Calculating End-to-End Series and Parallel Solution-System Availability.

Slides:

Advertisements

Similar presentations

Solutions to Text book HW

Advertisements

DC circuits and Kirchhoff’s rules Direct current (dc) circuits are those where the direction of the current is constant Circuits are in general not as.

Discuss the keywords in question Has the same gradient as…

Physics 1161: Lecture 10 Kirchhoff’s Laws. Kirchhoff’s Rules Kirchhoff’s Junction Rule: – Current going in equals current coming out. Kirchhoff’s Loop.

Fundamentals of Circuits: Direct Current (DC)

DC Circuits Series and parallel rules for resistors Kirchhoff’s circuit rules.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Conditional probability Independent events Bayes rule Bernoulli trials (Sec )

Using a Centered Moving Average to Extract the Seasonal Component of a Time Series If we are forecasting with say, quarterly time series data, a 4-period.

ENM 207 Lecture 7. Example: There are three columns entitled “Art” (A),“Books” (B) and “Cinema” (C) in a new magazine. Reading habits of a randomly selected.

Systematic Circuit Analysis Nodal Analysis Chapter 4 Section 1.

7/2/20151 T-Norah Ali Al-moneef king saud university.

Capacitance (II) Capacitors in circuits Electrostatic potential energy.

Parallel Resistors Checkpoint

Electric current and direct-current circuits A flow of electric charge is called an electric current.

1) Connect the Battery Which is the correct way to light the lightbulb with the battery? 4) all are correct 5) none are correct 1) 2) 3)

Combined Series and Parallel Circuits Objectives: 1. Calculate the equivalent resistance, current, and voltage of series and parallel circuits. 2. Calculate.

Solving and Graphing Inequalities on a Number Line

Chapter 3 – Linear Systems

ConcepTest 4.1aSeries Resistors I 9 V Assume that the voltage of the battery is 9 V and that the three resistors are identical. What is the potential difference.

Geometric Properties of Linear Functions Lesson 1.5.

Table of Contents The goal in solving a linear system of equations is to find the values of the variables that satisfy all of the equations in the system.

ECE 201 Circuit Theory 11 Source Transformation to Solve a Circuit Find the power associated with the 6 V source. State whether the 6 V source is absorbing.

Kirchhoff’s Laws SPH4UW. Last Time Resistors in series: Resistors in parallel: Current thru is same; Voltage drop across is IR i Voltage drop across is.

Example We can also evaluate a definite integral by interpretation of definite integral. Ex. Find by interpretation of definite integral. Sol. By the interpretation.

Ohm’s Law “Current (I) is proportional to Voltage (V) and inversely proportional to Resistance (R)”

X = 11 X 2 = 9 X = 3 Check: X = 3 x 3 +2 = 11 We can solve this equation by:

DC/AC Fundamentals: A Systems Approach

1 ENGG 1015 Tutorial Circuit Analysis 5 Nov Learning Objectives  Analysis circuits through circuit laws (Ohm’s Law, KCL and KVL) News  HW1 deadline (5.

Copyright © Cengage Learning. All rights reserved. CHAPTER 9 COUNTING AND PROBABILITY.

Algebra I CAHSEE Review. Slope-Intercept Form  Graphs 1. Which of the following graphs represents the equation ? A.B. C.D.

Fall 2008 Physics 121 Practice Problem Solutions 08A: DC Circuits Contents: 121P08 - 4P, 5P, 9P, 10P, 13P, 14P, 15P, 21P, 23P, 26P, 31P, 33P, Kirchoff’s.

RESISTANCE OF A SYSTEM OF RESISTORS Resistance can be joined to each other by two ways: Electricity Combination of Resistors 1. Series combination 2. Parallel.

Practice 1.) Solve for y : 4x + 2y = -8 2.) Solve for y: 3x – 5y = 10 3.) Graph the equation: 3x – 2y = 5 x y O

1 Component reliability Jørn Vatn. 2 The state of a component is either “up” or “down” T 1, T 2 and T 3 are ”Uptimes” D 1 and D 2 are “Downtimes”

Chapter 6.  Use the law of sines to solve triangles.

1 3. System reliability Objectives Learn the definitions of a component and a system from a reliability perspective Be able to calculate reliability of.

1 Electronics Parallel Resistive Circuits Part 1 Copyright © Texas Education Agency, All rights reserved.

Circuits. Parallel Resistors Checkpoint Two resistors of very different value are connected in parallel. Will the resistance of the pair be closer to.

Lecture 3. Combinational Logic 1 Prof. Taeweon Suh Computer Science Education Korea University 2010 R&E Computer System Education & Research.

Simple Trig Identities

MATHPOWER TM 12, WESTERN EDITION Chapter 5 Trigonometric Equations.

Series and Parallel.  a single resistance that can replace all the resistances in an electrical circuit while maintaining the same current when connected.

Resistors in Series and Parallel and Potential Dividers Resistors in Series and Parallel Potential Dividers.

a b Center at( h,k ) An ellipse with major axis parallel to x -axis c Definition.

CHARACTERIZATIONS OF INVERTIBLE MATRICES

EEE 205 WS 2012 Part 4: Series & Parallel 118 R 1 R 2 R 3 Elements in series are joined at a common node at which no other elements are attached. The same.

DC Circuits Series and parallel rules for resistors Kirchhoff’s circuit rules.

Math II UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: How do you recognize and write.

1.4 Properties of Real Numbers ( )

APPLICATIONS OF INTEGRATION AREA BETWEEN 2 CURVES.

#21. Find the following quantities R T = I T =V 30  = I 50  

Solving multi step equations. 12X + 3 = 4X X 12X + 3 = 3X X 9X + 3 = X = X =

Chapter 6 Principles of Electric Circuits, Conventional Flow, 9 th ed. Floyd © 2010 Pearson Higher Education, Upper Saddle River, NJ All Rights.

EXAMPLE 1 Solve a triangle for the AAS or ASA case Solve ABC with C = 107°, B = 25°, and b = 15. SOLUTION First find the angle: A = 180° – 107° – 25° =

ConcepTest 19.1aSeries Resistors I 9 V Assume that the voltage of the battery is 9 V and that the three resistors are identical. What is the potential.

Hoda Roodaki Boolean Algebra Hoda Roodaki

MESH ANALYSIS. EXERCISES

Conditional probability

Analyzing Circuits Kirchoff’s Rules.

8.7Systems of Linear Equations – Part 1

Piecewise-Defined Functions

The Law of SINES.

Kirchhoff’s Rules Limits of Progressive Simplification

Who Wants To Be A Millionaire?

LESSON 7: RELIABILITY Outline System with series components

73 – Differential Equations and Natural Logarithms No Calculator

Proving Trigonometric Identities

COMPASS Practice Test 16.

Presentation transcript:

Calculating End-to-End Series and Parallel Solution-System Availability

page 2 End-to-End Solution Availability End-to-End Solution Availability is calculated by modeling the solution as an interconnection of components in SERIES and in PARALLEL. Use these rules to decide if components should be modeled in SERIES or in PARALLEL: – If the un-availability of one component leads to the combination of components becoming un-available, the components are operating in SERIES. – If the un-availability of one component leads to the other components taking over the operations of the un-available component, the components are operating in PARALLEL.

page 3 Series Availability

page 4 Calculating Series Availability Components X, Y and Z are considered to be operating in SERIES if the un-availability of any one results in the un- availability of the combination. The combined system is available only if components X, Y, and Z are all available. From this it follows that the combined availability is a product of the availability of the components: – (combined availability) = (X availability) x (Y availability) x (Z availability) The implication of the above equation is that the combined availability of the components in series is always lower than the availability of every one of its individual components.

page 5 Series Availability Example Example – (X availability) = 75% – (Y availability) = 80% – (Z availability) = 85% – (combined availability) = (X availability) x (Y availability) x (Z availability) – (combined availability) = 0.75 x 0.80 x 0.85 – (combined availability) = 0.51 – (combined availability) = 51%

page 6 Series Un-Availability Example Example (2 components) – (X availability) = a (X un-availability) = 1-a – (Y availability) = b (Y un-availability) = 1-b – (combined availability) = ab (combined un-availability) = 1-ab – (combined un-availability) = (1-a)+(1-b) – ((1-a)(1-b)) Proof –1-ab = (1-a)+(1-b) – ((1-a)(1-b)) – = 2-a-b – (1-a-b+ab) – = 2-a-b – 1+a+b-ab – = 1-ab

page 7 Series Un-Availability Example Example (3 components) – (X availability) = a (X un-availability) = 1-a – (Y availability) = b (Y un-availability) = 1-b – (Z availability) = c (Z un-availability) = 1-c – (combined availability) = abc (combined un-availability) = 1-abc – (combined un-availability) = (1-a)+(1-b)+(1-c) – ((1-a)(1-b)+(1-a)(1-c)+(1-b)(1-c)+((1-a)(1-b)(1-c))) Proof –1-abc = (1-a)+(1-b)+(1-c) – ((1-a)(1-b)+(1-a)(1-c)+(1-b)(1-c)+((1-a)(1-b)(1-c)))

page 8 Series Availability Calculator Try it ! – Double-click on the table and change the X, Y, or Z availability and see the new combined availability. Note: Entering an availability value of 100% is equivalent to saying that that component does not exist. So if there are only 2 components, enter 100% for one of the components to simulate it not being there.

page 9 Parallel Availability

page 10 Calculating Parallel Availability Components X, Y, and Z are considered to be operating in PARALLEL if the combination is considered unavailable only when all the components are unavailable. The combined system is available if any component is available. From this it follows that the combined availability is 1 - (the probability that all components are unavailable at the same time) : – (combined availability) = 1- ( (1 - X availability) x (1 - Y availability) x (1 - Z availability) ) The implication of the above equation is that the combined availability of components in parallel is always higher than the availability of every one of its individual components. Thus, parallelism is a powerful mechanism for making a highly reliable system from low reliability components.

page 11 Parallel Availability Example Example – (X availability) = 75% – (Y availability) = 80% – (Z availability) = 85% – (combined availability) = 1- ((1 - X availability) x (1 - Y availability) x (1 - Z availability)) – (combined availability) = 1- ((1 – 0.75) x (1 – 0.80) x (1 – 0.85)) – (combined availability) = 1- (0.25 x 0.20 x 0.15) – (combined availability) = 1- (0.0075) – (combined availability) = – (combined availability) = 99.25%

page 12 Parallel Availability Calculator Try it ! – Double-click on the table and change the X, Y, or Z availability and see the new combined availability. Note: Entering an availability value of 0% is equivalent to saying that that component does not exist. So if there are only 2 components, enter 0% for one of the components to simulate it not being there.

page 13 Parallel Availability Calculator II If all the parallel components are identical (have the same availability value) use this calculator. Try it ! – Double-click on the table and change the components’ availability and the number of identical components to see the new combined availability.