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### Functional Decomposition

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in the last class we discussed about the functional decomposition ofsystems and we discussed about one method called Hatley–Pirbhai template or HPtemplate and how to use this HP template for decompositions of functions and thengetting a functional architecture based on the hierarchy of the functions.As mentioned, there is one more method I would like to discuss today and this method isknown as IDEF0. Basically, we use a template called IDEF0 and using this template wedecompose the functions and with the sub functions and then we see these sub functionswe create a hierarchical function structure. IDEF0 is basically a graphical methods wherewe identify the functions and their inter relationships and all the control signalseverything we represented using a graphical method and create graphical sketches ofthese functions in order to identify the sub functions.(Refer Slide Time: 01:14)
Basically, this method known as Integrated Definition for Function Modelling or in shortIDEF0, 0 was added I mean is a first initial chart that is why it is known as IDEF0, it is aintegrated definition for function modelling. This was developed by US Air Force in
order to develop some of the aircraft systems or defence systems and to identify thefunctions needed. So, this actually answers definitive questions about the transformationof inputs to outputs. Basically, every function can be considered as a relationshipbetween input and output and there therefore, this method answers the question abouttransformation of inputs to outputs. So, what actually happens to the inputs and what arethe transformation the input is going through in order to get the outputs and this canactually be clearly answered using the IDEF0 chart and it is a coordinated set ofdiagrams using both the graphical language and natural language.So, there are there is a basically a graphical representation. So, we use some of thegraphical language as well as the natural language to describe the functions. Here, weuse different diagrams A-0 or A0 page is the context diagram. So, basically this diagramgives the overall function of the products or the system and gives the inputs outputs and
the control signals as well as the mechanisms through which the system operates. So, A-0 is the context diagram and then we use different diagrams like A0, A1, A2 which are
the level 0, 1, 2 diagrams. So, and this is actually goes on till we reach the final or thelast sub functions which we do not need to decompose further.So, the number of levels are not fixed, but actually depends on the systems and it isfunctions.(Refer Slide Time: 03:14)
So, as I mentioned there are different levels of diagrams. We can actually show it as theA-0 page that is the context or system function diagram; it defines the inputs, controls,outputs and mechanisms or known as ICOMs. So, in this diagram we represent all theinputs, the controls, outputs and mechanisms for the single top level function and this toplevel function is labelled as A0. So, A0 is a function in the context diagram A-0 and herewe represent all the inputs, controls, outputs and mechanisms.Then we have the A0 page which is the A0 function be composed into it is level 1functions. So, level 0 diagrams, A0 is the level 0 diagram with first tier functionsspecified. When A0 diagram we specify the first tier functions and they will be referredas A1, A2, A3 and so on, as the number of functions. So, A-0 or the context diagramcontains the function A0 and A0 diagram or the level 0 diagram contains the functionslevel 1 functions A1, A2, A3 etcetera and so on, it goes.The A1 diagram A1, A2 etcetera are the level 1 diagrams with second tier functionsspecified and A11, A12, A21, A22 etcetera are the level 2 diagram with third tierfunctions and so on and it is go on till we reach the final decomposition stage.So, here as mentioned there are context diagram and then A0, A1, A2, A11, A12 andA21, A22 diagrams, level 1, level 0, level 1 and level 2 diagrams.(Refer Slide Time: 40:50)
So, this is actually shown over here. So, this is the diagram this is known as A0. So, thisis the A0 diagram here and then you have the inputs, outputs and control diagrams. So,here you can see the inputs I1, I2 are the inputs to this top level function or the A0function and then C1, C2, C3 are the controlled inputs and then O1, O2, O3 are theoutputs and then you have here the mechanism through which this transformation takesplace. So, that is the top level context diagram A-0, it is a context diagram and the samediagram can be expanded to the next level which is known as the A0 diagram where youwill show the A1 functioning, A2 functioning and A3 functioning.So, this is shown as separately in more detail with explanation. So, you can see here thisis the first level A0 diagram with I1, I2 as the input, C1, C2, C3 as the controlled inputs,O1, O2, O3 as the outputs and control inputs, sorry, this is the control input and this theoutput and this is the mechanism through which it is converting the I1, I2 into O1, O2,O3 as determined by C1, C2 and C3. So, that is the top level function A0 and then thisA0 function is divided into it is sub functions in the A0 diagram or the level 1 diagram.So, here we show the input I1 and C1, which is acting on the function A1 which actuallyconverts, transforms input 1 to output 1 and output 2.1 as determined by C1 and C2,using M1.1. So, this is the M1.1 mechanism and then here you can see the transform thisis another function, this is A1 function, this is A2 function and this is A3 function. So, themain A0 function is divided into or decomposed into 3 functions A1, A2 and A3 and allthe inputs and the controls are shown separately for this one. So, here you can see I1 isan input to A1, I2 is an input to A3, but I1 is going again to A2 also.Similarly, C1 is a controlled input to A1, C2 is a controlled input to A2 and C3 is acontrolled input to A3 and the outputs are O1 is coming from A1, O2 is coming from A2and O3 is coming from A3. So, this is just a typical representation, it is not necessary thatO1 should come from A1 or O2 should come from A2. It actually depends on thefunction, depending on the function the output may come from function or the outputmay come from different functions, but the beauty of this representation is that we canactually show all the inputs and the controls, as well as the outputs separately and theirinteraction between the sub functions.As you can see here the output from A1 which is the output O1 this is actually going toA2 as a control input to this and then this is going to this as a another input also O2.1 is
going to as an input. So, similarly the output is O2.2, which is going from here and thatis again going back to that is coming from A1 also. So, like this you can have differentinteractions between these controls and outputs within the function. So, this can berepresented using the IDEF0 diagram.(Refer Slide Time: 08:33)
So, take an example to show the functional decomposition you will see IDEF0 diagram.So, here we take the example of elevator which we discussed earlier also. Now, you arefamiliar with the elevator system and it is requirements. So, we will actually take thissame case study and then use that one for explaining the functional decomposition usingIDEF0 diagram.As you can see, this is the context diagram or you can this A0 is the top level functionwhich is provide elevator services and all others are inputs and control signals andoutputs and you have the mechanism as the elevator system as the mechanical systemwhich actually provides this service.
(Refer Slide Time: 09:14)
So, there are different inputs. You can show it in a better way in this diagram. So, youcan see here this is the context diagram.(Refer Slide Time: 09:19)
So, these are the inputs; the passenger characteristics are inputs, electric power andemergency communication response are the input, the service tests and repairs are theinputs here.
(Refer Slide Time: 09:31)
And here you have other inputs like the request for emergency support and emergencymessage, request for floor and exit support, request for elevator service and entrysupports.(Refer Slide Time: 09:43)
Similarly, the structural support, alarm signals and building environment and modifiedelevator configuration and expected usage patterns. This is basically from the patternsthat also will be given as an input to the system. So, these are all the inputs going to thesystem and the output coming from the system are the passenger environment, what is
the status of passengers in this particular scenario, then the acknowledgement thatrequest was received and status information; basically, as an output the present status ofthe request are provided by the customer, so, what is the status and an acknowledgementand diagnostic and status messages whether any problems are there or any troubleshooting is to be done or servicing to be done, that kind of diagnostic messages given asoutput and emergency communication from the elevator to the external system to thepolice or the fire service or to the building administrator. So, that will be given asemergency communication then elevator entry exit opportunity provided by the system.(Refer Slide Time: 10:46)
And them emergency support and emergency situations like supporting the passengers inthe case of emergency by providing; opening the doors or going to the next level ofwherever the access is available. So, these are the outputs coming from the system. So,as we can see here elevator system is the main mechanical system which actuallyprovides elevator services. So, here the elevator system is converting all these inputs tooutputs and giving it as outputs.You must have noticed a red line over here and a dotted line, so this is basically to foranother purpose. This diagram can be used for tracing any input and finding out whatactually happens to this input or what kind of conversion taking place these inputs or wewill see that later, once we complete the discussion about the IDEF0 diagram and one ofthe application for IDEF0 diagram I will explain this at a later stage.
So, this is the context diagram which provided the overall main function of the elevatorsystem as well as the inputs and outputs.So, the next task is basically to divide this function into sub function. So, the contextdiagram will provide you the top level function A0 and the A0 diagram or the level onediagram will provide you the sub functions A1, A2, A3 and see how to show that usingIDEF0 diagram.(Refer Slide Time: 12:09)
So, this looks difficult to read, but I will show you another diagram where other detailsare given. So, overall picture is shown here. So, you can see that this is the acceptpassenger request and provide feedback as one function, control elevator cars as anotherfunction, move passenger between floors as another function and enable effectivemaintenance servicing as another function.So, in A0 diagram that is the level 1 diagram we divide the, decompose the top levelfunction or A0 function into A1, A2, A3 and A4. Similarly, with identify the inputs andoutputs, inputs to the A1 function and the output going from the A1 function and whetherthese outputs are used by the A2 function or they are going directly to outside the system.So, all those can be represented using this diagram. So, here we write down the signals,the input signals as well as the output signals and is represented if there is any input,output coming from the system represented separately with the descriptions.
(Refer Slide Time: 13:22)
So, to go into the details as you can see here, this is basically the decomposition A1, A2,A3, A4. Basically, we are taking the A0 function and dividing them to A1, A2, A3 andA4 as shown here.(Refer Slide Time: 13:35)
As you can see here, so this is the first one A1 function, accept passenger request andprovide feedback, that is the first function of decomposition A0 and the inputs arerequest for emergency support and emergency message, request for floor and exitsupport and request for elevator service and entry support and these are the main inputs
coming from the passengers. And other inputs are electric power and emergencycommunication response that will be coming to this function. So, these are the inputscoming to this and from here we will be getting output, many outputs from here andsome of the outputs will be going to function A2.(Refer Slide Time: 14:15)
As you can see here, one of the output from this function is digitized passenger request.So, here the passenger request is digitized and send to the next function called controlelevator cars. So, this is the function A2 and from here you can see there are other inputsalso coming like modified elevator configuration and expected usage pattern. Wediscussed about these inputs, the context diagram. So, that input is coming to controlelevator cars.
(Refer Slide Time: 14:45)
And other inputs are coming from other sources, from other functions also inputs will becoming to this function and if you process all this inputs and give the output likeconfiguration controls and assignments of elevator cars. That is one of the importantoutputs from this function assignment for elevator car. So, which car should go to whichfloor and where it is always information should be processed and the assignments will besend to this one.And that will go to the third function called move passengers between floors. So, that isthe A3 function. So, here the one input is basically the elevator car assignment, the otherone is the building and environment depending on the structural support alarm signalsand other inputs will be provided and that input also will be processed along with theconfiguration control inputs will be processed here, plus you will be getting other inputsfrom here like a electric power emergency communication and passenger characteristics.So, all these will be processed and this function called the move passengers betweenfloors.
(Refer Slide Time: 15:47)
And then we will be having the passenger environment as the output and elevator entryexit opportunity is output from the A3 level function. So, this is A3 level function.(Refer Slide Time: 16:00)
And then the last function is basically to enable effective maintenance of and servicing ofthe system. So, in order to provide the elevator services we need to have the effectivemaintenance servicing also. So, the inputs from various sources will be coming about thestatus of all the functions and other controls will be coming here and the sensedmalfunctions also will be coming as input and based on this function will process the
diagnostic and status messages and that will be send to as an output from here and thisqueries also will be used by other functions in order to execute their functions. So, likethis you can see the main function A0 is divided into A1 function, A2 function, A3 andA4 function, 4 sub functions and the inputs and controls to these functions are shownclearly in the A0 diagram or the level 1 diagram.So, this first level is basically to with the decomposition of the main function into the toplevel or the top tier level 1 functions and then now this level 1 function each function inthe level 1 need to be decomposed further to it is sub component or the sub functions andthis is done in the level 2 diagram or A1 diagram. In A1 diagram we use our A1, our A2,A3 diagram; basically, A1 diagram will show the decomposition of A1 function, A2diagram will show the decomposition of A2 function and A3 will show thedecomposition of A3 functions. So, this is shown here.(Refer Slide Time: 17:30)
So, this is the A11 function, 11 is missing here. This is basically A11 function, this is A12function and this is A13 function. So, in order to provide service to the waitingpassengers, there are 3 functions you need to be there; one is that support waitingpassengers, support riding passengers and support passengers in emergency. So, this theprovide service to the passengers that is the A1 function is divided in to 3 sub functionslike support waiting passengers, support riding passengers and support emergencypassengers in emergency.
Then we will see how these you can see this is the diagram A1 diagram, which is acceptpassengers requests and provide feedback which is the main function and that is dividedin to 3 functions over here. We will see the details of the input and output for this.(Refer Slide Time: 18:22)
So, as you can see here this the A11 function. A11 function is the support waitingpassengers. So, you can see here the inputs are request for elevator service and entrysupport and the elevator position and direction, these are the inputs and of course, thediagnostic queries coming from the maintenance function is also coming here. So, basedon these this will provide the information to waiting passengers.
(Refer Slide Time: 18:53)
Basically, the waiting passengers need to know, where the elevator is and where it ismoving, what is the status of the elevator? Whether it is in a working condition or it is inthe service mode or it is under the breakdown or it is going to serve the passengers. So,that information need to be processed here and given as an output to the passengers.(Refer Slide Time: 19:15)
So, you can see here the output will be this is the output acknowledgement that requestwas received and status information. This will be given as an output from this particularfunction. So, acknowledgment and status for waiting passengers as the output from the
function A11 which is support waiting passengers. So, similarly we need to have supportfor the riding passengers also. So, in case of there is any malfunction you can take that isalso an output from here. The sensed malfunction will be going to the service andmaintenance function or it is going as an output from here and it will go to sensedmalfunction as a output from these particular block that is from the A1 block and it willgo to the A4 function which we discussed in the previous slide.(Refer Slide Time: 20:02)
So, next one is support riding passengers. So, riding passengers the information arebasically the inputs are elevator service and entry support input and floor and exitsupport and digitized request from waiting passengers. So, that is the waiting as well asyeah waiting passengers also will be also going as a input to the elevator. Apart fromsupporting the riding passengers it has to take care of the input request coming from thewaiting passengers also. So, support riding passengers it is also is a input.And other inputs are like elevator position and direction and diagnostic queries are theinputs. So, it will process these inputs and then provide the output like digitized requestfrom riding passengers. So, the riding passengers will be giving some commands orgiving input and based on the little process the requests and give the digitized requestsand give to the control as output to the control elevator car function.
(Refer Slide Time: 20:55)
And similarly, acknowledgement and status for riding passengers or riding passengersalso will get some acknowledgement and a present status of the elevator or whether therequest has been accepted or it has been received. So, that information also will providedby this particular function.(Refer Slide Time: 21:19)
The third one is support passengers in emergency. So, you can see this is first wassupport to waiting passengers and next one is support riding passengers and the third oneis support passengers in emergency. And here also the input basically the input will be
from the passengers riding passengers or the waiting passengers both will be giving ainput and the emergency support and emergency message will be the input. You have tosend the message and that input will be there and of course, malfunctioning messagesalso will be coming here.(Refer Slide Time: 21:49)
Based on this function will generate necessary control signals, emergencycommunication signals and emergency support and the information will be passed toother functions also.So, like this these are the input outputs coming from these functions. As you can seethere is lot of interaction between these functions within the system.
(Refer Slide Time: 22:07)
So, the input from one function will be, output from one function will be an input toanother function and similarly the output will be can be one function can be input to aprevious function also. So, you can divide the main A1 function into A11, A12 and A13in this diagram. So, this diagram is basically, the A1 diagram where the A1, A2, A11,A12 and A13 functions are decomposed and their interactions are clearly as shown. So,that is the A1 diagram.(Refer Slide Time: 22:44)
Similarly, we can have A2 diagram also. So, in this A2 diagram we divide the A2function that is from the A1 or the level 1 diagram you take the A2 function which is thecontrol elevator cars and divide this in to sub functions A21, A22, A23 and A24. As youcan see here this is the A21 function which is monitor location of all cars. Basically, inorder to control the elevator cars we need to monitor the location of all cars, you need tomonitor and location and direction of all priority waiting passengers and we need tomonitor the location and direction of all non priority waiting passengers and all allocatecars to passenger pick up stops. These are the sub functions to be provided in thisfunction, that is, control elevator cars need to have these functions in order to satisfy therequirement of controlling elevator cars.So, the first function is monitor location of all cars. Let us see the input and output of thisfunction as you can see here.(Refer Slide Time: 23:44)
This is the monitor location of the all cars. So, the diagnostic queries will be there andthe inputs will be coming from the passenger, output from the location.
(Refer Slide Time: 23:54)
That is this is the one of the input that is allocated cars to passenger that information willbe there and that information will be going to this one to monitor the location of the car.So, based on these information it will continuously monitor location of all cars and givethis as an output to the other function of allocating the functions. So, and any sensedmalfunction also will be given as an output.(Refer Slide Time: 24:22)
So, there will be an output which actually gives the position of the elevator cars and amalfunctioning of these cars, if any. And other one is monitor location and direction of
all priority waiting passengers. So, priority waiting passengers will be having a separateinput processing. So, that data will be coming digitized passenger request will be comingover here and the location of cars also will be coming here. And based on this it willactually locate what the cars are and that information will be send to the next levelfunction or to process the input for the allocating the cars.(Refer Slide Time: 24:57)
So, this output from here the monitor location and direction of all priority waitingpassengers, the output will be send to the allocate cars to passenger pickup and stops. So,list of all floors with waiting priority passengers and desired direction will be sent fromhere to this function, that is, to allocation of cars. Similarly, the location and direction ofall non priority waiting passengers also will be monitored again using the input from thepassengers and these inputs will be used to find out where the passengers, whether a nonpriority passengers are there, what are their request and that is information also will besend to the allocate cars to passenger pick up stops.So, this is the main function which actually will allocate the cars, but basically it requiresthe information from these other functions in order to process the information, about thepriority passengers and other passengers and based on these inputs, it will allocate thecars to different floors and for different services by this assignment of elevator cars.
(Refer Slide Time: 25:57)
So, we can see here the control elevator cars is a function in order to satisfy therequirement in has to provide the sub functions like monitory location of all cars thenmonitor location and direction of all priority passengers as well as the monitor locationof non priority passengers and this information will be used by the function to allocatecars to different floors. So, that is the decomposition of A2 function in to A21, A22, A23and A24.(Refer Slide Time: 26:32)
Similarly, we can divide this A3 function which is move passengers between floors, thatis, the function A3, again in level 0 diagram we identified these functions A1, A2 A3 andA4. So, based on this we can actually decompose this A3 function into it is sub functions.So, move passengers between floors, one sub function is; receive and dischargepassengers. So, that is one function we need to receive and discharge passengers. Weneed to travel to next stop, so the elevator has to travel to the next stop and providecomfortable atmosphere within the elevator.So, these 3 functions need to be satisfied in order to satisfy the function move passengersbetween floors. Here, again you can see receive and discharge passengers you can see theinputs are configuration controls and other information coming from the travel stopmessages coming from the other elevator cars and then the electric power and otherinputs are also here. Similarly, it will get the input from other location like elevator cardoor status, cars component are the mechanisms which actually use this mechanism toprovide the receive and discharge passengers.
So, these are the mechanisms through which the this function will be executed, that is,elevator car doors, elevator car component as the mechanism and that will provide theopening and closing of the doors to receive and discharge passengers and the output willbe the sensed discharge malfunction, in case there is any problem with the doors thenthat will be sensed here and will be send to the maintenance function. And the messagewill be send to the next one, that is, travelled to next stop that is if the function to receiveand discharge passengers has been accepted or it is functioning properly then thatmessage will be send to the next function, basically, it will go to the next floor. If thepassengers have been accepted or gone into the car safely or they have been gone out ofthe car safely then the that message will be send to the elevator when based on thatinformation elevator will be moved to the next floor to accept passengers or to dischargepassengers.That is the next level function travel to next and provide comfortable atmosphere for thepassenger. So, that I get, as a function you need to provide good atmosphere within thecar, that again is a function. So, there will be many systems inside to provide the comfortto the passenger like the fan or air conditioning or other emergency services. So, all thoseservices will be monitored and in case of any malfunction that will be send thatinformation will be processed and send to the maintenance function. So, that passenger
will be always getting a good comfortable atmosphere within the car. So, in order tomove passengers between floors we need to provide these functions within the elevator.