Reliability Analysis of Ion Thruster Engines-Road to Mars…

45 min readMay 18, 2021

Reliability Analysis of Ion Thruster Engines (VASIMR: NSTAR: DS4G)

Abstract:

With increasing interest in space exploration and commercialization of space technologies for our day-to-day life process, like internet and mobile communication, the need of developing new technologies which more efficient and reliable is increasing rapidly. Efficient in terms of performance and reliable to reduce initial and maintenance cost. To deploy these commercial space systems we are using electric propulsion system from last many years, but the race is now about their reliability for extended life time. A launch of single space mission costs around millions of pounds per Kg of payload, which means there has to be 99.9% reliability from customer’s point of view. To achieve this high level of reliability in our conventional and under development ion thruster engines, concerns have been made on putting more efforts on testing the prototypes engines to achieve maximum reliability.

This research paper will try to analyze the reliability of three major contenders of ion propulsion system, VASIMR, NSTAR, and DS4G, by using techniques such as FMECA and reliability Block Diagram. We will also try to take the first-hand knowledge of the complex subsystems involved in the working of these ion thruster engines in detail. The results thus generated will be studied and then at the end, some techniques that can be deployed to increase system reliability will be considered and validated.

1 INTRODUCTION

1.1 Motivation

We have been using chemical propulsion system i.e. either solid or liquid, as primary propulsion for spacecraft’s since last many decades. Chemical propulsion systems are characterized by large vehicle acceleration, α, large power to mass ratio and small exhaust velocity (Ve< 5000 m/s). These are said to be energy limited and for this reason only we use multistage rockets. However, Electric propulsion systems are characterized by small vehicle acceleration, α, small power to mass ratio, but large exhaust velocity (Ve>5000 m/s) of almost 30Km/s which of great interest for interplanetary missions. We will discuss the concepts of electric propulsion system and its history of development in more detail further in chapter 2. Now, because of its performance characteristics (e.g. exhaust velocity and efficiency) which are ideal for commercial applications in earth orbit, Ion thruster engines are used primarily for station keeping and orbit raising of large commercial space vehicles.

The future of space exploration will be characterized by the missions that have more ambitious goals, and in order to achieve these goals it is often more important to explore new directions. Our growth in space explorations, need of accomplishing a mission more efficiently and cost effectively, with the missions like man landing on Mars standing ahead, have focused the interest of scientists and technologist to develop this technology further so as to be used as primary propulsion system of spacecraft for interplanetary missions, to make true the science fiction classic 2001 of Arthur C. Clarke’s 1968: A Space Odyssey, wherein a team of American astronauts are sent to a nine month mission to Jupiter using a giant spacecraft named ‘discovery 1’ which needs a ∆V of 50 Km/s to reach Jupiter in nine months. Clarke, trained as an engineer, In his book lost words of 2001 stated that he conceived the giant spacecraft as being nuclear powered with some form of electric propulsion[3].

Many space agencies and scientists are working together for the development this technology to be used as primary propulsion for spacecraft. Ad Astra rocket company, run by Dr. Franklin R. Chang Diaz, is working extensively on developing Variable Specific Impulse Magnetoplasma Rocket (VASIMR) and its associated technology, NASA has already used this technology in NASA Solar Technology Application Readiness (NSTAR) program, in his Deep Space 1 mission, which visited the asteroid braille in July 1999 and comet borelly in September 2001 [1], and ESA is also working on the development and testing of Dual Stage Gridded Ion Thruster engine (DS4G).

It is very much clear about the need of developing a primary electric propulsion system for spacecraft that can be deployed for deep space missions, lunar cargo transport, in space refueling, in space resource recovery and many more. But the thing that carries such a technology to next stage is an ability to make it reliable from systems point of view to fulfill a mission. The main motivation of this paper is to investigate the reliability of ion thruster engine; in particular as other subsystems that are used in spacecraft are available from heritage, however some aspects of these subsystems, associated with thruster engine like power, thermal, material selection, fuel, etc. will also be covered in this research paper to investigate the reliability of spacecraft from systems point of view.

1.2 Objectives

The main objective of this research paper is to draw a conclusion, between the three electrically propelled engines, VASIMR, NSTAR and DS4G, about which one is more reliable as well as efficient. We will also try to figure out the criticality of the failures involved in them while fulfilling their missions on the basis of the published test data. But one major concern while fulfilling this reliability analysis is the availability of the test data, which is published by the manufacturers of these engines after testing their prototype systems and subsystems for over years. Because most of these thruster engines are under development or testing, the manufacturers does not publish their test results publicly due to their concerns about market impact or the customer. Also, to develop these test results in laboratory by developing the prototype thruster engines is beyond the reach of this research paper. For these reasons we will assume some approximate failure rate, test time and other data needed in our research paper, and which will be standardized data throughout this project, to make comparisons between the reliability of these three ion thruster engines.

Reliability analysis of these three propulsion systems will be done by using the techniques in literature, such as Failure Mode Effects and Criticality Analysis (FMECA), Monte-carlo simulation, and reliability block diagram methods on a system level approach. Now, one question that arises in our mind is what do we understand by the term System level approach? The term System means an integrated form of subsystems or equipment’s to be précised, in to a consistent whole to accomplish the desired task for which it is designed. In system level approach the whole system to be analyzed is divided in to manageable functional elements or subsystems and then each subsystem is studied for its critical failures, their effects, failure rate, severity ranking, and MTTF (Mean Time to Failure). We will cover this topic in more detail further in chapter 3.

The present thesis is divided in to four major parts the first part is introduction which tells about history of development of ion propulsion system. The second part concentrates on the various types of electric propulsion systems which are available in our literature and are used so far or under development. The third part of report gives us the detailed description of the theory involved in the reliability analysis and various techniques which are used for reliability analysis of any system in general. The fourth and main part of report is involved in the application of theory and techniques studied in chapter 3. Then chapter 5 compares the results obtained by doing reliability analysis of various ion engines.

2 Electric propulsion system

2.1 Development of electric propulsion system

Before understanding the theory behind electric propulsion system, we will first try to investigate its significance over chemical propulsion system. A chemical rocket (solid or liquid) produces thrust by the combustion of fuel and oxidant at a high pressure and temperature. This propellant mixture is accelerated through a convergent-divergent nozzle which allows a supersonic (M > 1) exit flow to be produced. The thrust produced is given by the equation: [2]

The first term in the equation (1) signifies the thrust produced by the change in momentum and the second term due to change in pressure.

Now, a space mission is also characterized by a performance parameter known as the velocity, achieved by a vehicle to reach its destination i.e. ∆V. for e.g. an object must achieve certain velocity to reach earth orbit similarly, a vehicle must achieve ∆V > 11000 m/s to escape from the gravitational force of earth and enter interplanetary space. Today large rockets are used to propel probes to these high speeds. However, as the desired speed of the probe increases, the size of the probe should decrease. To understand clearly, the reason behind this, we will consider the Tsiolkovsky rocket equation:-[2]

This equation relates the total velocity achieved by the vehicle to the initial mass of the vehicle, when the vehicle is full of propellant, final mass of the vehicle, when the fuel is completely burnt, and the exhaust velocity. The main conclusion that can be drawn from this relation are, the rocket can travel faster than its exhaust velocity if the mass ratio (Mf/Mi)> 2.718, because the typical values of mass ratios are = 8 which implies that a rockets initial mass comprises of 87.5% of fuel. [2]

If we plot a graph between the mass ratios and exhaust velocity (4.5 Km/s for chemical and 41 Km/s for electric) through a ∆V of up to 50 Km/s, we will see that the mass ratio decreases exponentially as ∆V increases. Moreover, from the graph below it is evident that to achieve ∆V of 20 Km/s with chemical propellant, 99 percent of the initial mass of the vehicle must be propellant. And for 50 Km/s ∆V, the ratio of the delivered mass (including payload and structural mass) to the initial mass, must be <1/150,000 for the vehicle using chemical propellant [3]. This implies that for every Kg of mass to be carried away, an equivalent of 150,000 Kg of airliner will be needed. Such a mission is clearly impractical if not possible. Thus we can conclude that a huge amount of fuel can be saved if we switch from chemical rocket to electrical one, which in turn implies the reduction in cost which is of our great concern.

Figure 1: Mass ratio vs. ∆V for propulsion exhaust velocities of 4.5 and 41 Km/s. [3]

Unlike chemical rockets the energy required to accelerate the propellant, in electric propulsion is derived from the separate source (solar, nuclear or fuel cell), so constraints on performance of these engines relates to achieving acceptable levels of thrust and energy efficient conversion. However, the thrust produced and mass flow in an electric propulsion system is very low as compared to that of chemical but high values of specific impulse and exhaust velocities can be achieved by them. The main aspect behind the reason that despite of its invention in early 90’s it is still under development to be used as primary propulsion for spaceflights, is its low thrust-to-weight ratio as compared to chemical rockets that have thrust-to-weight ratio of almost unity. An analysis of electric propulsion system leads to a modified version of Tsiolkovsky rocket equation:

The development of ion thruster engine could be attributed to the passage of Professor Goddard notebook written while he was conducting experiments with gas discharge tube in 1906 [3].he noted that the charged particles are accelerated to great velocities by the electric field within the tube, without heating the walls of the tube. However, no material can tolerate the heat required to propel the charged particles but the electric around the tube can do that without being in contact with them and he concluded that this could be the basis of high exhaust velocity propulsion system. He even postulated that rocket will initially use chemical propulsion to reach the earth escape velocity and then use the electric propulsion to propagate further and to decelerate once reached the destination [3].

Other important aspect to be considered while talking about ion thruster engines is propellant. Between 1970 and 1990, United States focused research on electric propulsion propellant with mercury-and later xenon, Teflon-propelled pulsed plasma thrusters (PPTs) and argon-propelled MPD thruster and hall thrusters.[nasa] An important property to be considered while selecting a propellant is its mass-to-charge ratios, which are desirable to minimize the size of ion engine for a given thrust level.

A lot of research on using nuclear power to accelerate these gas ions through the exhaust chamber is being carried throughout from our history, but the largest space nuclear reactor ever build, the soviet Topaz that produces power of around 10 KW and power-to-mass ratio of 10 W/Kg [4]. If we make this dream come true, of using space nuclear reactor, then we would be able to achieve an exhaust velocity of about 100 Km/s by using nuclear electric propulsion or nuclear thermal propulsion, in which nuclear energy will be used to heat liquid hydrogen [L. R. Shepherd and A. V. Cleaver, 1940’s].

2.2 Types of Electric propulsion systems

Electric propulsion can be categorized in to three main groups:

· Electrothermal propulsion system

· Electrostatic propulsion system

· Electrodynamic propulsion system

Electric propulsion must be able to covert the onboard electric power in to directed kinetic power of the exhaust stream to produce a suitable amount of thrust level for reasonable short trip times. The propulsion system should be as light as possible as should not affect the life of the spacecraft in any way. We will now discuss these three techniques of electric propulsion briefly.

2.2.1 Electrothermal propulsion

Electrothermal propulsion utilizes power supplied by the spacecraft to increase the enthalpy of the expellant by resistive heating. Once heated, the propellant is allowed to expand and is converted in to kinetic energy by accelerating it through a nozzle. Practically tungsten element is used to provide resistive heating and the propellant can be hydrogen, nitrogen or ammonia. The equation that shows this process for an ideal nozzle is :

This is the basic principal used in chemical propulsion with the only difference that here electric heating is used instead of combustion of fuel. The above equation can be understood well in the figure below, which shows the propellant entering the nozzle at low velocity (U1), which is also at higher pressure then exhaust pressure, this propellant is heated to high temperature (T1) by electricity, and the gas leaving the nozzle at high velocity (U2), and lower pressure and temperature (P2 and T2) respectively.

Figure 2 : Operating principles of Electrothermal propulsion system. [3]

The trick in creating efficient electrothermal propulsion is to put a lot of energy in to small mass of propellant and then converting this in to kinetic energy by accelerating this heated propellant through divergent convergent nozzle, which possess pressure difference inside the chamber and at exhaust, to produce sufficient amount of thrust. Typical velocities are of the order 10 Km/s with thrust around 0.5 N, a mass flow of (10 raise to power -5 Kg/s) and a specific impulse of around 1000 s [2].

Examples are like Vela satellites of U.S. defense department, Resistojets which are used for station keeping of commercial satellites for some 20 years after 1965 that have specific impulse of 300s (as compared to 200s in chemical propulsion) and uses Hydrazine as propellant. These provide thrust efficiencies of above 50% at a temperature of 2,000° C, input power of about 465–885 and total impulses above 500,000 Ns. Other electrothermal devices are like arcjet. They operate same as resistojets except it uses an electric arc for heating the gas to temperatures of about 3,000°C. they came in to industry in 1983 and were used for about 10 years thereafter for commercial satellites.

2.2.2 Electrostatic propulsion

The electrostatic propulsion system also converts energy from the spacecraft power system in to kinetic energy of beams of ions (ionized molecules). This beam when exits the thruster at a very velocity, propels the spacecraft in opposite direction. As an electric propulsion technology, the ion thruster engine consists of five major components namely, a computer for monitoring system performance and its control system, a power source that can be a solar array, RTG, or nuclear power, a power processing unit (PPU) which converts the power from the power source to desired voltage and current levels of equipment’s used in engine, and at last the thruster itself.

Figure 3: Schematic of Ion thruster engine

Now, we will try to understand architecture of ion thruster engine considering figure 3 (working of typical ion engines will be discussed in more depth in chapter 5). Basically an ion engine consist of an node that could be a positively charged wall of discharge chamber, a cathode which emits electrons or an electron gun, used to ionize the gas propellant or plasma, a source of magnetic field to increase resident time of electrons inside the chamber so as to increase ionization efficiency, an exhaust nozzle that could be surrounded by magnetic field or in some cases two separate grids with holes in it, which are at different potential voltage are used to accelerate ions from exhaust at a high speed to produce a desired amount of thrust, and at last a neutralizer cathode. Neutralizer cathode is used because the exhaust stream of ions from the thruster must be neutralized to avoid build up of charge, opposite to that being carried away from the spacecraft in the beam which could lead to thruster stalling.

As discussed above, it is always advantageous to use expellant with large mass-to-charge ratio. For this reasons mercury was initially used but is toxic. However, other possible expellant like argon or xenon are widely used in ion thruster engines because of their advantages discussed in chapter 1. Typical velocities are of the order 30 Km/s with thrust around 0.1 N, a mass flow of

Kg/s and a specific impulse of around 3000 s. Examples are deep space mission 1 by NASA in 1999 that used NSTAR ion thruster engine, Hall thruster developed in 1960 that alleviated the thrust density limitations of ion thrusters that results from space charge effects between the grids and marked a golden era in the development of ion thrusters.

2.2.3 Electrodynamic propulsion

Electrothermal propulsion has imposed some limitations for a number of deep space missions because of their performance constrains placed due to excessive frozen flow and electrode losses. In electrothermal propulsion about 20% of the power remains associated with the electrodes as heat and can’t be converted in to kinetic energy. Moreover, the specific impulse of arcjets operating on standard propellants, like hydrazine, is limited to a value of around 700 s and thrust efficiency of about 40% [3]. Few years back US air force have developed arcjets that produces specific impulse of about 800 s but with the thrust efficiency of 30% using ammonia as propellant. Ironically, it was these disadvantages in high performance of electrothermal propulsion that led to the development of electromagnetic engine, called as Magnetoplasmadynamic (MPD) thruster.

The MPD thruster was invented accidently when arcjet researchers were trying to understand the effect of mass flow rate on thrust. While their test they noticed that thrust of the arcjet initially dropped with the decrease in mass flow rate, which was genuine but then as they decreased the mass flow rate to a sufficient low level, the trust started increasing and this seemingly impossible result marked the transition from electrothermal heating to electromagnetic acceleration as flow rate decreased.

Now, we will try to understand the operating principle of MPD and physics behind it. Electromagnetic devices pass a large amount of current through the gas to ionize. Once ionized, the plasma thus produced is accelerated by crossed electric and magnetic fields that induces a Lorentz force. The current is provided between the positive and negative electrodes, while the magnetic field is induced by the current itself or it is applied externally by using an electromagnet. The Lorentz fore that accelerates plasma, in self-induced magnetic field, is directly proportional to the ratio {(J*J)/m}, where J is the total current and m is the mass flow rate. In electrostatic thruster only positive ions contribute to thrust, while this is not the case in electrodynamic thruster.

Figure 4: Operating principles of magnetoplasmadynamic (MPD) thruster

MPD thruster’s can provide high specific impulse (>4000 s) and high power density as well, which makes it suitable candidate for high power and high ∆V missions of the future. The concern of its developers is the substantially high amount of power on the order of hundreds of kilowatts is required for its optimum performance, and our current interplanetary space power systems e.g. Radio Isotope Generator (RTG’s) and solar arrays are incapable of producing this much power. MPD thruster is not used in any space mission yet However, NASA, Moscow Aviation Institute and many other educational institutions are working on this technology for its development.

3 RELIABILITY ANALYSIS FOR ENGINEERING

This section is based to a large extent on Ref. [4], Ref. [5] as well as Ref. [6]. The purpose of this chapter is to understand some reliability terms, its need in engineering, and some implications of basic formulae connecting them. We will also analyze some techniques used for reliability analysis of any system, so that before moving on to its application over electric propulsion system we may get quite familiar with the approach used in our next chapter.

3.1 Introduction

Reliability is that volatile property of an item or service that we all desire, but we all too often find it missing. Ask a man in the street what he understands by the term reliability and the answer will be that it is an ability to do the thing in a better way, and to on doing with some extent of assurance, or some similar qualitative statement but rarely there would be any response that resembles the quantitative statement that we often find in our literature, a type of which is given below. Moreover, there are many people, engineers, and numerate individuals who know how fast their car can run, its petrol consumption, and even have some opinion about its reliability, but they have no idea about its mean time to failure or mean time between failures. We will cover all these aspects of reliability and the statistics involved in its calculation in sections below.

Also, there is a debate in the reliability community concerning the value for its measurement and prediction, as it is perceived property. A hidden aspect of reliability which must never be forgotten is that high reliability depends on good engineering, and that no amount of data collection and analysis can improve reliability by itself. On the other hand it is frequently quoted that you cannot manage what you cannot measure especially when you are producing a complex system in a project that may take several years, high reliability can only be achieved if the project is well managed. There are many reasons for measuring reliability for e.g. to gain assurance when you are purchasing goods, for contractual purposes, to optimize purchasing policies or to predict running costs and spare holdings of complex equipment.

3.2 Failure

Basically, failure mechanisms are fundamental events, electrochemical or otherwise, which represent an unacceptable change from a previously defined and stable condition. Failure mechanisms are always present and usually become more significant as time increases, so this is an essential part of spacecraft engineering to consider the failure potential, or mission risk of a design and the subsequent software and hardware involved. Therefore it is essential to understand all the possible failure mechanisms that may degrade or terminate the performance or life of the system under consideration to ensure that correct design has been established. To facilitate the design process in resolving impossibly complex reliability equations, failure mechanisms are divided in two main classes; those that occur randomly in time and those that are time-dependent. The former group contains all failures for which the exact time of failure has not been identified even after testing their prototypes in a particular situation for a number of times. However, the components for which time dependent failures are determined, can also fail abruptly under higher stress environment of the mission demand. As an example, banning of wire filament fuses of long-life satellite missions due to a gradual glass seal leakage causing the fuse to operate in an unpredictable fashion.

Failure mechanisms are determined by life testing of components at lowest level of system construction i.e. independent components or subsystems are tested at increased rating (power or temperature etc.) and stress conditions until their destruction.

3.3 Reliability

The reliability of a product is the measure of its ability to perform its function, when required, for a specified time, in a particular environment. It is measured as probability, so the probability of no failure is reliability of a component. For constant failure rate λ, reliability is

R (t) = e-λt

The definition contains four important terms; function, environment, time, and probability, which are needed to be considered while designing a reliable system. We try to understand try to understand these terms in more depth separately.

3.3.1 Function

This means desired performance of a component or subsystem in fulfilling the task for which it is used in system design. It may seem an easy matter to decide whether or not a component is functioning correctly, but this simple aspect of reliability has caused more distress in the relationship between customer and supplier than any other. There could also be more than one level of performance (war or peace, for example, for a military system) for any system and the reliability at each level of functioning has to be determined and monitored. For example, the function of a domestic fridge is to keep the food and drinks cold, but what if the light fails? Will it still performs its primary function, and few of us would discard it because of such a failure. This demonstrates two levels of failures in a simple system.

3.3.2 Environment

Reliability of any equipment is very dependent on its surroundings or environment. This can be climatic conditions, as for spacecraft or satellites which are exposed to adverse environment conditions of space and others are like packaging, transportation, storage, installation, dust, chemical etc. examining the environment is an essential part of specifying and estimating reliability. Not doing so will make the consideration of reliability meaningless.

3.3.3 Time

Reliability decreases with time, in the sense that as the mission duration increases, its probability of malfunction or failure also increases. For this reason only test data is generated by testing the equipment until it ruptures. However, the duration of task may not be measured in units of time, but could be in terms of distance travelled, as for a vehicle, or duty cycles, as for batteries, or some combination of these or other parameters.

Ageing will also affect the reliability of a system, as mentioned earlier, as it decreases its ability to perform its function. Ageing will also be calculated as a function of time, duty cycle, or combination of these.

3.4 Probability

Reliability is measured as a probability, moreover a probability that changes with time that a product will perform its function successfully for a given time. The relative frequency with which these events occur in time is indicated by probability distribution. Probability is used to indicate the relative frequency of the arrival of an unsatisfactory state of the product. Consider a large number of items which are identical, same manufacturer, same design, and even same batch which are put under test together at the same environment of operation, then also they all will not fail at the same time. It is said that the lifetime are distributed. If we plot a graph of their lifetime with horizontal axis showing the time, ageing parameter, or mission

duration and vertical axis showing the proportion of items failed in the ith interval, as shown in Fig 5, then it can interpreted that

is the proportion of items that fail by time ti.

This implies, 1- Fi is the number of items that are still functioning at time t.

And so, Ri = 1 - Fi

Here Ri the desired reliability of the items tested. This graph of Ri is shown in Fig. a noticeable point in this graph is that reliability decreasing with time as mentioned earlier. The number of survivors becomes less and less as time passes, until they all fail.

Moreover, the probability of reliability or failure is not a constant value obtained from a life test data, it is usually distributed over certain period of time. For example, if we select 100 components from a production batch, that has 98% of reliability, and put them under test then the number of failures will not always be ‘2’. This means that the number of failures can either be 0, 1, 2, 3, or even 4, i.e. they are distributed.

3.5 Mean time to failure (MTTF)

The mean time to failure (MTTF) for non-repairable component, or the mean time between failure (MTBF) for repairable component is defined as the average time for which the component can be used before it fails. This is just an average time, and the can component can even last longer than MTBF or even shorter that it. It can be calculated as

3.6 Failure rate

The failure rate, also known as hazard rate or force of mortality is defined as the frequency at which the equipment fails at certain time interval. It is given as

λi = Fi / R(i — 1)

Where, fi is the proportion of items that fails between the time interval ti-1 and ti, and λi is the probability of an item to fail, or failure rate.

It has been identified that for most of the items, a graph of failure rate resembles like the one shown in Fig. 6. Because of the shape of this graph, it is often known as bath tub curve. Now, to understand the significance of this graph we will take an example. Consider a sample of item that is selected from a large batch and tested. There will definitely be some faulty or week components, no matter how good the quality control is, these will fail early and are manifested as initial high failure rate, shown in the first section of the graph. Once these

Figure 6: Qualitative function of failure; Bathtub curve

failures are debugged, the failure rate will be stay low or moreover constant, this period is known as useful life period and is shown by the second section of the graph. After a long period of operation for any component or system, some wear-out failures began to assert themselves due to ageing process, the failure rate will start increasing again and it is the time when the component should be change before its failure. This region is known as wear-out operation and is shown in the last section of the graph.

3.7 Reliability analysis techniques

3.7.1 Reliability block diagram method

A most simple method that can be used at all stages of the development is reliability block diagrams method. This method gives a pictorial representation of the reliability structure to be analyzed. To implement this technique the whole system under analysis is broken down to the lowest level of system construction or subsystems, to what level we should break down the system depends on the objective of analysis. For example, consider an ignition system of car. The components that may be required while starting the car, as shown in Fig: 7 may consist of the points, distributers, cables, coil, and battery.

Figure 7: RBD of ignition system of car when starting.

Once the car is started and is running, it will take the electrical power normally from the generator, although in emergency situation it will run by extracting the power required from battery. Thus there is some level of redundancy in the system and this is represented in the Fig: 8 by RBD method.

Figure 8: RBD of the ignition system of car when running.

From reliability system modeling technique, one thing that becomes very clear is whether the component is in series redundancy or in parallel/standby redundancy with other component. Now after making all these considerations from reliability block diagram, and knowing the failure rate of each component or unit, obtained from life test data, we can calculate the overall reliability of the system by applying the two rules illustrated below:

Series Rule

Suppose we have two systems C1 and C2 which are in series or we can say are dependent to each other. i.e. the system will function only if both C1 and C2 functions, and they have reliabilities R1 and R2, then overall reliability of the system can be combined as [6]

Rs = R1 R2

Summation Rule

Suppose we have two systems C1 and C2 which are independent of each other, that is the system will function if either of them will function, and they are having reliabilities of R1 and R2, then the overall reliability of the system can be obtained as [6]

Rs = R1 + R2 — R1 R2

This is also known as Active Redundancy.

3.7.2 Failure modes effects and criticality analysis (FMECA)

FMECA was initially known as FMEA (Failure Modes and Effects Analysis). The C in FMECA indicates the criticality of the various failures considered and ranked. This is the most widely used reliability analysis technique used at the initial stage of design to ensure that all the potential failures are considered and proper provisions have been made to eliminate these failures. This analysis is often known as ‘bottom up’ analysis as we examine low level components or functional grouping of components and considers the system failures that result from all their different failure modes.

There are many benefits of performing FMECA, out of which some of them are stated here;

· It helps in understanding the structure of the system, and the factors that influences the reliability.

· It helps in selecting much reliable design alternative which may include high safety potentials by assigning risk priority numbers, thereby provides a means of deciding priorities for corrective actions.

· It identifies if there are any operational constraints resulting from the design.

· It identifies where additional effort is needed at the time of manufacture, or assembly.

· Provides a basis for quantitative or qualitative reliability analysis.

FMECA can be performed either at design, process, or system level. Here the former two methods looks at the failures involved during equipment design and manufacture whereas the later looks at the potential failures and bottlenecks involved in large process, such as entire production line [7][4]. The main steps involved in FMECA procedure are

1. FMECA prerequisites

2. System structure analysis

3. Failure analysis and preparation of FMECA worksheet

4. Corrective actions

FMECA prerequisites involves defining; system boundaries i.e. which parts of the system could be included in the analysis and which will not, main functions of the system and its mission, operational and environmental conditions to which the system has to be exposed, must be defined properly and should be considered.

Thereafter, the system structure should be analyzed by breaking it down to its lowest level of components or functional grouping. It is likely advised to make a reliability block diagram of the system under consideration that contains minimum level of functional grouping, for better transparency and consideration of all potential failures.

The most important part of FMECA is its worksheet, which contains following columns in tabular form; [4][5][7][8]

Column1. The component under discussion or Item No.

Column2. A reference number for that component. It should be unique.

Column3. Code number for that particular component. This should also be unique.

Column4. This contains the component function/functions. This is an important column as it suggests that the analyst understands the functioning of the system and its each component. It also forces the author to think that there are no residual elements left in the system analysis.

Column5. This column includes the failure modes of the component under study. For example, leak, rupture or block for a pipe, fail open or closed for a valve, open winding for solenoid, short or open circuit for switch etc.

Column6. This includes the cause of the failure mode. Such as, ageing, misuse, dirt ingress, wear, fatigue or some other parameter.

Column7. This column contains the failure mode ratio, which is the proportion of failures of the component that has lead to the particular failure mode. It is denoted by α. In principal, the sum of the failure mode ratios for every component should be one, but in practice this is not the case, because it is not possible for any engineer to know all the possible failure modes involved with the components in his equipment.

Column8. This column contains the failure rate of the component (note that not of failure mode) which is denoted by λ, and is obtained by lifetime testing of the prototype equipment. The failure rate of the failure mode is given by the product, λα. If failure rate is not available, as it takes many years of operation of the prototype equipment then some standard values for the components should be considered. As in the case of this research paper.

Column9. This includes the effects of the failure on the immediate level (subassembly).

Column10. Consist of the influences of the failure mode, failure effect on the next level i.e. assembly. In case of complex systems like spacecraft, the effects on further different levels like mission should also be considered. The effect of a failure mode in different phases can also be analyzed. E.g. if the washer in a tap wears, then the tap may drip, which will be irritating, but anyhow it will not affect the flow of water from the tap.

Column11. This column represents the symptoms of the failure mode, it is different from the effects on immediate and next level, and is indicative for the fault diagnosis before it becomes serious. If there are no such symptoms until its catastrophic failure, then it should be highlighted.

Column12. Severity level of the failure mode is represented in this this column. A most simple definition of severity is, the proportion of times that failure mode under consideration will cause the system failure. When sufficient data is not available then this value is just a result of engineering judgment. As in the case of this research paper. Two important parameters that are needed to be considered are; one is the measure of the functionality of the system should be considered, and other Is taking in to account any other effects such as degree of damage to the operator or even death, financial losses etc. it is denoted by S.an example of severity levels is given in table 1.1

Column13. The criticality of the failure is indicated in this column. The criticality is the combination of the effects of the failure mode on the system and its frequency of occurrence. This is given as

Cm = λαS

And the criticality of each component is given by the sum of criticality of each failure mode.

Cc =∑ Cm

And the criticality of the subsystem is given by

Cs =∑ Cc

Column14. This last column contains any further remarks that the analyst wants to make to be noticed by the customer or reader. Any safety measures that are needed to be taken in regard to that component can be highlighted in this column.

Further down, in upcoming chapters/sections, we will use this FMECA analysis to study the reliability of Thruster engines under our scrutiny. See table 5, 7, 9.

4 Application of reliability analysis techniques

4.1 Reliability analysis of VASIMR

The development of VASIMR (Variable Specific Impulse Magnetoplasma Rocket) engine was initiated by NASA in 1970’s because of the limitations imposed by electrostatic field configuration such as high ion velocity, especially when combined with high Ion flux density. These challenges becomes more difficult when a deep space mission that demands high power (>100 KW), high ion velocity (>60 Km/s) and very long lifetimes (> 4 years), is under consideration. One solution to these problems is to eliminate the use of electrodes, instead using radio frequency (RF) power which enables dense energetic plasma flows. Moreover, magnetic field can be used to control the flow of plasma thereby preventing the surrounding material body from erosion. All these features desired for future propulsion are incorporated by Variable Specific Impulse Magnetoplasma rocket.

Now before moving on to the reliability analysis of VASIMR, we will first try to understand how it operates, its main components, their functioning, and its main functional groups.

4.1.1 VASIMR operation

The VASIMR engine is a high power, electrothermal plasma rocket capable of exhaust modulation at constant power. It consists of three main stages encompassed inside a magnetic cell; a helicon plasma source, ICRF booster, and magnetic nozzle. This type of magnetic configuration is called asymmetric mirror. In first stage the gas is injected in to helicon source, where cold plasma, although its temperature is about thousands of kelvins, is generated by launching helical waves through the gas thereby releasing an electron from each gas atom. The surrounded magnetic field holds the ionized gas and directs it towards the second stage. In second stage that is called RF booster acts as an amplifier, in this stage the plasma receives further RF waves from second antenna that hits the ions and electrons along their orbits around field lines at resonance, which results in accelerated motion and increase in plasma temperature to an order of about millions of kelvins. The last cell acts as a hybrid two stage nozzle that converts the thermal energy of the plasma in to directed flow, while protecting the nozzle walls and ensuring efficient plasma detachment from the magnetic field to produce an exhaust velocity of about 150,000Kph. Moreover, in this stage only the adiabatic expansion of the ions takes place by Electromagnetic Ion Cyclotron Waves (EMIC) which converts the perpendicular motion of the electrons in to direction parallel to the thruster direction [9–13][17][18]. A simple schematic diagram showing these stages and operation is shown in Fig 10.

Figure 10 : Principals of operation of VASIMR.[10]

The key advantage of a VASIMR engine is its electrodeless design, which makes it suitable for high power density and long component life by reducing plasma erosion and other material complications. The other advantage of VASIMR engine is its ability to vary its specific impulse and trust by controlling RF power supplied to helicon source and ICRF. For example, if high thrust is desired, RF power is predominantly fed to the helicon injector, with an appropriate reduction in ICRF heating. Similarly if high specific impulse is required, RF power is diverted to ICRF system with concomitant reduction in thrust. However, the total power supplied remains constant. This process of exhaust modulation in VASIMR is known as Constant Power Throttling (CPT).

The general spacecraft system parameters for VASIMR engine are listed in Table 2.

4.1.2 Functional/Reliability block diagram

As discussed before the functional block diagram of the system, taken in to account for reliability analysis, resolves the complication of a complex system by breaking it down to its lowest level of component functionalities. This gives us or the analyzer a clear picture of the components and their hierarchy in system design. The functional block diagram of VASIMR propulsion system is represented below in Fig 11. [9][12][15][16]

PSE = Power Supply Equipment, ICRF = Ion Cyclotron Resonant Frequency.

Figure 11 : Functional block diagram of VASIMR propulsion system

4.1.3 Analysis using reliability block diagram technique

Reliability analysis of any system is completely dependent on test data, as stated before, performing which is out of the boundaries of this project. Because of this reason we will make some assumption of MTBF’s, not MTTF as the system is non-repairable, of the components involved. Moreover we are doing this analysis by taking in to account that the components have constant failure rate.

Before moving on to calculations involved in reliability analysis, we will first look at the different subsystems of VASIMR propulsion system, with the components involved in each of them, in a tabular form;

Table 3: Various subsystems of VASIMR propulsion system [9–15]

Now, to calculate the reliability of the complete system we will first calculate the reliability of each subsystem by using the formula stated in section 3.3, 3.5, and 3.7.1 i.e.

R (t) = e-λt

λ = 1 / MTTF

Moreover, if system contains one component then, R1 = e-λt (series rule)

And if system contains two components in active redundancy then,

R2 = e-λ.t + λ e-λ.t ……….. (Summation rule)

The calculations involved in calculating the reliabilities of individual components and of complete system, are presented in appendix 1. The complete unit configuration, with their mean time between failures, reliabilities of individual component and complete system reliability is presented in table 4. The test data of MTBF’s considered here for each component is assumed in a time frame of 600 hours of operation, and this will be same for these components in analysis of other systems also, which are presented in this report.

The table presented in last page shows that the reliability of VSIMR propulsion system, within system boundaries that comes out to be (0.812499) i.e. the complete system under consideration is 81.25% reliable. Although these values are assumed but while selecting the MTBF’s the component properties and operations are considered. If original test is available then the reliability can be calculated by using the method applied above for any system.

4.1.4 Analysis using FMECA technique

The theory involved in FMECA is completely discussed in section 3.7.2; however, the worksheet required for doing the analysis of system is being presented in table 5. Here also, the failure rate (λ) and failure mode frequency (α) of the components are assumed. The assumed data used here will be same for other FMECA analysis as well in this report. By doing this analysis we will try to calculate quantitative value of the criticalities of failures involved in the system along with studying systems various modes of failures and their causes.

While performing the analysis presented in table 5, we have categorized all possible failures on the basis of the components involved in the system and their operation. The criticality of the failures involved in the system comes out to be 2.03. Some major areas of concentration that can be depicted from the analysis are

· The magnetic field surrounding the three successive stages in VASIMR is generated by magnetic coils, so any failure i.e. either variation or fracture, can lead to a critical failure of thruster engine. It will not be insignificant saying that operation of complete VASIMR engine is dependent upon the magnetic field surrounding the thruster and so these solenoids must be tested for all possible failures like excessive heating, wear, open winding etc.

· The other area of interest which is worth considered is functioning of RF antenna, both in helicon source and ICRF heating stage, as plasma ion production and its heating is done by these two components. This point further moves our interest towards the RF power generator, power conditioning unit and other electrical power supply subsystems. Power generation and conditioning unit is thereby also an important section to be designed with maximum reliability.

Now we will look at the worksheet prepared during the FMECA analysis which will explain us all the things in more detail.

(The worksheet here is presented in .jpg format to present the entire table in one page)

4.2 Reliability analysis of NSTAR

After rigorous development and research of about 40 years, in 1998 the first spacecraft propelled by using electric propulsion for deep space mission (DS1) was NSTAR (NASA solar Technology Application Readiness program). DS1 marked a major milestone in the development of advanced deep space propulsion system. This engine was developed to deliver a total ∆V of 4.5 Km/s to the 486 Kg (initial wet mass) DS1 spacecraft while consuming only 81Kg of Xenon. Thereafter ion propulsion system entered the mainstream of deep space missions as well as for keeping commercial satellites in space. [20][21][22]

Now we will try to give a close look to the theory and principals involved in working of NSTAR engine which will familiarize us to NSTAR components and functional levels to perform its reliability analysis.

4.2.1 NSTAR operation

The NSTAR ion thruster engine is composed of a number of subsystems: the discharge chamber, the discharge cathode assembly (DCA), the grids also known as Ion optics, and the neutralizer. Initially the propellant is injected both through the hollow cathode and through the main flow injector rings. The DCA provides a stream of electrons, which are considered to be monoenergetic, in to the discharge chamber because of the potential difference between DCA and discharge chamber that acts as anode. These electrons have enough energy to knock out the electrons from external orbit of neutral gas thereby ionizing it. Every bombardment of an electron and gas atom releases an Ion and two electrons in to discharge chamber, due to this reason, the mass flow towards DCA is less than the mass flow through the main propellant injector. The ‘ring cusp’ magnetic field surrounding the discharge chamber is used to improve the ionization efficiency of the engine by confining electrons in to chamber for more time. This is done to increase the collision frequency of electrons with gas atoms to produce more ions with less input power [20][21][22]. A simple schematic diagram showing the operation of NSTAR is shown in Fig 12.

Figure 12 : Schematic of NSTAR engine.[20]

The last and an important component of NSTAR configuration is the Ion optics, which is a pair of molybdenum grids that accelerate ions from the chamber to produce thrust. These grids are present at the rear of DCA and have thousands of holes to pass electrons through them. The plasma inside the chamber is maintained at the potential equal to, or slightly above, than the potential of anode. The screen grid which is present in the upstream is maintained at the potential equal to DCA, which is around 1090 V at full thruster level and due to this setup ions in the discharge chamber are slightly attracted towards the screen grid, while electrons are repelled away. The other grid, known as accel grid, is biased to about — 225 V. both the grids are less than 1mm thick and are 0.7 mm separated to each other. The ions thereby produced in the discharge chamber enters the holes of screen grid and are accelerated by some 1300 V of potential difference between the grids to produce a thrust of about 90 × (10 raise to power–3) N.

4.2.2 Functional/Reliability block diagram

PSME = Power Supply and Monitoring Equipment

PCCE = Power conditioning and Control Equipment

PSE = propellant Supply Equipment

Figure 13: Functional block diagram of NSTAR [5]

4.2.3 Analysis using reliability block diagram technique

Here also we will use the same formulas given in section 4.1.3, for calculating the reliability of different components. A table showing different components in individual subsystem, their assumed MTBF’s, and reliability of individual component, subsystem and whole system is shown in below. The calculations involved are present in appendix. In this analysis we will find the reliability with one thruster engine and then we will see the effect of deploying a redundant thruster engine in system assembly.

As calculated in table 6, the reliability of whole system with one thruster engine comes out to be (0.729185). The reliability of thruster, subsystem, independently is (0.938115). Now, if we consider the redundant thruster also, then the reliability of thruster will become (0.99617), while considering standby redundancy (Ref Appendix 1) and the total reliability of system thereafter will become (0.774310), which is increased by 5%. This is the reason behind providing two thrusters in NSTAR engine.

4.2.4 Analysis using FMECA technique

Table 7: FMECA worksheet of NSTAR engine

From the worksheet of FMECA, presented above we can point out the areas of opportunity present in the technology. The one serious problem associated with grid ion engines, that we can identify in worksheet as well, is grid erosion or sputtering which is caused due to ejection of surface atoms from a material when it is struck by high energy atoms or ions. Moreover, in vacuum these ions go in to gaseous state and form a thin layer over nearby surfaces. A noticeable aspect of this phenomenon, in context with NSTAR thruster, is that it is most noticeably seen on the accel grids. The accel grid is biased negative to prevent electron backstreaming as well as to extract current from the discharge chamber[]. In normal operational condition the beam ions which are originated in the discharge chamber do not impinge the grid material directly. However, when operating below crossover limit or above the described limits then high energy ions strikes the grid with enough momentum to cause sputtering.

There are several factors that affect the amount of sputtering, such as the weight of incident ion or atom, weight of the target atom, velocity and angle of incidence of the striking ion, temperature of the target material and also the density of grid material. By considering all these complications, the grid material which is most often used is molybdenum because it has most of the sputter characteristics, and also its density high as compared to others, more density means more atoms available per unit volume to be sputtered. In last few years carbon is also used instead of molybdenum, although it is not dense but provides much better shielding for sputter to take place. The most common form of carbon materials are pyrolytic graphite and carbon-carbon composites. The strength of sputtering taking place on a target material is known as sputter yield and has a unit (atoms/Ion). The total sputter yield for xenon ions, impinging upon molybdenum, titanium, and carbon as a function of ion energy is shown in Fig 14. []

Figure 14: Total sputter yield for xenon ion impinging on three materials.[21]

Sputtering is one of the major problems that can lead to several grid failure mechanisms and hence is a great concern as-far-as reliability of NSTAR is concerned. Some of the failure mechanisms of grid caused due to ion impingement are:

1. Electron backstreaming

2. Structural failure

The former one occurs when high negative potential applied at the accel grid, fails to stop backstreaming of electrons within the downstream plasma to move towards the high potential discharge chamber potential. These electrons can gain enough energy while moving through the large potential difference between the plasma and deposit significant power in to discharge chamber which may to overheating of components. This can occur due to combined result of aperture diameter enlargement and grid thinning. The latter is caused due to the erosion of grid material from its surface.

4.3 Reliability analysis of DS4G

As stated earlier, to perform reliability analysis of any system we must first understand its operational principals and functions performed by different components or subcomponents.

In conventional electrostatic grid engine the ion thrusters perform the extraction and acceleration of ions simultaneously in a single stage using two permeable grids closely spaced in series. This technique ultimately limits the performance of ion thruster engine that can be achieved, in terms of power density, exhaust velocity, and specific impulse. This is because of the reason that the inter-grid potential is limited to a certain value to avoid excessive penetration of the grid electric field in to the discharge chamber that contains plasma. The excessive penetration of ions usually results in the formation of curvature in the plasma sheath attached to the holes in the screen grid as shown in Fig. 15. The higher the beam potential (VB), the greater the curvature and hence increased beamlet divergence. This problem can be reduced by using a third grid, which will act as decel grid, by doing so the significant direct impingement of ions will occur on the accel grid and decel grid.

Figure 15: triple grid system showing the formation of plasma curvature

But this technique is also not suitable from reliability point of view, because direct impingement of electrons on grid causes sputtering of the grid material as discussed before in section 4.2.4. Leading to excessive grid erosion and hence widening of holes. In order to avoid sputtering, erosion, and beamlet divergence the grid potential in our conventional ion thruster engine is limited to 2–4 KV and this limits the achievable Isp < 10,000 s, thrust density to < 0.5 mN/cm2, and power density to < 20 W/cm2 while using Xenon propellant.

4.3.1 Operating principals of DS4G

The limitations studied in the last section do not have any impacts on the missions to near earth solar system or even those out of Jupiter as they require Isp of around 10,000 s. however, the missions which are far outer to the solar system and beyond which requires Isp of around 50,000 s, so the propellant mass fraction will influence the payload budget for high ∆V concerns (about 30- 100 Km/s). With all these concerns in mind and to eliminate the limitations imposed by 2 or 3 grid engine, ESA (European Space Agency) is working on the development DS4G (dual stage 4 grid engine). As name suggests, in DS4G the extraction and acceleration stages are decoupled by essentially creating a two-stage process with the addition of fourth grid. Moreover, the distance between first two grids and other two grids, while proceeding upstream, is also increased. Schematic diagram of DS4G ion thruster arrangement is shown in Fig 16.

Figure 16: Grid assembly of Dual Stage 4 Grid (DS4G) Ion Thruster engine.

The entire components, operation, and subsystems of DS4G are same, as we studied in NSTAR. The only difference here is the additional two grids, their operating potential, and spacing between the first two and last two grids. In the first stage, the first two grids which are closely spaced and both are operated at a very voltage (> 5KV to avoid beamlet curvature/impingement/divergence problems), and very low potential difference between the two (3 KV) enables the ions to be extracted from the discharge chamber without hitting the grids (mostly). Then, in the second stage two more grids are positioned at a greater distance downstream and are at low potential. This high voltage difference (typical acceleration potential of 80 KV) between the two pairs of grids accelerates the extracted ions to produce thrust.

4.3.2 Functional//Reliability block diagram

The functional block diagram of DS4G Ion thruster engine will be same as the NSTAR engine with an addition two grids at the end of the thruster assembly. For this reason we will consider the same block diagram as in section 4.2.2 by taking in to consideration that it has four grids instead of two. Similarly as before the RBD analysis of DS4G ion thruster is presented in table

Table 8: RBD analysis of DS4G Ion thruster.

4.3.3 FMECA analysis of DS4G ion thruster

Table 9: FMECA worksheet for DS4G thruster engine

5 Comparison of reliabilities of VASIMR, NSTAR, DS4G

Table 10: reliability comparison of three thrusters under study

Table 10, shows the individual reliabilities of the three ion thruster engines. Both the analysis shows that there is gradual decrease in the reliabilities of ion thrusters, in the order stated above, this proves the theoretical aspect of reliability which says that reliability of any complex systems decreases with increase in components i.e. more components, more failures and therefore less reliability. VASIMR as we studied is small in size have less components as compared to NSTAR and DS4G, such as it does not have any electrode in its structure. Moreover, there are no grids used in VASIMR for accelerating electrons which reduces the component complexity of VASIMR engine and hence it has maximum reliability as compared to others. The overall criticality of failures involved in VASIMR is also lowest as compared to other ion engines.

NSTAR ion thruster engine has reliability less than VASIMR as it has more components like cathode, neutralizer, anode, accel grid, and screen grid. However, overall reliability of NSTAR ion engine with a redundant pair of thruster is more than this, as shown in section 4.2.3. Similar is the case with DS4G as it have even more components than NSTAR, therefore it has minimum reliability as well as maximum criticality of failures.

All these results validate that the data assumed in our report is quite close to the real life test data.

6 Methods to increase reliability

As studied so far, reliability of spacecraft system plays an important role for the success of mission. This is the reason for which spacecraft system and its subsystems undergo a testing of couple of years to eliminate all the possible failures that can occur during mission. Areas of critical failures are studied and these critical paths of failures are eliminated by redundant system or components. Redundancy plays an important role in increasing the reliability of any system, so that in case the primary system fails, the secondary takes the control of the system thereby increasing the operational life of the system. Apart from redundancy there are many other preventive steps to be taken before launch. We will discuss them one- by- one in this section in brief as they are available from heritage.

6.1 Redundancy

Redundancy can be either active or passive, i.e. the redundant item may be switched on while the system is functioning, as in the case of multiengine aircraft that can fly even if some of its engine fails, or they may be left unused as in the case of spare tire on a car. The latter case is often also known as standby redundancy. The redundant system uses a switch that switches the system between the two, which will now act as a single point of failure. But because of their less complexity they are more reliable. The reliability of active redundant system is given as;

RT = R1 + R2 — (R1 R2)

And the reliability of passive redundancy is given as;

Or, in general form for ’n’ components,

The redundancy is often also classified as m-out-of-n redundancy. In this type of redundancy the system consist of ’n’ components out of which any ‘k’ functioning will ensure the system functioning. The reliability of such systems is calculated by using binomial distribution. For constant hazard rate the total reliability RT is given as,

Fig.17, 18, and 19 shows the basic examples of three types of redundancy.

Moreover, we have already discussed and witnessed in section 4.2.3 that by incorporating redundancy the overall reliability of NSTAR system has increased by 5%, so is the case with other redundancies also.

6.2 Pre-space and space environment

By pre-space environment, it means the problems that can be avoided by better project management, proper test schedules, implementation of contingency and time plans. Then comes the pre-launch environment to avoid system from vibration/ shock, shipping contamination and the launch complexities such as high launch vibrations, staging shock, angular shock, nose fairing heat etc. should be considered while system design and testing to be dealt properly to avoid any failure.

Considerations of space environment should be taken in to account. This involves thermal and heat effects due to short and long eclipse cycles which can be avoided by using radiation/absorb surfaces of spacecraft’s, careful material selection and increase in conduction path. Other factors are weightlessness effect on structure, electromagnetic interference, exposure to cosmic rays, space debris etc.

The techniques used to avoid all these problems while material selection and system design are numerously present in our literature and these should be taken in to account while generating life test data and performing reliability analysis.

7 Future work

Future work associated to this project will be generating life test data by testing individual subsystem for elongated period to study the practical areas of opportunity. VASIMR and DS4G thruster engines are still in development, DS4G test schedules are to be done in years to come, so if laboratory setup (for 1/50 or 1/100 prototype testing) can be organized for developing these test results then this could be a major step in the development of these future propulsion systems.

The immediate step for this project could be to develop the matlab code for performing statistical reliability analysis of any system by using its inbuilt functions in statistics tab. This generalized code can then be used to analyze the test data which will be gathered at later point of time. An important thing that should be considered while designing this code is to develop a logic that can resolve mesh networks or at least a network that consist of series and parallel combinations, to a highest level of complexity. This is so because any generalized block diagram of a system is almost same as the electrical network of resistances in series & parallel combination and the system has to decide on its own the type of combination.

8 Conclusion

Hereby, we complete the main objective of the report which was to do the reliability analysis of the three major contenders of ion propulsion engines. The results obtained are well in context to the theoretical principals of reliability analysis. The analysis has shown that the VASIMR ion propulsion engine is most reliable among the three because of its many advantages discussed in our report and possesses minimum overall criticality of failures. At the end we have discussed and validated some methods to improve the overall reliability of any system.