study is another step in the system effectiveness modelling and theoretical justification.; Ch. II reviews the better known system effectiveness models and their attributes. A system effectiveness model is proposed where the system effectiveness is the joint probability measure of availability and reliability; availability describes the degree of readiness for service and reliability describes the degree of failure-free operation under specified conditions.; In Ch. III, instantaneous availability of an on-off system is derived based on renewal theory. The availability expression is general and can be applied to any adjusted system cycle time and on time distributions. A simulation approach is presented for evaluating the system availability for any empirical data.; Availability in Ch. III is the probability that a system is in an available state. If in addition to finding the availability at time t we also want to find the probability that the system can function well for at least a period of time x, we then apply the system effectiveness model proposed in Ch. II. Ch. IV develops a general solution to the proposed system effectiveness model by means of renewal theory. Again, a simulation procedure based on the general solution is presented.; The proposed system effectiveness simulation model in Ch. IV is used for a case study of Ch. V. In Ch. V, an attempt is made to develop a model for a system which is required to carry out various types of missions. This case study is based on the data from an actual test of a military system.; Ch. VI critically reviews the reliability problems approached by Bayesian inference.; In Ch. VII, we consider the gamma distributed system cycle time and on time, and hence the time-dependent availability function as found in Ch. III is applied in the discussions. Bayesian inference based on this time-dependent availability function is mainly concerned in this chapter. Several results are obtained with the problem: (1) maximum likelihood estimate of availability is derived, (2) Bayesian availability is derived when the scale parameters of system cycle time and on time are both exponentially distributed and the sample data are not available, and (3) Bayesian estimates of (2) is derived while the sample data are available.; In Ch. VIII, the distribution functions of reliability, availability, and the product of reliability and availability are derived under certain conditions.; Finally, the significance of the present study is briefly discussed in Ch. IX. Several future investigations on system effectiveness are proposed as extensions of the present study.