By Jingshan Li, Semyon M. Meerkov
ISBN-10: 0387755780
ISBN-13: 9780387755786
ISBN-10: 0387755799
ISBN-13: 9780387755793
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Additional info for Production Systems Engineering
Sample text
An ]. 4(a). , the chance experiment E results in an outcome ζ, which belongs to A). What is the probability that B takes place? Clearly, the answer is 0. 4(b). Assume again that A takes place and ask the same question. , P [A ∩ B]. 1. RANDOM EVENTS 17 has occurred, the sample space for the question at hand is not S but A, and the value of P [A ∩ B] should be viewed relative to P [A] rather than P [S] = 1. 2) (assuming, of course, that P [A] > 0). This is the second important formula of Probability Theory.
35, pp. 291-305, 1987. A. G. Shantikumar, Stochastic Models of Manufacturing Systems, Prentice Hall, Englewood Cliffs, NJ, 1993. This is an encyclopedic book covering many topics of manufacturing, including production systems, scheduling, and others. Mostly the queueing theory approach is used. T. Papadopoulos, C. Heavey and J. Browne, Queueing Theory in Manufacturing Systems Analysis and Design, Chapman & Hall, London, 1993. One of the first monographs on the queueing theory approach to production systems.
Let that Ai , i = 1, 2, . . , n, be a partitioning of S, and F an event in S. Then, by the conditional probability formula, P [Ai |F ] = P [Ai ∩ F ] . 8), we obtain: P [Ai |F ] = P [F |Ai ]P [Ai ] P [F |A1 ]P [A1 ] + P [F |A2 ]P [A2 ] + . . 9) This expression is referred to Bayes’s formula and is the fifth important formula of Probability Theory. 3 and given that the transmission in a car that failed within ten years of operation, what is the probability that this transmission came from supplier A?
Production Systems Engineering by Jingshan Li, Semyon M. Meerkov
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