Internet of Things for Flexible Manufacturing Systems` Diagnosis Calin Ciufudean and Corneliu Buzduga Stefan cel Mare University, 13 University, Suceava, Romania Keywords: Internet of Things, Flexible Manufacturing System, Discrete Event Model, Memory Buffer, Markov Chain. Abstract: This paper deals with an actual topic concerning the diagnosis of Internet of Things (IoT) controlled flexible manufacturing systems (FMS). We focus on models realized with Markov chains of FMS with stochastic and not equal throughput rates. Discrete-event models assume that FMS is decomposed, and we study the following events: an Internet server fails, an Internet server is repaired, an Internet server memory buffer fills up, an Internet server memory buffer empties. The IoT diagnosis is performed with by calculating the time to absorption in Markov model of the IoT controlled FMS. Future development of IoT diagnosis of FMS are also discussed in this work. 1 INTRODUCTION In this work, we assume that a flexible manufacturing system controlled and monitored by Internet of Things (IoT) is similar to a discrete event system (DES) and we model it in a discrete stochastic space. Absorbing states of Markov chain models display a steady-state i.e., the absorbing state attended after time T; therefore, only transient analysis displays the system performance. Our approach deals with an IoT controlled system which displays in time a trajectory modelled with a Markov chain 0} t {x(t); ≥ with state space ...} 1, {0, S = and space generator W. Let i, j ∈ S and, we have (Viswandham, 1992), (Kemeny, 1960): i} j/ x(0) P{x(t) (t) p j i = = = (1) (t)] [p A(t) ij = (2) The following equations describe the behavior of the above mentioned Markov chain (Buzacott, 1993), (Narahari, 1994), (Ciufudean, 2008), (Viswandham, 1994): W A(t) [A(t)] dt d ⋅ = (3) A(t) W * [A(t)] dt d ⋅ = (4) Where A(0) = I. For matrix components we have: ) t ( p w (t) p . w (t)] [p dt d ik j k kj ij ij ij ∑ = ⋅ + = (5) ∑ = ⋅ + = i k kj ik ij ii ij ) t ( p w (t) p . w (t)] [p dt d (6) The solution is: t W e A(t) ⋅ = (7) ( ) ∑ ∞ = ⋅ ⋅ = 0 k k t W ! k t W e (8) The state probabilities ...] (t), p (t), [p Y(t) 1 0 = where S j j}, = P{x(t) = (t) p j ∈ , are given by the following equation: W . Y(t) Y(t)] [ dt d = (9) The solution is: t W e . Y(0) Y(t) ⋅ = (10) i} X(0) j/ P{X(t) (t) p ij = = = (11) For t > 0, and T the time to reach the absorbing state, we obtain: n)} + m , ... 1, + (m P{X(t) = t} > P{T ∉ (12) Where m ≥ 0, n > 0, we have (m+1) states, and the next states are absorbing ones. () ∑ = + = > n 1 j j m , 0 t p - 1 t} P{T (13) 468 Ciufudean, C. and Buzduga, C. Internet of Things for Flexible Manufacturing Systems‘ Diagnosis. In Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2016), pages 468-471 ISBN: 978-989-758-184-7 Copyright c  2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved