The Reliability Predictions for the Avionics Equipment

Universal Journal of Applied Mathematics 2(8): 277-282, 2014 DOI: 10.13189/ujam.2014.020801 http://www.hrpub.org The Reliability Predictions for the Avionics Equipment Zahid Khan 1,*, Radzuan B.Razali 2, Sarfaraz Ahmed 3 1 Department of Statistics, Hazara University Mansehra Pakistan 2 Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Malaysia 3 Department of Mathematics, Hazara University Mansehra Pakistan *Corresponding Author: zahid.hazara@gmail.com Copyright 2014 Horizon Research Publishing All rights reserved. Abstract The Reliability Prediction is an important tool for designing, decision making and estimating future system success. Design engineers are often required to develop and estimate Reliability before the product is produced. Inaccurate predictions can lead to over design and/or excessive spare parts procurement. This work is based on the study of Reliability Analysis carried out on Electronic Communication Systems used in the aircraft avionics. This system was applied in the beginning for the Secure Speech Equipment designed specifically to encrypt voices as well as for fax and computer data. The Part Stress Analysis modeling is used in this study which is a worldwide standard for performing reliability predictions. The Reliability Block diagram is also developed as a tool for reliability prediction. Keywords Reliability Prediction, Part Count Analysis, Parts Stress Analysis, Mathematical Models, Reliability Block Diagram 1. Introduction Reliability prediction entails estimating the reliability of equipments or products in the earliest stage of their design and development. Developing a reliable model generally ensures a successful prediction of a system. The purpose of this estimation is to prevent the failure, to discard the failure and to improve the product quality as reliability is also one of the dimensions of quality which is further explained in [1]. It is important part of the product design and engineering practice process. Customer s decision about the product depends upon the characteristics of different comparable brands of a product. Sales and marketing of the product are based on product s warranty. So one of essential component in product warranty is reliability prediction of the product. For more reliable system, more warranty can be listed [2]. Selection of reliability prediction technique is one of the contentious procedures in reliability engineering. Different prediction models namely, MIL-HDBK-217, HRD4, Siemens, CNET and Bellcore may be used for prediction purpose and for each model the sensitivity parameter is different as described in [3].Currently reliability predictions are done in the electronic industry almost solely with the model of MIL-HDBK-217 which has a long history as a tool for predicting reliability on electronic equipment and is kept up to date [4], [5]. As the system is the network of its components so it is compulsory to understand the relationship between the system and its components before applying any reliability model to evaluate the reliability of the whole system. It should be kept at front that actual system and the reliability model required to assess the reliability may not have the same topological structure [].Reliability prediction of a system is a finding about the failure rate during the useful life of the system. This is just a guess in terms of probability not the absolute assurance. In modeling such predictions past experience and data play a significant role. Data used to quantify the model, can be obtained from sources like, company records, customer maintenance records, component suppliers, design experts or field service engineers and model may be used from already mentioned handbooks. Comparisons of models are not useful because of effects of different sensitivity parameters on the failure rate. Mostly it is suggested to user, that working in telecommunications, to use telecommunication based models while for others working in military field, military based models are useful because of similarity of equipments to the applied field. However one can best predict the reliability by using field data as basic tool. But it should be kept in mind that field behavior of equipment may not be the same as predicted because models are just the approximation of random nature of the system failures. The high cost is involved in aerospace industry with a new product, prior to its installation in aircraft. For this reason great attention is required for near to accurate reliability estimation. This dilemma had remained a significant issue in avionics industry since beginning of 1950s.Research was taken at hardware aspect of reliability for electronic system in order to develop a methodology for identifying potential weaknesses in design and operational life. A number of techniques for prediction of reliability are available in different reliability database but we will focus to system reliability block diagram due to complexity of system design

278 The Reliability Predictions for the Avionics Equipment and algorithm process. Based on this the article analyzes the reliability through Monte Carlo experiment. Details of our system reliability block diagram and basic assumptions for our system are as follows. 2. Reliability Block Diagram Model Complex system reliability may be predicted in terms of reliability block diagram (RBD) of a system.we can predict the reliability because it is a graphical snapshot and evaluation tool to model the system reliability. An electronic system can be considered to be a network of components, all interlinked to one another in complex ways; so it is best viewed by RBD.RBD is the logical interaction of failures within system and its successful operation [7]. Between input and output nodes blocks are arranged either in series, parallel or combination of these. RBD can be used as a prediction tool for both basic as well as mission reliability. For modeling the system reliability, in depth knowledge for structure and functional processes is required. Through probability s rules and mathematical models we can then assess the system reliability. This article analyses the prediction for mission reliability model. For observed system we assume the following: I. Connectors of system are highly reliable. II. Each component and whole system are bimodal that is either good or failed, there is no third state. III. System is independent of input error IV. Failure rate of different components is statistically independent. By understanding the composition, principles, functions and other aspects of system, the reliability block diagram for our system is designed in Figure.1.Mission reliability is then evaluated in section 4.MIL-HDBK-217 predictions are based on complex methods to estimate the failure data. A brief introduction of both methods is as follows. 2.1. Part Count Prediction Technique This method used in early design phase, provides the estimate of failure rates. As it requires less information about system s design than part stress analysis hence it is mostly applicable in design phase [3].It is based on the generic failure rates of the anticipated quality and type of parts to be used in the assembly. The method assumes that successful function of the system is supported if its entire components are operating, that is if the system s components are in series network. System failure rate is then obtained by the following equation n λ= λj j=1 where λ j is the reliability failure rate of jth component. This method has been highly criticized; details can be found in [8].Parallel to MIL-HDBK-217, many other advanced methods have been developed in other reliability databases. 2.2. Part Stress Prediction Technique This technique requires knowledge about the stress levels on each part to find their failure rates. It is usually applicable later in design phase and it requires detail information about design configuration to find actual stress level for each part application. In addition to base failure rate, it also includes different other factors like power factor, quality factor, environmental factor and other application related factors, for estimating a part s failure rate [9]. Date on various factors and basic failure rates are present in MIL-HDBK-217.Following are some parts stress mathematical models for different electronic components [10].In short, there are many sources and other relevant information about application environment that may be considered in predicting the reliability of a system at the early stage of their production. 3. Mathematical Models Deterministic expressions for micro-circuits, gate, arrays and micro-processors are essentials for estimating the failure rates of required system. The following models are generally applied in different military hand books such as MIL-HDBK-217 for micro-circuits that include Bipolar and MCC devices, digital and different types of arrays either linear, programmed or logic [11].Equation-1 gives data on failure rate. Failures/ Hours Where: 1 λ P= ( C1T A+C2E) Q L (1) C = This factor is based on number of gates or transistors, in other words based on die complexity. A look up table gives a value based on how many gates or transistors in device under studied, keeping in view the type of arrays like linear, programmed etc. T = Temperature based factor which can be calculated from a specified model. C 2 = Packaging failure rate factor applied for micro-circuits, this takes into account the reflection of device packaging. E = This factor capture the environmental operational aspect. This factor changes according to given environment of operation. This includes number of factors such as ground benign, naval sheltered, airborne inhabited cargo, canon launch etc. A = Application factor i.e. used for application of device for MMIC appliances applied in a high power environment a factor of three will be used whereas digital device will utilize a factor of one.

Universal Journal of Applied Mathematics 2(8): 277-282, 2014 279 Q = Quality factor i.e. appliances are for commercial or military level specification purposes. = This factor is used to reflect the age in years that L an appliance has been in production. Equation-2 gives Micro-circuits, Gate / Logic Arrays & Micro-processors data as: λ P= ( C1 T+C2E) QL Failures/10 Hours (2) Equation-3 is for Gaas Mmic and Digital Devices. λ P= ( C1T A+C2E) Q Failures/10 Hours (3) Equation-4 is for Resistors λ =λ /10 P B T P S Q E Failures Hours (4) For transistor,(4) is modified as λ =λ P /10 (5) P B T A R S Q E Failures Hours and for capacitor the modified failure rate equation will be λ =λ P /10 () P B T C V ST Q E Failures Hours Reliability Data Calculation for Resistors The common factors are as follows Family = CHIP Base failure Rate ( ) B Temperature Factor ( T ) Power stress factor ( ) Quality Factor ( Q ) Environmental factor λ = 0.0037 = 1.3 S = 10 =different values E = 4.0 Part no Resistance Tem ( ο C ) Table 1. Reliability Data Calculation for Resistors Rated power Actual power Opr. Voltage Power stress ( S ) Power factor ( P ) Part failure - P (λ )10 hrs 001 1.K 50 ¼ w 0.015 5 0.7 0.19 0.027 002 10k 50 1/10 w 0.0025 5 0.72 0.09 0.012 003 10 50 1/10 w 0.0025 5 0.72 0.09 0.012 004 10k 50 1/10 w 0.0025 5 0.72 0.09 0.012 005 110k 50 ½ w 0.0002 5 0.71 0.04 0.005 00 1k 50 ¼ w 0.0250 5 0.79 0.23 0.034 Board part no Tem ( ο C ) Table 2. Reliability Data Calculation for Transistors. Power rating factor ( R ) Applied voltage Rated voltage Voltage stress factor ( ) S Part failure rate ( )10 hrs Q200 50 4.3 5 40 0.0 0.01 Q201 50 4.3 5 40 0.0 0.01 Q202 50 4.3 5 40 0.0 0.01 Q203 50 4.3 5 40 0.0 0.01 Q204 50 4.3 5 40 0.0 0.01 Q205 50 4.3 5 40 0.0 0.01 Table 3. Reliability Data Calculation for Capacitors Part no Capacitance ( µ P ) Capacitance factor ( C ) Tem ( ο C ) Operating voltage (volt) Voltage stress ( S ) Voltage stress factor ( V ) Part Failure hrs ( )10 0.01μf 0. 50 5 0.200 1.0 0.125 0.1μf 0.81 50 3.3 0.20 1.0 0.153 0.1μf 0.81 50 5 0.3125 1.1 0.18 0.1μf 0.81 50 5 0.3125 1.1 0.18 0.1μf 0.81 50 5 0.3125 1.1 0.18

280 The Reliability Predictions for the Avionics Equipment Reliability Calculation for Transistors The common factors are as follows Family =PNP Base failure Rate ( ) B λ = 0.00074 Temperature Factor ( T ) = 1.7 Application Factor ( A ) = 4.3 Quality Factor ( Q ) = 5.5 Environmental factor ( E ) =4.0 Component Reliability Calculation for Capacitors The common factors are as follows Family = Ceramic λ 0.0009 Base failure Rate ( B ) = Temperature Factor ( T ) =2.9 Stress Resistance Factor ( ST ) = 0. Quality Factor ( Q ) =10 Environmental factor ( ) E =10 The last column of each table contains time dependent reliability R(t) of different parts, resulted from the exponential distribution model. It is not only reckoning the basic failure rates but clearly illustrates that the system failure rate λ is also adjusted by considering various multipliers namely π factors. These π factors reflect those parameters which can affect the system and component failure rates like, quality, environment, stress level and temperature. The part count technique is implied to be appropriate near the beginning in the design stage. By assigning values to different parameters which are used in early period of design, models can be established from this prediction technique. Part stress technique is based on the assumption that there is perfection in basic design and failures are resulted from manufacturing stage defects which are accelerated by different operational stresses. Design, manufacturing, storage and transportation all play a significant role in the reliability estimation of any electronic equipment and all these processes differ from company to company. External failure mechanisms and flawed report writing methods may also become sources to affect the failure data. Consequently no statistical confidence is attached with values which are resulted from these models. Development of these models is based on assumption of constant rates of failure. This means that component failure rates are age independent. This assumption is taken on the ground that system will start its mission after discarding early failures and before wear-out period mission will be completed [11].The modern prediction techniques are available today which can be used to analysis thousand of components for months and possibly years to get sufficient data in order to establish a precise empirical model. 4. System Reliability Evaluation System reliability now can be estimated by taking into account the individual parts failures Reliability Block Diagram is an important tool used for estimating the failure probability of a complete system which is briefly discussed in previous section. In our case, failure of the system is defined as intersection and union of individual failures as shown in Figure 1. As the individual failure modes of our system have been identified, now the system reliability involved, evaluating the probability of union and intersection of events and considering the statistical dependence between them. The corresponding failure probabilities are mentioned in Table-4 below. Table 4. Failure probabilities of system components. Units Resistors Capacitors Transistors Failure rate 1.02 10-7 * 7.83 10-7 * 1.12 10-7 * System Failure rate: 9.97 10-7 * The reliability of the system and units are calculated on probabilities laws of union and intersection for events. As mission reliability model is looked complex to derive the general equation for solution so Monte Carlo simulation methods can be used to find the interval estimate for the failure of the system. In our case these bounds have been estimated by assuming that all the events are statistically dependent. The first order bounds for our system based on simulation study of Ang and Cornell [12], are [7.83 10-7, 9.97 10-7]. We have also calculated the second order bounds for more accurate and narrowest estimate, based on study of Ditlevsen [13].These estimated bounds are [9.9 10-7, 9.97 10-7 ] which is approximately the same failure probability as mentioned above.

Universal Journal of Applied Mathematics 2(8): 277-282, 2014 281 RESISTOR 003 = 0.012 RESISTOR 001 RESISTOR 002 RESISTOR 005 = 0.027 = 0.012 = 0.005 RESISTOR 00 = 0.034 RESISTOR 004 = 0.012 TRANSISTOR Q200 CAPACITOR 1 CAPACITOR 1 CAPACITOR 1 CAPACITOR 1 CAPACITOR 1 = 0.01 = 0.125 = 0.153 = 0.18 = 0.18 = 0.18 TRANSISTOR Q201 TRANSISTOR Q202 TRANSISTOR Q203 TRANSISTOR Q204 TRANSISTOR Q205 = 0.01 = 0.01 = 0.01 = 0.01 = 0.01 Figure 1. Reliability Block Diagram of Avionic Electronic System. 5. Conclusions This work has briefly described how reliability prediction methods can be applied in any avionics industry to predict the failures in the operational life of a component. Currently none is most accurate for determining the reliability values for electronic components but due to rapidly changing impact of technology, highly effective predicting techniques are being introduce that have also influence even in extremely short failure data on electronic components. Reliability Prediction is a technique used all over the world to predict failures. It can be easily applicable in any avionics industry and helps in product performance enhancement. REFERENCES [1] D. Montgomery, "Introduction to Statistical Quality Control," th ed, New York: John Wiley, 2009. [2] Z. Liu, "Optimal Reliability and Price Choices for Products Under Warranty," Proc Annu Reliab Maintainab Symp, 200, pp. 14 151. [3] J.Jones and J.Hayes. Joness, A Comparison of Electronic-Reliability Prediction Models, IEEE Trans Reliab., vol. 48, no. 2, 1999. [4] J W. Harm, "Revision of MIL-HDBK-217, Reliability Prediction of Electronic Equipment," Proc Annu. Reliab. Maintainab. Symp (RAMS), 2010 pp. 1 3, Jan. 2010. [5] Y.Liu, and W.Wu," Research on the System of Reliability Block Diagram Design and Reliability Prediction," International Conference on System Science, Engineering Design and Manufacturing Information, 2011. [] R.Billlinton, R. Allan, "Reliability Evaluation of Engineering Systems: Concepts and Techniques,". Springer, 1992. [7] E. Zio, An Introduction to the Basics of Reliability and Risk Analysis, Ser. Qual. Reliab. Eng. Stat., vol. 13, 2007. [8] J. G. Elerath and M. Pecht, IEEE 1413: A Standard for Reliability Predictions, IEEE Trans. Reliab., vol. 1, no. 1, pp. 125 129, 2012. [9] J. G. McLeish, Enhancing MIL-HDBK-217 "Reliability Predictions with Physics of Failure Methods," Proc Annu. Reliab. Maintainab. Symp., pp. 1, Jan. 2010. [10] A. Goel and R. T. Graves, Electronic system reliability: Collating prediction models, in IEEE Transactions on Device and Materials Reliability, 200, vol., no. 2, pp. 258 25. [11] G. A. Klutke, P. C. Kiessler, and M. A. Wortman, A Critical Look at the Bathtub Curve, IEEE Trans. Reliab., vol. 52, no. 1, pp. 125 129, 2003.

282 The Reliability Predictions for the Avionics Equipment [12] C.Cornell, Bounds on the Reliability of Structural Systems, J. Struct. Eng. ASCE, vol. 93, pp. 171 200, 197. [13] O.Ditlevsen, Narrow Reliability Bounds for Structural Systems, J. Struct. Mech., vol. 3, pp 435 451, 1979.