Causal & Frequency Analysis

Transcription

1 Causal & Frequency Analysis Arshad Ahmad

2 Fishbone Diagram 2

3 The Cause and Effect (CE) Diagram (Ishikawa Fishbone) Created in 1943 by Professor Kaoru Ishikawa of Tokyo University Used to investigate a problem, exploring, identifying, and displaying the possible causes. Main Objective To identify the causes of a defined critical event in a system. To classify the causes into groups. To acquire and structure the relevant knowledge and experience of the study team. The cause and effect diagram analysis is done by a study team as a brainstorming session.

4 Fishbone Diagram Cause 4 Cause 1 EFFECT Cause 3 Cause 2

5 Reliability Block Diagram 5

6 Reliability Block Diagram A reliability block diagram shows the logical connections of functioning items that are needed to fulfill a specified system function. Each function is represented as a functional block and is drawn as a square The RBD Systems can be connected in series or parallel configuration 6

7 Reliability of Series Systems R s R1 R2... R n = = n i= 1 R s R i R = s For constant per-unit failure rates R i (t)= e λ i t!!!!!!!!!!!!!!! R! system = e λ i t!!!!!!!!!!!r system = e Λt!!!!!!!!!!!!!!Λ = λ i

8 R s = 1 Reliability of Parallel Systems = 1 F s = 1 F F F [( 1 R ) ( 1 R )...( 1 R )] n n 0.99 n R s = 1 1 R i ( ) i= R s = EML

9 Example Find the system reliability of the following combinational system with both serial and parallel arrangements. Assume all sub-systems have a reliability of R s = = = ( R )( R4+ )( R [ 1 (1 R1 )(1 R2 )(1 R3) ][ 1 (1 R4 )(1 R5 )] [ 1 (0.1)(0.1)(0.1)][ 1 (0.1)(0.1)][0.9] = (0.999)(0.99)(0.9) = ) R 6

10 For constant per-unit failure rates (example: two systems in parallel) R R system system = 1 = e λ ( λ t )( t ) 1 λ2 1 e 1 e 1 t + e λ 2 t e ( λ +λ )t 1 2 System does not have constant per-unit failure rate even if components do System reliability for parallel systems is always greater than the most reliable component Most systems are not designed in parallel (redundancy) due to cost considerations (unless needed due to safety and life-protection considerations) Series Transmission line, Power train Parallel Multiple airplane engines, Two headlights EML

11 Reliability of Large Systems Most systems are neither parallel nor series, but a hybrid combination Calculation of overall system reliability, however, is done following the simple principle shown before Parallel systems are used when extremely high reliability is needed (by use of redundancy) EML

12 Fault Tree Analysis 12

13 Fault Tree Analysis (FTA) FTA is an effect and cause diagram that uses standard symbols developed in the defense industry and is used heavily in safety engineering. FTA is a structured approach for analyzing the root causes of a failure mode not yet fully understood In Fault Tree, undesired system failure mode can be expressed in terms of component failure modes and operator actions. FTA is used to model the failure of a system resulting from multiple components 13

14 Basic Fault Tree Structure TOP EVENT INTERMEDIATE EVENT INTERMEDIATE EVENT BASIC EVENTS BASIC EVENTS In FTA, the system failure mode to be considered is termed the top event and fault tree is developed in branches below this event showing it causes., connected by using logic gate 14

15 Basic Elements of Fault Tree Event Symbol Diamond Undeveloped event. Meaning of Symbols Not analyzed for various reasons Rectangle Event represented by a gate Circle Basic event with sufficient data Triangles AND gate Transfer symbol Output event occurs if all input events occur simultaneously. OR gate Output event occurs if any one of the input events occurs.

16 Understanding the Gates AND gate means, for this upper failure to occur, all of these failures must occur Failure OR gate means that for this upper failure to occur, only one of these failures must occur Failure 16

17 Developing FTA Step 1 Identify Top Level Fault Step 3 Link contributors to top by logic gates Step 2 Brainstorm first level contributors basic event cannot be broken down any further Step 5 Link contributors to upper level by logic gates Step 4 Brainstorm second level contributors Step 6 Repeat / continue for each lower level failure event that is not analyzed for various reasons 17

18 Example: Pump S E F1 C1 C2 E : ELECTRICITY F1,F2 : FEED PIPES M : MANIFOLD P1 F2 P2 C1, C2 : CABLES P1 M R P1,P2 : PUMPS R : REGULATOR S : SUPPLY TANK Acetic acid is pumped automatically from the supply tank to the process. When the regulator is energized, one of the pumps is started and acid passes through the feed pipes; if no acid is detected in the feed pipe the second pump is started. Construct a fault tree with the top event no flow to the process.

19 Failure Modes to Consider Component Symbol Failure Mode Cables C1 + C2 short-circuit Electricity supply E power cut Feed pipes F1 + F2 rupture of pipe Manifold M rupture Pumps P1 + P2 fail to start Regulator R fail to open Supply tank S level too low 19

20 Fault Tree NO FLOW TO PROCESS GENERAL PROBLEMS PROBLEMS WITH PUMPS PUMP P1 PROBLEMS PUMP P2 PROBLEMS Tanks level too low Regulator fails Manifold M fails Power cut Pipe F1 ruptures Pump P1 fails to start Cable C1 short circuits Pipe F2 ruptures Pumps P2 fails to start Cable C2 short circuits 20

21 Class Workshop 21

22 Class Workshop Work in your Group to draw a fault Tree for the following accident scenario 1. Explosion of a Diesel Tank 2. A car hitting the rear bumper of another car on a highway 3. Flash fire at a gas station Draw the fault tree and present to the class 22

23 RBD & Fault Tree 23

24 FT & its equivalent RBD (i) (ii) (iii) 24

25 FT & RBD b d b a c a b d b c

26 Class Workshop Work in your Group to draw a fault Tree for the following accident scenario FAILURE OF SMOKE DETECTOR The indicator light is on yet even with sufficient amounts of smoke directly below the detector vents the alarm does not signal. Draw the fault tree, compute the probability and present to the class 26

27 Class Workshop 1 Functional Block Diagram for Smoke Detector Inputs Presence of smoke Smoke enters through vent Smoke enters ionization chamber Process Detection of smoke Battery powers control box, indicator light, and smoke detector Smoke is ionized and causes increase in voltage Signal sent from smoke detector triggers control box circuit Outputs Alarm signaling Signal/power to siren turns motor Motor causes siren to sound Alarm signals Control Box sends signal/ power to siren 27

28 Class Workshop 2 Block Valve A Control Valve A FUEL SUPPLY FUEL DELIVERED Block Valve B Control Valve B Pump Top Event: No Fuel to Pump When Requested Draw the equivalent Fault Tree Diagram 28

29 END OF LECTURE 29