Elements of Information Theoretic Methods: Tutorial Introduction

The rudiments of information theoretic methods are introduced and companion papers dealing with solutions of some reliability problems using information theoretic approaches are preluded. Major elements of the communication system are outlined from an information processing point of view. Information is quantified following the work of Shannon. The concepts of uncertainty, self-and mutual information, and entropy are developed as seen at the encoder, channel, and decoder. Channel modeling is demonstrated using a binary symmetric channel as an example. Channel capacity is derived by maximizing transinformation. Elements of coding are described and Shannon's fundamental theorem of discrete noiseless coding is stated. The fundamental relations governing unique decipherability and irreducibility are given and demonstrated by examples. Code efficiency and redundancy are quantified and discussed as system parameters subject to tradeoff. Applications of information theoretic methods in various disciplines are discussed with emphasis on reliability and maintainability. Two unresolved reliability problem areas are identified where, potentially, information theoretic approaches may present a viable solution.     

Reliability Cost Estimation: Managerial Perspectives

This paper deals with selected sources of uncertainties associated with the reliability related life cycle costs (LCC). Some of the factors responsible for uncertainty in reliability cost estimation are identified and discussed. A practical approach to the use of Beta distribution in estimating the reliability-related costs within the LCC framework is detailed, and is illustrated using a hypothetical example. Improved estimation of reliability related LCC requires better understanding of sources of associated uncertainties and the methods of dealing explicitly with them. Numerous distributions can be used for modeling of cost variates besides the Beta demonstrated in this paper. The 3-parameter Weibull and Gamma distributions are two examples. Whichever distribution is chosen, given a sufficiently large cost data base, it is essential to test the cost variate for goodness of fit and to validate the model by appropriate test of hypothesis. However, in estimation of costs involving large capital expenditure over a period of years, the data base is not likely to be large. Lacking, then, a statistically significant sample which would allow testing for the underlying probability distribution governing the cost variate, modeling via the Beta or other appropriate distribution presents a practical alternative.