CABTREE V14 English
Contents
1. This Agreement is entered into for an undetermined period of time as of the date set forth in Article 3 ARTICLE 9 TERMINATION Each party may terminate this Agreement by registered mail with acknowledgement of receipt forwarded to the other party for any breach by such party of its obligations despite a notice remaining unresponsive for 15 days and this occurring with no prejudice to damages it could claim and provided that the last paragraph of Article 7 above be enforced At end of this Agreement or in case of termination for whatsoever reason the customer will have to stop using CABTREE software package pay all sums remaining due on date of termination and return all elements composing the software package computer programs documentation etc without maintaining any copy of it ARTICLE 10 ROYALTY As a payment for the operating right concession the customer pays CAB INNOVATION an initial royalty the amount of which is determined in specific conditions ARTICLE 11 PROHIBITED TRANFER The customer refrains from transferring the software package operating right granted personally to him by these provisions The customer also abstains from making documentation and supporting material CD ROM even free of charge available to a person not expressly set forth in second paragraph of Article 2 ARTICLE 12 ADDITIONAL SERVICES Any additional services will be subject to an amendment of these provisions possibly through an exch2. Sat3 ok Reconf 3 Renewal 3 Lifetime 4 Sat4 off Sat4 on Sat4 ok Reconf 4 Renewal 4 Lifetime 5 Sat5 off Sat5 on Sat5 ok Reconf 5 Renewal 5 Gate KaN 2 5 ac bc cc dc ec KaN 3 5 ad bd cd dd ed OR ab ac AND non a ab KaN 2 4 bd cd dd ed AND e non ad aqg OR bb bc AND non a bb non ab KaN 1 3 cd dd ed AND e non bd baq OR cb cc AND non a cb non ab non bb AND e non cd OR db dc AND non a db non ab non bb non cb AND e non dd OR eb ec AND non a eb non ab non bb non cb non d AND e non ed Initial Conditio Law 0 Tir 1 1 0 95 0 0 Return Law Tir 1 0 95 Pro 1 Pro 1 Exp 0 000004 Exp 0 00004 Pro 1 Exp 0 000004 Exp 0 00004 Pro 1 Exp 0 000004 Exp 0 00004 Pro 1 Exp 0 000004 Exp 0 00004 Pro 1 Exp 0 000004 Exp 0 00004 Ater t gt 17520 1 70080 0 0 not c not d b not af b not af ae b not bf b not bf be not ad ac not aa not aa not bd bc not ba not ba not cd cc not ca not ca not dd dc not da not da not ed ec not ea not ea Note The proposed renewal strategy in this example is not optimal as it does not anticipates the end of satellite life It may be improved simply by considering that a satellite is lost before its real end of life to consider the time allowance before launching 2 years or 4 years to compensate for any possible launching failure Renewal Pr
3. precautions to be assumed and back up files to be made for his operation his staff qualification as he received from CAB INNOVATION recommendations and information required upon its operating conditions and limits of its performances set forth in user s manual the use made for results he obtains CAB INNOVATION is liable for the software package conformity with his documentation The customer shall prove any possible non conformity CAB INNOVATION does not assume any whatsoever guarantee whether explicit or implicit relating to the software package manuals attached documentation or any supporting item or material provided and especially any guarantee for marketing of any products relating to software package or for using software package for a determined use any guarantee for absence of forgery etc Under no circumstances CAB INNOVATION could be held responsible for any whatsoever damage especially loss in performance data loss or any other financial loss resulting from the use or impossibility to use the CABTREE software package even if CAB INNOVATION was told about the possibility of such damage In the event where CAB INNOVATION liability is retained it is expressly agreed upon that the total amount of compensation to be paid by CAB INNOVATION all cases taken together could not in any way exceed the initial royalty price reduced by 25 per period of twelve months elapsed as from the mailing delivery date ARTICLE 8 DURATION
4. 3 1 Entering Using a Table 3 1 Entering Tree Directly 4 Entering Laws 5 Processing a Tree 4 1 Cut Sets 4 2 Calculating the Probability 4 3 Simulation 6 Saving 7 Printing 6 1 Printing the Tree 6 2 Printing the Table 1 The CABTREE Software 1 1 General Presentation CABTREE helps achieve and efficiently process the trees of faults or trees of events Despite its ability to perform right calculations without any approximation its original feature consists in integrating a dynamic simulation function of trees Monte Carlo This function in particular makes it possible to treat the gates DELAY temporization and AND WITH CONDITIONS B AND C if B before C ation 28 e f o h i 5 Sa FA To text 256 characters gt Program s main features are as follows Achieving directly the tree using utilities bars or automatic drawing from a word description preliminarily entered in a table o Assuming gates OR AND NOT NOR NAND exclusive OR and K among N drawing of conditioned gates AND and OR and Matrix gate Assuming Exponential Normal Lognormal Weibull and Gamma laws to define the occurrence probability of basic events Searching cut sets classified according to the occurrence order or probability Calculating exactly probabilities by applying Bayes theorem over a time interval curves Simulating dynamically the tree Monte Carlo allowing to assume laws of appearance and disappearance o
5. In the event where it is translated into one or more foreign languages only the French text will be deemed authentic in case of any dispute between the parties ARTICLE 18 APPLICABLE LAW DISPUTES The French Law governs this Agreement In the event of any disagreement over the interpretation and performance of any whatsoever provision of this Agreement and if parties fail to reach an agreement under an arbitration procedure only Toulouse s Courts will be competent to settle the dispute despite the plurality of defendants or the appeal for guarantee 35
6. box the initial time O by default maximum time and the sequence of calculation 22 Entering time value ajx Unit ie Hour Day Year Value M Curve Step ho Tmin Tmax jo 8 0 030631082 015524705 0 06619773 002722268 0 01109887 000451557 0 0018362 0 00074656 012345 67 8 9 10 0 00030354 0 00012341 i 1 2 3 A 5 5 7 O 9 10 hours Calculation performed by program is an accurate calculation which includes no approximation Such calculation is based on Bayes theorem which helps calculating the probability of an event from conditional event probabilities Its principle is illustrated by the following example in which cut sets are not independent each other events b and d being identified in different cut sets a b c b d e d f g P a P b 1 d 1 P c f g P b 1 d 0 P c g P b 0 d 1 P e f g P b 0 d 0 P g Different importance factors are provided by the tool The conditional probability P a ei Probability of a knowing the event e1 The important factor of diagnosis Vesely et Fussel P ei a Pei P a e1 Pa The factor of marginal importance Birnbaum 6Pa dPa P a e1 P a not ei The critical factor Lambert 6Pa dPa Pei Pa P a ei P a not ei The risk achievement worth P a e1 Pa The risk reduction worth Pa P a not ei 23 Note Gate Exclusive OR is not proces
7. specific to simulation function if one of relevant boxes was ticked see below or selection of following basic event Acting on button End Cancel closes such procedure zx E 2 xl Basle EEn Basic event h Type of law Probability Set event Forced at status 1 during transitions From O to 1 of Following AFber b gt fio events f hours fb f C days tenter these events separated by C years Parameters of law Reset event Forced at status 0 during value i transitions From O to 1 of Following events fenter these events separated by Previous dialog box Previous dialog box Entering information specific to simulation function ignored by calculation function 20 Periodic maintenance A periodic action of maintenance can be characterized by its effectiveness probability of repair in the event of failure and by a possible renovation in the case of elements subjected to degradation or wear Such a renovation can be modelled by a failure rate of the type K A t pPpkwT with 0 minimal maintenance lt p lt 1 perfect maintenance in which a virtual age is calculated starting from the last action of maintenance by considering a factor of renovation p corresponding for example to the proportion of the failure rate of the replaced parts The Exponential and Weibull laws allow to consider such actions of maintenance by the addition of specific parameters e Expone
8. the menu 10 2 5 Monte Carlo Fault Tree Simulation Ey DIDACT_5 Monte Carlo Fault Tree Simulation Palliative method to take into account some dynamic aspects Dynamic characteristics considered Gate delay Gate AND with condition of precedence Probability laws of appearance and disappearance of the basic events e Set Reset relations of dependence Forcing with 1 or 0 with the occurrence of another event Pru babille Temps hire Monte Carlo sunulation Example Return to the menu E DIDACT_5B Simulation Calculation Return to the menu 1 2 6 Step of development of the Fault Trees EW DIDACT 6 Step of development of the Fault Trees Top Down method of the general to the particular Begin from the feared event top of the tree Imagine the possible families of causes of the feared event Consider each families of causes as a new feared event Imagine the possible causes of each event at the level considered Go down gradually in the tree until the basic events Don t consider the basic events immediately a component failure for example Example Return to the menu E pmact b SS O x Operator Des ors Consumption i V4 Tank High level sensor C1 and very high level sensor C2 Valves normally open V1 and normally closed V4 Electrovalves V2 and V3 ordered by the sensors respectively C2 and C1 Alarm activated by the high level sensor C2 V1 block
9. 1 system loss b Loss of E1 Loss of E Loss of Ea Se E E Surival Failure A Failure B Redundanc are Box to be ticked Deleting previous drawing helps limiting the number of documents generated from a same table Values of probabilities pre entered or calculated by program may be initiated on the generated tree by ticking box Displaying probabilities 3 2 Entering Tree Directly Entering a tree directly requires to create preliminarily a blank table before initiating the menu U4 command Drawing the Tree So the dialog box below is initiated to define the top event a The same dialog box will be subsequently used to define or modify other tree events Define the event a Type Rectangle Circle Lozenge desdine Double Lozenge a Gate Combination M Tree updating local 16 Two scrolling lists help choose among the types of events and logic gates A third list makes it possible to select or create the events entering the gate The latter appear in the box located under the name of the gate Separated by commas In the case of a conditioned gate or a combination K N the box just located beneath is used to define the condition Example Exclusion or values of K and N Example 3 5 A box to be ticked helps commanding the tree drawing updating in addition to that of table after initiating button OK A second box to be ticked helps limiting this drawing to local modificati
10. Cab Innovation 3 rue de la Coquille 31500 Toulouse Tel 33 0 5 61 54 68 08 Fax 33 0 5 61 54 33 32 Mail Contact cabinnovation com Web www cabinnovation com CA B TR E E Version 14 using Microsoft EXCEL TREE 1 O x a b C Loss of El Loss of E2 E d f i h Loss of l E2 E Survival Fault Tree User s Manual FOREWORD The software CABTREE BASIC version 4 includes some of the CABTREE version 14 features It is not the subject of a specific user manual The copyright law and international conventions protect the CABTREE software and its User s Manual Their reproduction or distribution either wholly or partly through any means whatsoever is strictly prohibited Any person who does not comply with such provisions is committing an offence of forgery and is liable to prosecution and can be sentenced under the provisions prescribed by the law The Programming Protection Agency A P P references CABTREE at the I D D N Inter Deposit Digital Number index with the following reference IDDN FR 001 070017 00 R P 2000 000 20600 CONTENTS 1 The CABTREE Software 1 1 General Presentation 1 2 Installing CABTREE on Hard Disk 1 3 Starting CABTREE 1 4 Symbols used 2 Didacticiel 2 1 Fault Tree definition 2 2 Symbology of the Fault Trees 2 3 Method of calculation 2 4 Errors to be avoided 2 5 Monte Carlo Fault Tree Simulation 2 6 Step of development of the Fault Trees 3 Entering a Tree
11. Heading Variable Gate Initial Law After t gt Return Law After t gt Condition hours A E Satellite 1 Launch 17520 SAT 0 5 10 10 0 1 0 9 15 A 1 1 0 9 15 2 1 0 9 15 Satellite 2 Satellite 3 29 Satellite Constellation 2 among 3 1 2 0 8 Service Q 2 aA Sat2 i Sat3 0 2 OrnitimnonwwrTewMonooOok ODD ra Time years Though voluntarily simplified the example shown below illustrates the program s modelling and simulation capacity Such generic example describes the problem of renewing satellites in an orbital constellation plan Example 4 Simulation of a complex system Constellation of 2 operational satellites plus a number of spare satellites in orbit Launching per cluster of 3 First launch at T I year Decision of a new launch on loss of any spare Time allowance before launching 2 years Launch Reliability 0 95 One year extension in case of failure Fault rate of an operational satellite Fault rate of an spare satellite amp lifetime years propellant limitation 30 Heading Variable Service Available First launch Not Renewed Time limit before launching Pulse Renewal Lifetime 1 Sat1 off Sati on Sat1 ok Reconf 1 Condition of renew 1 Renewal 1 Lifetime 2 Sat2 off Sat2 on Sat2 ok Reconf 2 Condition of Renew 2 Renewal 2 Lifetime 3 Sat3 off Sat3 on
12. SO LOIXLA of PERSO directory they will be directly read by program during simulations To write in this international additional macro type file pressing Shift and Control keys is necessary during the opening EXCEL procedure Format used is as follows example of exponential law Perso Law ARGUMENT T 1 ARGUMENT Waiting 1 ARGUMENT Law 2 Exponential IF LEFT Loi 3 Exp GOTO R 4 C SET NAME Lambda VALUE LEFT RIGHT Law LEN Law 4 _LEN Law 5 SET NAME d_T waiting LN RAND Lambda RETURN D_T Next function IF LEFT Law 3 XXX GOTO _ Name of functions is limited to 3 characters Exp Arguments used are as follows T current time Attente time of writing in table which adds up to transition time Loi name of function and of its arguments as entered in table decimal points in numbers being replaced by dots Exp 0 7 In return function returns the time before transition d_T 2 6 Saving Only the table should be saved as any spreadsheet document Obviously the tree saving is not necessary as it may be regenerated by the program from the table whereas inversely obtaining the table from the tree is not possible 7 Printing 7 1 Printing the Tree Menu command Printing the Tree enables to cut and format the tree depending on original document formatting portrait or landscape So the printing documents with a system of cross reference between pages are gen
13. ange of letters so as to specify the contents modalities of achievement and the price ARTICLE 13 CORRECTIVE AND PREVENTIVE MAINTENANCE 34 The corrective and preventive maintenance may be subject upon customer s request to a separate Agreement attached to these provisions ARTICLE 14 ENTIRETY OF THE AGREEMENT The user s manual defining the CABTREE software package features is appended to these provisions The provisions of this Agreement and his Appendix express the entirety of the Agreement entered into between the parties They are prevailing among any proposition exchange of letters preceding its signing up together with any other provision stated in documents exchanged between the parties and relating to the Agreement s subject matter If any whatsoever clause of this Agreement is null and void with respect to a rule of Law or a Law in force it will considered as not being written though not involving the Agreement s nullity ARTICLE 15 ADVERTISING CAB INNOVATION could mention the customer in its business references as a CABTREE software package user ARTICLE 16 CONFIDENTIALITY Each party undertakes not to disclose any kind of documents or information about the other party that it would have been informed of on the Agreement s performance and undertakes to have such obligation fulfilled by the persons it is liable for ARTICLE 17 AGREEMENT S LANGUAGE This Agreement is entered into and drawn up in the French language
14. calculus based exclusively on the 3 logical operators of union OR w of intersection AND 4 and of negation NOT P AUB P A P B P AMB Theorem of Poincare P AMB PCA P B ifand only if A and B independent Pld LEON The basic events of a Fault Tree have to be independent Continuation Return to the menu EE DIDACT 3b Method of calculation continuation P AMB 4 P A x P B if A and B are dependent P a black queen in set of 32 charts 2 32 P Queen P Black 1 8 1 2 1 16 P a black queen in set of 32 charts without the ACE of spade 2 31 P Queen P Black 4 31 15 31 60 961 P Event lt P minimal cut sets Civ Cj Ci Cj Cin Cj P Event S Pammuimal cut sets Cin Cj 0 CABTREE carries out an exact calculation but other tools make this approximation Return to the menu 2 4 Errors to be avoided E DIDACT_4 Errors to be avoided Not compliance with the rule of independence between the basic events Examples Dependence between failures of distinct elements Common mode failure propagation etc Conditioned maintenance between elements Common repairers or means in a limited number synchronized periodic maintenance etc Modification of state to the occurrence of another event Suppression of the safety measures in phase of maintenance absorbing states etc Stochastic dependences modification of the probability laws of occurrence depending on the stat
15. complying with purchase conditions stated on specific conditions especially defining the maximum number of users authorized to use the software package from their terminal and the maximum number of users authorized to use it simultaneously The customer is therefore authorized to perform a number of software package documentation copies equal to the maximum number of users allowed to use it CAB INNOVATION will be in a position to perform inspections either itself or through a specialized entity purposefully authorized by CAB INNOVATION at customer premises to verify if customer has met its requirements number of software package copies used location of such copies etc Parties will agree as regards the practical modalities of performance of such inspections so as to disturb minimally customer s activity ARTICLE 3 DELIVERY INSTALLATION AND RECEPTION The software package and attached supplies will be delivered to the customer on mail reception date The customer installs at its own costs the software package using relevant manual delivered by CAB INNOVATION The customer performs the inventory and shall inform CAB INNOVATION within three working days of the delivery of any apparent nonconformity with respect to the order The customer is liable for any loss or any damage caused to supplies as from the delivery ARTICLE 4 TESTING AND GUARANTEE Guarantee is effective as from the mail delivery date set forth in Article 3 and has a thre
16. dards CEI 61025 ou UTE C 20 318 Symbol Name Symbol meaning Circl Basic event of which the probability of failure is known ircle Event which could be subdivided in basic events but which will Lozenge not be to it for lack of information or for lack of interest Event resulting from combination of other events through logic Rectangle gates Event whose causes are not developed vet but will be subsequently Double lozenge developed Continuation Return to the menu EW DIDACT_2b Symbology of the Fault Trees continuation Gates Rf me The output event is gener ated f ali the input events are true Cate OR The output event is generated if at least ane input event Appeare Combinaison gate The output event is generated tfat least k ofn input events are ken simultane ously true Gate NOT The output event is generated ifthe input event is mot true ane comversely Continuation Return to the menu SBowactze O SA Symbology of the Fault Trees continuation Gates 2 Conditioned The output event is gene AND vate The output event is generate d if atleast one input event is true Conditioned and if ihe condition is verified OR gate The auf put event is generated if the input event is true and if the condition is verified Return to the mena Gate Exclusive OR is defined by a Conditioned OR gate whose condition is Exclusion 2 3 Method of calculation EW DIDACT 3 EEE Method of calculation Probability
17. e month validity During the guarantee validity if the customer experiences a software package operation trouble he should inform CAB INNOVATION about it so as to receive any helpful explanations with the purpose of remedying such trouble If the trouble is continuing the customer will return the C D ROM to CAB INNOVATION at CAB INNOVATION s Head Office at his own expense and with registered mail with acknowledgement of receipt by specifying exactly the troubles encountered Within the three months of reception of consignment set forth in preceding paragraph CAB INNOVATION will deliver at its Own expense a new product version to the customer This new version will be benefiting of the same guarantee as benefited the first version The customer looses the benefit of the guarantee if he does not comply with the instructions manual recommendations if he performs modifications of configuration set forth in Article 2 above without obtaining a prior written consent from CAB INNOVATION or if he performs modifications additions corrections etc on software package even with the support from a specialized service company without obtaining a prior written consent from CAB INNOVATION ARTICLE 5 PROPERTY RIGHT CAB INNOVATION declares to be holding all the rights provided for by the intellectual property code for CABTREE package software and its documentation As this operating right granting generates no property right transfer the custome
18. e of the system Cold redundancy with Aon Aoff variable wear according to the request etc Warning Risk of error with availability calculations in average value uff A nu for reparable equipment Exp A T 2 or A T 2 for a periodic maintenance af period T Continuation Return to the menu EW DIDACT_4b Errors to be avoided example 1 Repairers in a limited number Absorbing State no more repair if loss of event a MTBFa MTBFb MTBFe 2000 hours MTTRa MTTR MTTRe 50 hours Average availability aft Matrices of Markov Pia 0 999985 Pia 0 999913 Pia 0 963 10000 hr STATES 2 3 4 5 6 Ff 8 2 3 4 5 6 7 B 12 3 4 5 6 7 8 d c b 2 Pome ROE Wike Ta N a1 eae a E A oes a ae eS d cnb dnc b d nc nb nd c b O Reliabiltyofa nd cnb nd nc b nd nc nb N repairers Single repairer Absorbing State final loss of A The taking into account of the dynamic aspects requires the use of suitable methods Markov Monte Carlo simulation etc Continuation Return to the menu EW DIDACT_4c Errors to be avoided example 2 Periodic maintenance Average availability Expat T2 Probability of loss of A it tt WEL dll udh ul a aco TT dl sooo s0 O O 1000 2000 3000 4000 smo ewoo 7O00 sow hours 0 000373 Unavailability can be much higher than that calculated starting from average values in particular before the synchronized actions of maintenance Computation table Return to
19. ed open 707 Art V2 and Y3 blocked open 107 prt Yd blocked closed 4 7077 Art CI and G2 failure sensor 10 Ar Alanne failed 70 7 hr Operator OK a590 In case of alarm activation the operator closes the normally open valve V1 and opens the normally closed valve V4 Continuation Return to the menu 12 EY DIDACT_ 6c Sensor 2 is used to command the nominal loop and the safety loop Maintenance actions are necessary to limit the risk over the duration Table Return to the menu 13 3 Entering a Tree The tree may be generated from a word description pre entered in a table or achieved directly by assembling different types of events and gates on graph This second method is recommended Used with a posterior version of Excel to version 4 the tree can be cut out on several sheets of a work book in order to improve its clearness 3 1 Entering Using a Table Menu command New table helps obtaining a table as shown below ordinary table Type e e dim Event a is the top of the tree and utilities bars Type and Gate are offered to user to create other events and define their type together with the relevant logic gate in the case of rectangle type events B Type Rectangle gt oe q Circle Lozenge ___y a K lt 4 Double lozenge House p mn lt q Switching of table to relevant tree Activating a button of utilities bar Type creates a new event of type ch
20. eliminarily defined typical parameters is optional Time interval during which such values will be calculated is defined by Tmin 10 hours and Tmax 20 hours Calculation of accuracy depending on number of simulations carried out is also optional The reliability interval at level required 60 may be calculated for each event Box to be ticked Simulation Duration helps assessing the duration of a simulation together with the overall processing duration for the number of simulations required Such duration depends mainly on number of transitions of conditions of various events for the analysis duration Box to be ticked Debug allows to obtain the timing diagram of a simulation for test purposes Following examples illustrate the program s different functionalities Example 1 Variable Gate Initial Law Aftert gt Return Law After t gt Condition pO pO AND b c Results after 100 simulations Probability 2 34 5 6 f 6 9 10 11 12 13 14 15 16 17 18 19 20 Time hours Aye DUT 0 970 0 900 0 390 UDT 0 950 0 950 0 290 MDT hrs 2 979 2 509 4 247 gma MUT hrs 3 238 5 000 3 266 gma Proba Moy 0 381 0 479 0 833 0 002 0 003 0 007 Average values between Tmin 10 and Tmax 20 25 on of o D w l w cn b Reliability interval Of a 60 P taf i ed N a amin 60 a max 60 5 ho Ly o i a 0123405 6 T7 a
21. enu 2 Teachware The teachware presents the Fault Trees by means of various tables and demonstrations 2 1 Fault Tree definition Ga DIDACT_1 EEx Fault Tree definition Chart of the combinations of events involving the realization of an undesirable event Objectives Seek causes of an undesirable event by a deductive reasoning e Representation of the causes in the shape of a logical tree structure Mathematical treatment of the tree produced so to identify the minimal cut sets to calculate the probability of the various events if probabilistic data on the basic events are available The minimal cut sets are the smallest combinations of basic events whose realization induces the undesirable event The cut set order is the number of basic events which constitutes therm The basic events are independent They can correspond to human breakdowns failures errors particular conditions etc The Fault Tree representation is static absence of sequential events Example Retur to the menu Ey DIDACT_1b System of leak Example of Fault Tree x detection i gt Valves VI Risk V2 3 explosion Gas leakage S a e b c e b d e Minimal Cut Sets Not leak detection order 1 Nothing order 2 ae Leakage of order 3 b c e Dale joint tank Return to the menu V1 open V2 open V3 open 2 2 Symbology of the Fault Trees EH DIDACT_2 Symbology of the Fault Trees Defined by the stan
22. erated by the program In a dialog box the user selects the printing scale and may keep such documents or command their effective printing Note Width of original document columns is stored in printing documents except when the latter is not uniform 7 2 Printing the Table Menu command Printing the Table enables to print the entry table 28 APPENDIX Application of simulation to problems of the space field As an example two functions used for evaluating the availability of satellite constellations are originally provided in file LOI XLA Function TIR defines the launching date of a satellite and function SAT that of its loss TIR Premier_Tir Retard_si_ chec Fiab_lanceur Dernier_Tir Premier_Tir date of first launch in years to be omitted if such date is undetermined Retard_si_ chec delay prior to next launch in years in case of launcher failure no new attempt in case of omission Fiab_lanceur Reliability of launcher equal to 1 if omitted Dernier_Tir late date of a launch in years to be omitted if it corresponds to the end of simulated mission The waiting period may be used to simulate the duration prior to a spare satellite launch see example below SAT Fiab_sat T_Fiab D_vie Fiab_sat Satellite reliability for time T_Fiab Exponential Law T_Fiab Duration corresponding to Fiab_sat in years D_vie Maximum satellite lifetime in years Example 3 Use of personalized probability laws
23. f basic elements together with certain dependence relations between events and to treat the gates DELAY temporization and AND WITH CONDITIONS Automatic cutting and formatting of the tree or one of its branches for printing 1 2 Installing CABTREE on Hard Disk Please comply with instructions shown in CD ROM 1 3 To Start CABTREE In EXCEL open file CABTREE xla Program functionalities are then made accessible through menu Tree spreadsheet functionalities remaining always available C2 e Classeur CABTREE V 11 Accueil Insertion Mise en page Formules Donn es Revision Affichage Tree T Help Teachware HH New table wl 4p Oe A sca Changing jf Entering laws E EE z ah Minimal cut set ia Other menus W Drawing the tree d Cy a aa a 3 Cutting m Save Di Fet sp ce Probability calculation amp gt Pa 8 CY Refreshing FA a as Monte Carlo simulation General Entering a table Table Entering the tree Tree Processing Banner on Excel versions after 2007 E CABTREE V 11 Classeur Eat Fichier Edition Affichage Insertion Format utils Donn es Fen tre Helo Teachware Okher menus New table Utilities bars Drawing the tree Table lt gt Tree switching Changing the tree double click Entry of laws uk sets Probability calculation Simulation Printing the tree Printing the table Menu on Excel versions prior to 2007 A help and a teachware are proposed in the m
24. lected on drawing Helps event selected on drawing by initiating the pre described dialog box to define the top event Such dialog box may also be displayed using simply a double click on mouse or menu command Changing the tree Allows to cut out the tree on several sheets of work book on the level of the selected event This same button makes it possible to remove such a cutting system of reference between the sheets of the tree makes it possible to pass from an event to its decomposition and reciprocally by a simple click of the mouse Activate the command Entering Laws of the menu U Oo E p Regenerate all events classification letters of the tree in order to improve its legibility Save the table of the tree starting from this last Commands the printing of tree just the same way as relevant menu command see chapter Printing 18 gt Commands the switching of the tree to the relevant table Menu command Table Tree Switching has a similar effect 4 Entering Laws Menu command Entering Laws helps defining laws of probability regarding basic event occurrence using dialog box shown below Entry of laws P x Basic event lh F m Initial condition if g 4 Z Type of law Normal After t gt Probability Probability of h 20 Exponential hours days C years Parameters of law Average 5 Sigma 1 5 M Return to initial condition simulation Ba
25. mp 9 1011 12 13 14 15 16 17 18 19 20 Time hours Example 2 Variable Gate Initial Law After t Return Law After t gt Set Reset Condition gt Dependence AND b c Relation 1 Exp ol 0 Ep00 0 fe oc 0 Pom 200 Prot 5o Dependence Set of b by c Probability 200 300 400 500 600 700 Time hours 100 200 300 400 500 600 700 800 300 Time hours In this example event b is forced to status 1 during rising transition from O to 1 of event If event b is already in status 1 transition of c has no effect 26 Notes Operator Not may be used in columns Set and Reset so that forcing is carried out on decreasing transition of event from 1 to 0 So c can be replaced by not c in previous example Such operator may be used in a logic gate of type AND OR NAND or NOR to facilitate the entry of a simulation table So it may be entered AND b not c in gate column but such easy step is only allowed for the simulation function Personalized Probability Laws In addition to standard probability laws offered to user the simulation program offers the possibility to construct personalized probability laws Though in most cases such laws can be obtained by combination of standard laws by possibly using dependence relations they facilitate the processing of generic problems and reduce simulation duration Entered in the form of de macro functions EXCEL in file LOL PER
26. ntial Lambda Period Effectiveness e Weibull Beta Gamma Sigma Period Effectiveness Renovation Periodic maintenance _ V eibull Exponential 21 5 Processing the Tree 5 1 Cut Sets A cut is a combination of events the achievement of which generates that of event considered Cut sets represent the smallest combinations leading to such event So the tree s top event of page 10 shows the following cut sets Cuts of a classified in increasing order JI P DP set x Symbol means negation operator AND is replaced by d g h d AND NOT g AND NOT h The order is the number of events entering in cut Menu command Cut Sets helps obtaining cut sets of any event of a tree classified depending on the occurrence order or probability The event may be preliminarily selected on tree or table or selected in a dialog box using a scrolling list Probability of any of cut sets may be obtained whether basic event occurrence probability laws were preliminarily entered 5 2 Calculating the Probability As soon as basic event occurrence probability laws are entered menu command Calculating the probability allows to calculate the probability of any event of the tree or the factor of importance of the basic events Such calculation may concern all tree events or be limited to a specific event In this case the evolution curve of probability depending on time may be reached by defining in a dialog
27. ocess Order of renewal Sat5 4 3 31 Time years Sat1 ok Sat2 ok Sat3 ok Sat4 ok Sa5 ok Time bef taunching Reconfiguration Process Sat off Sati on Sat2 off Sat2 on Sat3 off Sat3 on Sat4 off Sat4 on Sat5 off 23 45 67 8 9 Sie on Operating order Satl 2 3 Time years Constellation of 2 satellites plus 3 spares Service Sati ok Sat2 ok Sat3 ok Sat4 ok Sat5 ok Availability 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Time years Satellite Constellation Orbit Plan Modelling a2 OPERATING LICENCE AGREEMENT OF CABTREE SOFTWARE PACKAGE ARTICLE 1 SUBJECT The purpose of this Agreement is to define the conditions in which the CAB INNOVATION Company grants the customer with a non transferable non exclusive and personal right to use the software package referred to as CABTREE and whose features are specified in user s manual ARTICLE 2 SCOPE OF THE OPERATING RIGHT The customer may use the software package on one single computer and on a second one provided that the second computer does not operate at the same time as the first one The customer can only have one software package copy maintained in a safe place as a backup copy If this license is regarding a performance on site the customer may install the package software on a server while scrupulously
28. ons when tree structure is not modified modifications limited to the active sheet when the tree is cut out on several sheets After initiating button OK similar dialog boxes are successively displayed to define the different events entering in gate of event a Circle type events are offered by default to user and he may modify immediately or subsequently such events from a first drawing The latter is initiated when all events have been defined a Dialog box below is initiated with the tree drawing Such box helps modifying the tree directly on graph while updating the relevant table Buttons meaning 1s as follows Reduces the display zoom factor A Increases the display zoom factor 17 Cuts an event selected on drawing as well as the branch which defines it if being of Rectangle type Copies an event selected on drawing as well as the branch which defines it if being of Rectangle type Adds a pre cut or pre copied event with possibly the relevant branch to gate events of event selected on drawing In the case of a pre copied event a dialog box helps user to insert directly this one or insert a similar event with same features though with a different name So a similar branch is automatically redesigned if it is a rectangle type event a Deletes an event selected on drawing together with the branch which defines it if of Rectangle type Adds a Circle type event to events of gate of the event se
29. osen by user on line below the selected cell when this one is in the table Modifying a type of event already created is made possible by pre selecting such event in cell of table field Type 14 AND__y ae lt OR Combination K N p ei oe lt q NAND NOR gt ey 4 NOT Conditioned AND __y ate eres lt Conditioned OR Delay p E aia lt q Matrix Activating utilities bar button Gate enables to define the logic gate of a rectangle type event This one commands the display of a dialog box in which user enters the names of events entering in gate separated by a decimal point Entering a Conditioned Or gate Entering a Conditioned Or gate Ed Enter events separated by Enter condition to be verified Exdusion In the case of a conditioned gate or a combination K N a second dialog box is used to define gate The heading of each event may contain up to 256 characters Press ALT with return to return to line in cell Probabilities of basic events may be directly entered in relevant field or will be calculated subsequently by program from the laws of probabilities see chapter Entering Laws Menu command Drawing the Tree helps drawing the entire tree corresponding to the table or confining oneself to the drawing of one of its branches using the dialog box below Event ja E FA M Last drawing deleted Print the probabilities x cms 15 215
30. r abstains from any CABTREE software package reproduction whether it is wholly or partly carried out whatever the form assumed excepting the number of copies authorized in Article 2 any CABTREE software package transcription in any other language than that provided for in this Agreement see Appendix any adaptation to use it in other equipment or with other basic software packages de base than those provided for in this Agreement To ensure this property protection the customer undertakes especially to 33 maintain clearly visible any property and copyright specifications that CAB INNOVATION would have affixed on programs supporting material and documentation assume with respect to his staff and any external person any helpful information and prevention step ARTICLE 6 USING SOURCES Any CABTREE software package modification transcription and as a general rule any operation requiring the use of sources and their documentation are exclusively reserved for CAB INNOVATION The customer holds the right to get the information required for the software package interoperability with other softwares he is using under the conditions provided for in the intellectual property code In each case an amendment of these provisions will set out the price time limits and general terms of performance thereof ARTICLE 7 LIABILITY The customer is liable for choosing CABTREE software package its adequacy with his requirements
31. sed by the calculation function It is only processed by simulation 5 3 Simulation Such function helps assessing using Monte Carlo simulation the probabilities of various events of the tree depending on time together with average values of following typical parameters within a user defined time interval DUT Down Up Transition average number of transitions from 0 to 1 UDT Up Down Transition average number of transitions from 0 to 1 MDT Mean Down Time mean time at condition 0 MUT Mean Up Time mean time at condition 1 Average probability It may assume laws of appearance and disappearance of basic events together with certain dependence relations between events Set Reset The gate DELAY temporization AND WITH CONDITIONS B AND C if B before C and Exclusive OR can be thus treated by simulation Monte Carlo Simulation x Events a b c Enter events separated by Number of simulations 100 it Step 0 1 hor day Duration 20 r IW average values between Tmin 10 and Tmax 20 IW Accuracy calculation Confidence level eo Do Simulation duration Debug Events to be assessed may be pre selected on tree or in table or directly entered in relevant box The number of simulations 100 the analysis sequence 0 1 hour and duration of this one from 0 to 20 hours are entered by user in relevant boxes 24 Calculation of average values of pr
32. sic events may be selected in the dialog box using a scrolling list For each event the user may define the initial condition O or 1 a duration in unit selected during which the event remains in this condition After t 20 hours as well as a law featuring the change of condition which is chosen using a scrolling list among following probability laws Probability value Simple probability value Exponential lambda With or without periodic maintenance Normal average sigma LogNormal a b Weibull beta gamma sigma gt With or without periodic maintenance Gamma beta lambda Availability lambda mu Availability Unavailability of an element of fault rate and repair rate u 19 Parameters of laws entered in parentheses should be entered respectively in relevant boxes as shown in previous example Normal law with average 5 hours and standard deviation 1 5 hour Such parameters are defined in a unit relating to the hour A box to be ticked helps entering a law of return to initial condition which will only be considered by dynamic simulation function of the tree Similarly box Set Reset only concerns simulation It allows to define a condition of forcing at status 1 or O of event considered during transition from 0 to 1 of one or more other events Acting on button OK generates the updating of table from information entered in dialog box then the display of one dialog box
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