INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL Online ISSN 1841-9844, ISSN-L 1841-9836, Volume: 16, Issue: 3, Month: June, Year: 2021 Article Number: 4240, https://doi.org/10.15837/ijccc.2021.3.4240 CCC Publications Decision Tools Regarding Time Constraints Violation in Manufacturing Workshops N. JERBI, S. Collart-Dutilleul Nabil JERBI* Université de Sousse, Ecole Supérieure des Sciences et de la Technologie de Hammam Sousse, 4011, H. Sousse, Tunisie ; *Corresponding author: nabil.jerbi@essths.u-sousse.tn Simon Collart-Dutilleul COSYS/ESTAS, University Gustave Eiffel, 59666 Villeneuve d’Ascq, France ; simon.collart-dutilleul@univ-eiffel.fr Abstract This paper is dedicated to the study of constraints violation in manufacturing workshops with time constraints. In such systems, every operation duration is included between minimal and maximal values. P-time Petri nets are used for modeling. A new theorem is introduced, constituting a decision tool about the occurrence of constraints violation at the level of a synchronization transition when various types of time disturbances occur. It shows the robustness properties of a manufacturing system on a range that may include delay and advance disturbances. The theoretical result is illustrated step by step on a given workshop. Two other lemmas are elaborated contributing to the study of the constraints violation problem. The final goal is to generalize the robustness property towards simultaneous occurrence of two delays at two points of the system, each having its own robustness range. Keywords: manufacturing, maximum time constraints, time disturbance, constraints violation, robustness. 1 Introduction A system is said critical when its functioning failures may produce catastrophic consequences [5]. A particular class of dysfunction may occur when state duration constraints, being not fulfilled lead to non-acceptable situations. In this case, systems are said time critical. Time critical systems, including minimum and maximum constraints for operation duration, correspond to various industrial processes [2, 20, 24]. From a methodological point of view, time requirements formulations correspond to various kinds of time critical systems [8, 9]. Moreover, synchronization problems in case of crisis use to be critical in transport systems [7]. Maximal bound for an operation execution requires model and approaches [4, 6, 16]. Several works mainly focusing on robust control in the state of the art https://doi.org/10.15837/ijccc.2021.3.4240 2 concerning manufacturing [1, 3, 10, 11, 15, 22]. The presented works keeping the manufacturing area as an illustrative application provides properties that impact a wider field of application. The two following sections details fundamentals definitions and a classical modeling approach concerning manufacturing production including minimum and maximum operation duration. The third section considers more original assumption and studies time related decisions while mixing delay and advance disturbances in the same system. The section demonstrates the properties and illustrates them on a manufacturing example. The last section discusses the quality of the results highlighting the need of a formalism extension, addressing the analysis of more complex structures like time constraints ensuing from tele-operation in manufacturing and transport. 2 P-time Petri net Upper bound duration for state durations induces a particular structure of the mathematical prob- lem to be tackled. A dedicated modeling tool, providing useful structural and behavioral properties was presented by [16]. The following definition is used as a basis of a time constrained workshop functional decomposition, which is presented in the next section. The formal definition of a P-time Petri net is given by a pair < R; IS >, where [16]: • R is a marked Petri net, • IS : P −→ (Q+) × (Q+ ∪{+∞}) pi −→ ISi = [ai,bi] with 0 ≤ ai ≤ bi. ISi defines the static interval of staying time of a mark in the place pi belonging to the set of places P (Q+ is the set of positive rational numbers). A mark in the place pi is taken into account in transition validation when it has stayed in pi at least a duration ai and no longer than bi. After the duration bi the token will be dead. The synchronization mechanism is the reason of token death. A dead token means a non- compliance with the required specifications. The semantic specificity of P-time Petri nets was studied by Boyer and Roux [4]. Let us denote by: – T the set of transitions, – toi (resp. oti) the output (resp. the input) places of the transition ti, – poi (resp. opi) the output (resp. the input) transitions of the place pi, – qie the expected sojourn time of the token in the place pi, – qi the effective sojourn time of the token in the place pi, – Stie(n) the expected nnd firing instant of the transition ti. – Sti(n) the effective nnd firing instant of the transition ti. 3 Functional decomposition The current section details a functional decomposition, which is used to analytically express the local temporal margins. The functioning assumptions considers that the workshop is running in a repetitive mode, following a mono-periodic cycle. A workshop in repetitive functioning mode is modeled by a Strongly Connected Event Graph (SCEG) [16, 18]. Definition 1. An Event Graph (EG) is a particular Petri net in which each place has exactly one input transition and one output transition. https://doi.org/10.15837/ijccc.2021.3.4240 3 Definition 2. An EG is a SCEG if and only if it exists an oriented path connecting each node to another. Performances of a SCEG running in mono-periodic functioning mode are proved to be the same as when using the K-periodic functioning [16, 18]. Consequently, a mono-periodic functioning is used in order to decrease the complexity of the supervisory problem [6, 18]. In this case, for each transition t, Ste(n + 1) = Ste(n) + π0 where π0 is the period of the periodic functioning of the given discrete event system. In this paper, the scheduling task is supposed to be done. Therefore, the SCEG corresponding to the system is provided. Moreover, the setting of transitions firing instants is fixed too. Then, constraints violation will be studied in the following. The problem of time disturbances observability is not considered. It was studied by Jerbi et al. [12, 14]. As the sojourn times in places have not the same functional signification when they are included in the sequential process of a product or when they are associated to a free resource, a decomposition of the P-time Petri net model into four sets is made. The assumption of multi-product job-shops without assembling tasks is used: • RU is the set of places representing the used machines, • RN corresponds to the set of places representing the free machines which are shared between manufacturing circuits, • TransC is the set of places representing the loaded transport resources, • TransN C is the set of places representing the unloaded transport resources (or the interconnected buffers). Figure 1 shows a P-time Petri net (G) modeling a system composed by two sequential processes GO1 and GO2 with two shared machines (M1,M2), where: – RU = {p2,p4,p11,p13,p15}, – RN = {p6,p7,p8,p9}, – TransC = {p1,p3,p10,p12,p14}, – TransN C = {p5,p16}, – GO1 = (t12,p10, t6,p11, t7,p12, t8,p13, t9,p14, t10,p15, t11), – GO2 = (t5,p1, t1,p2, t2,p3, t3,p4, t4). The intervals (ISi) and the expected staying times (qie) associated to the places (pi) are: IS1 = [30, 50],q1e = 38,IS2 = [5, 12],q2e = 7,IS3 = [10, 20],q3e = 15,IS4 = [5, 20],q4e = 10,IS5 = [1, +∞],q5e = 10,IS6 = [0, +∞],q6e = 5,IS7 = [0, +∞],q7e = 8,IS8 = [8, +∞],q8e = 13,IS9 = [8, +∞],q9e = 15,IS10 = [5, 15],q10e = 12,IS11 = [15, 20],q11e = 17,IS12 = [3, 7],q12e = 6,IS13 = [2, 20],q13e = 5,IS14 = [2, 7],q14e = 5,IS15 = [15, 20],q15e = 16,IS16 = [1, +∞] and q16e = 19. The initial expected firing instants of each transition are: St1e(1) = 15,St2e(1) = 22,St3e(1) = 37,St4e(1) = 7,St5e(1) = 17,St6e(1) = 12,St7e(1) = 29,St8e(1) = 35,St9e(1) = 0,St10e(1) = 5,St11e(1) = 21 and St12e(1) = 0. The repetitive functioning mode is characterized by the period π0 = 40. See Figure 2. Definition 3. A mono-synchronized subpath is a path containing one and only one synchronization transition which is its last node [11]. Definition 4. An elementary mono-synchronized subpath is a mono-synchronized subpath beginning with a place p such as op is a synchronization transition [11]. In Figure 1, there are eight elementary mono-synchronized subpaths constituting a partition of G: – Lp1 = (p13,t9,p14, t10,p15, t11,p16, t12,p10, t6), https://doi.org/10.15837/ijccc.2021.3.4240 4 Figure 1: Functional decomposition – Lp2 = (p13, t9,p9, t1), – Lp3 = (p2, t2,p3, t3), – Lp4 = (p2, t2,p8, t8), – Lp5 = (p4, t4,p5, t5,p1, t1), – Lp6 = (p4, t4,p6, t6), – Lp7 = (p11, t7,p7, t3), – Lp8 = (p11, t7,p12, t8). https://doi.org/10.15837/ijccc.2021.3.4240 5 Figure 2: Expected firing instants 4 Decision tools for constraints violation The following section provide a set of properties, which are useful for decision making. Depending on the nature of the time disturbance, various kinds of policy may be used, like shifting firing instants of a set of controllable transitions, trying to perform a one line scheduling because the current scheduling cannot be maintained without constraints violations or doing nothing because the non-occurrence of time constraints violation can be proved. The main results of this section provide proofs that the current scheduling can be preserved without constraints violation, providing various types of robustness proofs. 4.1 Theorem Definition 5. Let us consider a Discrete Event System (DES) and G the associated Petri Net model. Let us call B(G) the behavior of G corresponding to the trajectory of states successively reached. Let C(B(G)) be the schedule of conditions established on the system behavior B(G). C(B(G)) is materi- alized by a series of constraints which must be checked by B(G). A non-respect of B(G) corresponds to a violation of C(B(G)) [11]. Definition 6. It is said that a DES has a passive robustness on [∆min, ∆max] in a node n if the https://doi.org/10.15837/ijccc.2021.3.4240 6 occurrence of a disturbance δ ∈ [∆min, ∆max] at the node n does not involve a violation of C(B(G)) [11]. Theorem 1. Let us consider: – ts a synchronization transition, – ots = { pi,pj/(poi = poj = ts) ∧ (pi ∈ TransC ) ∧ (pj ∈ RN ) } , – Respi the residue in pi of a time disturbance, – Respj the residue in pj of a time disturbance. The temporal residues Respi and Respj do not generate constraints violation in ots if and only if: Respj −Respi ≤ (bi −qie) + (qje −aj ). Proof. Let us consider the synchronization transition ts of Figure 3. Figure 3: Study of constraints violation at the synchronization transition ts Direction 1, hypothesis: the temporal residues do not generate constraints violation in ots. Without disturbance: Stse(n) = Stie(n) + qie = Stje(n) + qje Sts(n) = Stie(n) + qi + Respi Sts(n) = Stje(n) + qj + Respj Stie(n) + qi + Respi = Stje(n) + qj + Respj (Stie(n) + qie) + (qi −qie + Respi ) = (Stj (n) + qje) + (qj −qje + Respj ) Respj −Respi = (qi −qie) − (qj −qje) If there is no violation of constraints, then: qi ≤ bi qj ≥ aj qi −qj ≤ bi −aj Respj −Respi ≤ (bi −qie) + (qje −aj ) Conversely, hypothesis: Respj −Respi ≤ (bi −qie) + (qje −aj ). • If both residues have the same sign, three cases are distinguished: https://doi.org/10.15837/ijccc.2021.3.4240 7 – Respj −Respi < 0, – 0 ≤ Respj −Respi ≤ (qje −aj ), – (qje −aj ) < Respj −Respi ≤ (bi −qie) + (qje −aj ). Case 1: Respj −Respi < 0. If both residues are positive, Respj < Respi means that the token in pj keeps waiting until the sojourn time in pi is qi = qie. This wait does not involve a token death in pj since this place represents a free machine (bj = +∞). If both residues are negative, Respj < Respi means that the temporal advance in pj is strictly less than that in pi. This advance does not cause a token death in pj since this place represents a free machine. The token in pi sojourns as it is expected qi = qie since the token in pj is already available. Case 2: 0 ≤ Respj −Respi ≤ (qje −aj ). One has: Sti = Stie + Respi Stj = Stje + Respj Stse = Stie + qie = Stje + qje Stie −Stje = qje −qie Sts = Sti + qi = Stie + Respi + qi Let us show that the firing of the transition ts can take place when qi = qie. In other words, let us prove when qi = qie the token in the place pj is available (qj ≥ aj ). We have: Sts = Stie + Respi + qie (qi = qie) qj = Sts−Stj = Sts−Stje −Respj qj = Stie + Respi + qie −Stje −Respj qj = (Stie −Stje) + qie + (Respi −Respj ) qj = (qje −qie) + qie − (Respj −Respi ) qj ≥ qje − (qje −aj ) qj ≥ aj Therefore, the transition ts is fired when qi = qie and there is no violation of constraints. Case 3: (qje −aj ) < Respj −Respi ≤ (bi −qie) + (qje −aj ). Let us show if the firing of the transition ts occurs at qj = aj, the effective sojourn time of the token in the place pi satisfies: qie < qi ≤ bi. One obtains: Sts = Stj + qj = Stje + Respj + qj Sts = Stje + Respj + aj (qj = aj ) qi = Sts−Sti = Sts−Stie −Respi qi = Stje + Respj + aj −Stie −Respi qi = (Stje −Stie) + aj + (Respj −Respi ) qi = (qie −qje) + aj + (Respj −Respi ) (qje −aj ) + (qie −qje) + aj < qi ≤ (qie −qje) + aj + (bi −qie) − (aj −qje) qie < qi ≤ bi Hence, there is no violation of constraints since the transition ts is fired when qj = aj and qie < qi ≤ bi. https://doi.org/10.15837/ijccc.2021.3.4240 8 Interpretation. Let us take the worst case: Respj −Respi = (bi −qie) + (qje −aj ). If both residues are positive, the token in pj arrives late compared to that in pi. Part of this delay is compensated by (qje −aj ). Instead of staying qie, the token in pj sojourns only qj = aj. Indeed, the token in the place pj, representing a waiting machine, is available as soon as qj = aj, which makes it possible to reject part of the delay disturbance equal to (qje −aj ). Consequently, it remains a delay difference equal to (bi −qie). In the place pi, the token is blocked for the time (bi −qie) until the token in pj is available. The transition ts is fired when qi = bi and qj = aj which is the admissible limit case. Thus, there is no token death. If both residues are negative, the token in pi arrives in advance compared to that in pj. Part of this advance is compensated by the delay (bi − qie). Instead of staying qie, the token in pi sojourns qi = bi. The token in the place pj is available as soon as qj = aj which offers an advance (aj − qje) making it possible to avoid a token death in pi. Then, the transition ts is fired when qi = bi and qj = aj. • If one of the residues is positive and the other is negative, we distinguish two cases: Respj − Respi < 0 or 0 ≤ Respj −Respi ≤ (bi −qie) + (qje −aj ). Case 1: Respj −Respi < 0. Necessarily, we have a delay in the place pi and an advance in the place pj. The token in pj waits for the one in pi until qi = qie. This does not cause any constraints violation since pj ∈ RN . Case 2: 0 ≤ Respj −Respi ≤ (bi −qie) + (qje −aj ). Forcibly, we have an advance in the place pi and a delay in the place pj. This amounts to the study of the case where the residue in pi is zero and the residue in pj is a delay equal to (Respj −Respi ). This is a similar case to the occurrence of two delay residues, already studied. Since 0 ≤ Respj −Respi ≤ (bi −qie) + (qje −aj ), there is no violation of constraints. 4.2 Example Let us take the synchronization t6 of Figure 4. It comes: ot6 = {p10 ∈ TransC,p6 ∈ RN} and (b10 −q10e) + (q6e −a6) = (15 − 12) + (5 − 0) = 8. Figure 4: Study of constraints violation at the synchronization transition t6 • Case of delay residues. Let us suppose that the transition t4 is fired with a delay equal to 13 and the transition t12 with a delay equal to 5. In other words, Resp6 = 13 and Resp10 = 5 (Resp6 −Resp10 = 8). We have: St6e(2) = St4e(2) + q6e = St12e(2) + q10e = 52 St4(2) = St4e(2) + Resp6 = 60 https://doi.org/10.15837/ijccc.2021.3.4240 9 St12(2) = St12e(2) + Resp10 = 45 Since a6 = 0, the token is available as soon as it enters the place p6. The maximum sojourn time in the place p10 is q10 = b10 = 15. In order not to have a token death in p10, the transition t6 must be fired as: St6(2) = St12(2) + b10 = 45 + 15 = 60, which coincides well with the firing instant of the transition t4 and the availability of the token in the place p6. From Figure 5, it is clear that a residue difference strictly greater than 8 automatically generates a token death in p10. There is no longer an overlap in the token availability intervals (static intervals) relating to the two places p6 and p10. Figure 5: Case of delay residues • Case of advance residues. Let us assume that the transition t4 is fired with an advance equal to −6 and the transition t12 with an advance equal to −14, which means Resp6 = −6 and Resp10 = −14 (Resp6 −Resp10 = 8). We get: St4(2) = St4e(2) + Resp6 = 47 − 6 = 41 St12(2) = St12e(2) + Resp10 = 40 − 14 = 26. The token in p6 is available from the instant St4(2) = 41. To avoid a token death in p10, the transition t6 must be fired as: St6(2) = St12(2) + b10 = 26 + 15 = 41, which coincides well with the https://doi.org/10.15837/ijccc.2021.3.4240 10 Figure 6: Case of advance residues firing instant of the transition t4 and the availability of the token in place p6. From Figure 6, it is also clear that a residue difference strictly greater than 8 automatically generates a token death in p10. • Case of delay and advance residues. If the transition t4 is fired with a delay equal to 5 and the transition t12 with an advance equal to −3, which means Resp6 = 5 and Resp10 = −3 (Resp6 −Resp10 = 8), then: St4(2) = St4e(2) + Resp6 = 47 + 5 = 52 St12(2) = St12e(2) + Resp10 = 40 − 3 = 37 The token in p6 is available from the instant St4(2) = 52. To avoid a token death in p10, the transition t6 must be fired as: St6(2) = St12(2) + b10 = 37 + 15 = 52, which coincides well with the firing instant of the transition t4 and the availability of the token in place p6. From Figure 7, it is also clear that a residue difference strictly greater than 8 automatically generates a token death in p10. Figure 7: Case of delay and advance residues 4.3 Lemmas Lemma 2. Let us consider: https://doi.org/10.15837/ijccc.2021.3.4240 11 – ts a synchronization transition, – ots = {pi,pj/(pi ∈ TransC ) ∧ (pj ∈ RN )}, – (pk ∈ P) ∧ (opk = ts), – (ti ∈ T) ∧ (ti =o pi), – (tj ∈ T) ∧ (tj =o pj ), – δ1 (resp. δ2) a delay time disturbance at the input of the place pi (resp. pj), – Res1pk (resp. Res2pk ) the residue in pk of the disturbance δ1 (resp. δ2) when it occurs alone, – Respk the residue in pk of the disturbances δ1 and δ2 when they occur simultaneously. If the occurrence of δ2 alone does not cause a token death in ots then the simultaneous occurrence of δ1 and δ2 does not cause a token death in ots and Respk = max(Res1pk,Res2pk ). Proof. Let us consider the synchronization transition ts of Figure 8. Figure 8: Study of constraints violation when two delay time disturbances occur simultaneously The occurrence of δ1 alone does not cause a token death in ots since the place pj ∈ RN represents a free machine (bj = +∞). The disturbance δ1 is totally transmitted in pk : Respk = δ1. The place pj allows to compensate or reject part of the delay disturbance equal to (qje−aj ). When the disturbance δ2 occurs alone, it comes: Res2pk = max(0,δ2 − (qje −aj )). Case 1: δ1 ≥ δ2. The token in pj keeps waiting until the sojourn time in pi is equal to qie without any violation of constraints and we have: Respk = Res1pk = δ1 = max(Res1pk,Res2pk ). Case 2: δ2 ≥ δ1 + (qje −aj ). By hypothesis, the occurrence of δ2 alone does not cause a token death in ots. According to the theorem 1, it comes: δ2 ≤ (bi −qie) + (qje −aj ) δ1 + (qje −aj ) ≤ δ2 ≤ (bi −qie) + (qje −aj ) (qje −aj ) ≤ δ2 −δ1 ≤ (bi −qie) + (qje −aj ) −δ1 (qje −aj ) ≤ δ2 −δ1 ≤ (bi −qie) + (qje −aj ) According to the theorem 1, there is no token death. This corresponds to the third case of the theorem proof in the case where the disturbances have the same sign. The token in the place pi keeps waiting (qi ≥ qie) until the token in the place pj is available: qj = aj. Then, the firing of the transition https://doi.org/10.15837/ijccc.2021.3.4240 12 ts takes place when qj = aj and the sojourn time of the token in the place pi satisfies: qie ≤ qi ≤ bi. One gets: Sts = Stje + δ2 + aj (qj = aj ) Respk = Sts−Stse = δ2 + aj + (Stje −Stse) = δ2 − (qje −aj ) Respk = δ2 − (qje −aj ) = Res2pk = max(Res1pk,Res2pk ) (δ2 − (qje −aj ) ≥ δ1) Case 3: δ1 < δ2 < δ1 + (qje −aj ). One has: 0 < δ2 −δ1 < (qje −aj ) 0 < δ2 −δ1 < (bi −qie) + (qje −aj ) According to the theorem 1, there is no token death. This corresponds to the second case of the theorem proof in the case where the disturbances have the same sign. The token in the place pj remains waiting until qi = qie. Accordingly, one obtains: Sts = Stie + δ1 + qie (qi = qie) Respk = Sts−Stse = δ1 + qie + (Stie −Stse ) = δ1 + qie −qie = δ1 Respk = δ1 = Res1pk = max(Res1pk,Res2pk ) (δ1 > δ2 − (qje −aj )) Lemma 3. Let: – δ1 and δ2 two delay time disturbances respectively at the transitions t1 and t2, – [∆1min, ∆1max] and [∆2min, ∆2max] the passive robustness intervals respectively at t1 and t2. If δ1 ∈ [∆1min, ∆1max] and δ2 ∈ [∆2min, ∆2max] then the simultaneous occurrence of δ1 and δ2 does not involve any constraints violation. Proof. Let us denote by: – ts a synchronization transition, – ots = {pi,pj/(pi ∈ TransC ) ∧ (pj ∈ RN )}, – Res1pi (resp. Res1pj ) the residue in pi (resp. pj) of the disturbance δ1 when it occurs alone, – Res2pi (resp. Res2pj ) the residue in pi (resp. pj) of the disturbance δ2 when it occurs alone, – Respi (resp. Respj ) the residue in pi (resp. pj) of the disturbances δ1 and δ2 when they occur simultaneously. Lemma 2 gives: Respi = max(Res1pi,Res2pi ) and Respj = max(Res1pj ,Res2pj ). Four cases are possible, which are: – (Respi,Respj ) = (Res1pi,Res1pj ), – (Respi,Respj ) = (Res1pi,Res2pj ), – (Respi,Respj ) = (Res2pi,Res1pj ), – (Respi,Respj ) = (Res2pi,Res2pj ). https://doi.org/10.15837/ijccc.2021.3.4240 13 Case 1: (Respi,Respj ) = (Res1pi,Res1pj ). Respi and Respj are the residues of δ1 only. There is no token death since δ1 ∈ [∆1min, ∆1max]. Case 2: (Respi,Respj ) = (Res1pi,Res2pj ). Knowing δ2 ∈ [∆2min, ∆2max], according to the theorem 1 we have: Res2pj −Res2pi ≤ (bi −qie) + (qje −aj ) Respi = max(Res1pi,Res2pi ) = Res1pi −→ Res1pi ≥ Res2pi −→ Res2pj −Res1pi ≤ Res2pj −Res2pi ≤ (bi −qie) + (qje −aj ) According to the theorem 1, there is no constraints violation. Case 3: (Respi,Respj ) = (Res2pi,Res1pj ). Knowing δ1 ∈ [∆1min, ∆1max], according to the theorem 1 we have: Res1pj −Res1pi ≤ (bi −qie) + (qje −aj ) Respi = max(Res1pi,Res2pi ) = Res2pi −→ Res2pi ≥ Res1pi −→ Res1pj −Res2pi ≤ Res1pj −Res1pi ≤ (bi −qie) + (qje −aj ) According to the theorem 1, there is no constraints violation. Case 4: (Respi,Respj ) = (Res2pi,Res2pj ). Respi and Respj are the residues of δ2 only. There is no constraints violation since δ2 ∈ [∆2min, ∆2max]. Finally, this section presented an original kind of robustness towards a disturbance, which may be an advance or a delay. Some formal definitions are provided in order to build a proved way of computing the corresponding robustness values. Two lemmas provide first results towards concurrent time disturbances occurring on the same time. The last section of this paper stands the quality of the results and discuss the limit of the proposed approach, targeting new industrial applications. 5 Conclusion The paper has presented the theoretical background in order to build an original contribution to the state of the art in the area of manufacturing processes where every operation time has minimal and maximal values. The proposed study considers the effect of delays and advances all together in the same manufacturing process. The first step of the construction presents the classical modeling tool dedicated to duration constrained discrete event systems: the P-time Petri nets. Then, they are mapped on the dedicated historical functional decomposition of a manufacturing process. Using this framework provided by the state of the art, the fourth section presents new behavioral properties. It presented the mixed analysis of disturbance residues at the level of synchronization transitions. After building some proofs and providing illustrations and interpretations, two final properties are formalized. The first one is the robustness properties of a manufacturing system on a range that may include delay and advance. The second one is the generalization of the robustness property towards simultaneous occurrence of two delay time disturbances at two points of the system each having its own robustness range. Theoretical results of this paper are useful for alarm triggering at a plant supervision level. More- over, improving the quality of alarm filtering like presented in [13, 20], by enriching the class of disturbances from which the system robustness can be proved, is clearly a step forward. It is an evi- dence that increasing the range of the robustness properties will decrease the quantity of false alarms. The presented new results of this paper consider the possibility of a mix between advances and delays in running manufacturing processes, by getting deeper in the scenario understanding of a constraint violation clearly allows a better diagnosis. However, the historical functional decomposition only considers a local knowledge, but does not integrate a possible distant knowledge that is consulted through a communication network producing transmission delays. Taking advantages of distributed information centers is a modern proposition https://doi.org/10.15837/ijccc.2021.3.4240 14 used in the digital twin concepts and in the big data scientific area [17, 23]. A new functional decomposition will have to introduce new classes in order to address the specific needs required by industry 4.0, separating concepts of knowledge being immediately available and knowledge that have to be processed a given amount of time before being available. 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A Hybrid Method for Assigning Containers to AGVs in the Dynamic Environment of Container Terminals, Studies in Informatics and Control, https://doi.org/10.24846/v24i1y201505, 24(1), 43–50, 2015. https://doi.org/10.15837/ijccc.2021.3.4240 16 Copyright ©2021 by the authors. Licensee Agora University, Oradea, Romania. This is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial 4.0 International License. Journal’s webpage: http://univagora.ro/jour/index.php/ijccc/ This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE). https://publicationethics.org/members/international-journal-computers-communications-and-control Cite this paper as: Jerbi, N.; Collart-Dutilleul, S. (2021). Decision Tools Regarding Time Constraints Violation in Manufacturing Workshops, International Journal of Computers Communications & Control, 16(3), 4240, 2021. https://doi.org/10.15837/ijccc.2021.3.4240 Introduction P-time Petri net Functional decomposition Decision tools for constraints violation Theorem Example Lemmas Conclusion