REMAINING LIFE PREDICTION OF ELECTRONIC PRODUCTS USING LIFE CONSUMPTION MONITORING APPROACH

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1 European Mcroelectroncs Packagng and Interconnecton Symposum Cracow, Poland, June 2 REMAIIG LIFE PREDICTIO OF ELECTROIC PRODUCTS USIG LIFE COSUMPTIO MOITORIG APPROACH Satchdananda Mshra, Mchael Pecht CALCE Electronc Products and Systems Center, Unversty of Maryland, College Park, MD 742, Ted Smth, Ian Mcee and Roger Harrs QnetQ, Unted Kngdom, Abstract Varous knds of falures may occur n electronc products because of ther lfe cycle envronmental condtons ncludng temperature, humdty, shock and vbraton. Falure mechansm models are avalable to estmate the tme to falure for most of these falures. Hence f the lfe cycle envronment of a product can be determned, t s possble to assess the amount of damage nduced and predct when the product mght fal. Ths paper presents a lfe consumpton montorng methodology to determne the remanng lfe of a product. A battery powered data recorder s used to montor the temperature, shock and vbraton loads on a prnted crcut board assembly placed under the hood of an automoble. The recorded data s used n conjuncton wth physcs-of-falure models to determne the damage accumulaton n the solder jonts due to temperature and vbraton loadng. The remanng lfe of the solder jonts of the test board s then obtaned from the damage accumulaton nformaton. 1. Relablty Predcton Relablty s defned as the ablty of a product to perform as ntended (.e., wthout falure and wthn specfed performance lmts) for a specfed tme, n ts lfe cycle applcaton envronment. Over tme, technology mprovements have lead to hgher I/O counts n components and crcut cards of electronc products. Ths has resulted n sgnfcant downszng of nterconnect thcknesses, makng them more vulnerable n feld applcatons. At the same tme, ncrease n warrantes and severe labltes of electronc product falure have compelled manufacturers to predct the relablty of ther products n feld applcatons. An effcent relablty predcton scheme can be used for many purposes ncludng [1]: Logstcs support (e.g., forecast warranty and lfe cycle costs, spare parts provsonng, avalablty) Safety analyss Msson relablty estmaton End tem avalablty estmaton A relablty predcton for a product s dependent on ts structural archtecture, materal propertes, fabrcaton process, and the lfe cycle envronment. IEEE standard 1413, ttled Standard Methodology for Relablty Predcton and Assessment for Electronc Systems and Equpment presents the key parameters of mportance n relablty predcton. Defnng and characterzng the product lfe cycle envronment s often an uncertan aspect of a relablty predcton process. Product lfe cycle envronment descrbes the storage, handlng and applcaton scenaro of the product, as well as the expected severty and duraton of the load condtons for each scenaro [2]. Load condtons nclude temperature, humdty, pressure levels, vbratonal or shock loads, chemcally aggressve or nert envronments, acoustc levels, sand, dust, electromagnetc radaton levels, and loads caused by operatonal parameters such as current, voltage and power. Lfe cycle envronment characterzaton also requres knowledge of parameters lke the applcaton length, the number of applcatons n the expected lfe of the product, the product utlzaton or 136

2 non-utlzaton profle (storage, testng, transportaton), the deployment operatons, and the mantenance concept or plan. Due to uncertantes regardng the actual lfe cycle loads for a system, the common practce of desgn has been to provde a safety margn,.e., desgnng for a hgh stress and recommendng operaton at a lower value [3]. If the actual lfe cycle loads are dfferent from the desgned ones, ths desgn practce can lead to costly over desgn or hazardous under desgn, and consequently, ncreased nvestment. Sometmes product deratng may be performed to ncrease part lfe and reduce occurrence of overstress falures and hence the practce of deratng can be a way of extendng product lfe for a desred applcaton [4]. The actual lfe cycle envronment for an nservce product can be obtaned wth the help of sensors placed near and wthn the product. The physcs-offalure approach uses the materal propertes, geometry, and product archtecture along wth the lfe cycle envronmental and operatng load dstrbuton 1 to assess degradaton and predct relablty. 2. Lfe Consumpton Montorng Health montorng s a method of evaluatng the extent of a product s relablty n terms of product degradaton n ts lfe cycle envronment. By determnng the mpendng falure, based on actual lfe cycle applcaton condtons, procedures can be developed to mtgate, manage or mantan the product [5]. A products health can be determned n two ways,.e., condton montorng and lfe cycle montorng. Both methods use some combnaton of physcal degradaton (e.g., cracks, corroson, delamnaton), electrcal degradaton (e.g., ncrease n resstance, ncrease n threshold voltage), and performance degradaton (e.g., shft of the product s operatng parameters from expected values) to assess health. Methods employed for health montorng are nondestructve test (e.g., ultrasonc nspecton, lqud penetrant nspecton, and vsual nspecton) and operatng parameter montorng (e.g., vbraton montorng, ol consumpton montorng and thermography (nfrared) montorng) [7]. Condton montorng s a method of evaluatng the product s current operatng state. An example of health montorng s Boeng s extended-range twnengne operatons (ETOPS) program. Typcal examples of ETOPS are engne condton montorng (ECM) and ol consumpton montorng [8]. ETOPS operators are requred to use ECM programs to montor adverse trends n engne performance and execute mantenance to avod serous falures (e.g., events that could cause n-flght shutdowns, dversons, or turnbacks). The ECM program 1 Smulaton technques use the data recorded by the sensors and the materal geometry to fnd the load dstrbuton. montors engne parameters such as exhaust temperature, fuel and ol pressures, and vbraton. In some cases, ol consumpton data and ECM data are combned to dentfy problems n normal engne operaton. Bult-n-test (BIT) concept s another health montorng technque employed for dverse electroncs applcatons [9]. BIT s a hardware-software dagnostc mean to dentfy and locate faults. Two types of BIT concepts are employed n electronc systems, nterruptve BIT (I-BIT) and contnuous BIT (C-BIT). The concept of I-BIT s that normal equpment operaton s suspended durng BIT operaton. Such BITs are typcally ntated by the operator or durng a power-up process. The concept of C-BIT s that equpment s montored contnuously and automatcally wthout affectng normal operaton. Lfe consumpton montorng (LCM) s a health montorng method, whch can quantfy a system s degradaton from the measured lfe cycle envronment data nto lfe consumpton. The lfe consumpton montorng process nvolves contnuous or perodc measurement, sensng, recordng, and nterpretaton of physcal parameters assocated wth a system s lfe cycle envronment to quantfy the amount of system degradaton. The purpose s to support decsons related to the operaton and mantenance of the system. Arun and Pecht [] showed how to make the envronmental data (vbraton and temperature subjected to a test board) compatble wth the physcs-of-falure (PoF) models to estmate the amount of accumulated damage. The expermental analyss showed that the lfe consumpton montorng approach s possble for real lfe applcatons. The current work shows how to estmate the remanng lfe (e.g., tme n days or dstance n mles) of an electronc product from the collected envronmental parameters. Step 1: Montor approprate product parameters Envronmental (e.g., temperature, vbraton, humdty) Operatonal (e.g., voltage, power) Step 2: Conduct data smplfcaton to make sensor data compatble wth PoF model requrements Step 3: Perform physcs-of-falure damage accumulaton analyss Step 4: Estmate the remanng lfe of the product (e.g., tme n days, dstance n mles) Is the remanng-lfe acceptable? Yes o Schedule a mantenance acton Contnue montorng Fgure 1: Ths flow chart shows the four steps of lfe consumpton montorng approach for remanng lfe estmaton. A physcs-of-falure (PoF) based lfe consumpton montorng methodology to estmate the 137

3 remanng lfe has four steps (see Fgure 1). These stages are montorng crtcal parameters of the product s lfe cycle envronment, smplfcaton of the montored data, physcs-of-falure (PoF) damage accumulaton analyss, and remanng lfe estmaton based on damage accumulaton.. Montorng the product parameters of the product s lfe cycle envronment nvolves contnuous measurement of the loads that affect the relablty of the product. Data smplfcaton s the process of convertng the measured sensor data nto a form compatble wth the nput requrements of physcs-of-falure based relablty assessment models. Physcs-of-falure analyss nvolves usng the materal propertes and geometry of the product and the measured lfe cycle loads to estmate cycles to falure and hence the accumulated damage for the product n ts lfe cycle envronment. The remanng lfe of the product n terms of physcal parameters (e.g., tme n days, dstance n mles) s obtaned from the accumulated damage usng a software algorthm. 3. An Expermental Case Study To evaluate the lfe consumpton montorng methodology, a test board was placed n the underhood of a car (see Fgure 3) and hence subjected to normal drvng condtons for thrty-one days. The test board was clamped at two of ts four corners to an alumnum bracket makng the board act lke n cantlever fashon. The test board for the experment was a prnted crcut board (PCB) manufactured by ACI ApplCAD Inc. The board conssted of eght surface mount leadless nductors. A self-powered data-recordng devce called SAVER [11] (Shock and Vbraton Envronment Recorder) was used to contnuously record the shock, vbraton and temperature envronment of the test board. The temperature of the envronment was measured contnuously durng the experment by a temperature sensor (Kele s Model STR-91S two-wre strap-on RTD sensor) taped on the test board. A sngle-axs pezoelectrc accelerometer (Endevco s Model 2226C) was mounted near one of the clampng ponts of the test board to measure vbraton. The accelerometer was located to measure the acceleraton that excted the board to vbrate out-of-plane. A transstor-relay crcut was placed along wth the sensors to record any sudden change n resstance of the solder jonts. A sudden change n resstance can be an ndcaton of solder jont falure. 3.1 Lfe Cycle Envronment Temperature Due to dfferences n the coeffcents of thermal expanson of components and PWB, solder jonts used to attach the components to the PWB, are subjected to creep, whch causes plastc strans. Cyclc strans result n cumulatve cyclc fatgue damage, whch can lead to solder jont fatgue falure. Fgure 4 shows the temperature varatons on the test board as recorded by the SAVER durng the experment. Temperature based physcs-of-falure relablty assessment models estmate the cycles to falure based on type of temperature cycles. These models can estmate the amount of accumulated damage gven the number and type of cycles. Descrpton of temperature cycles requres nformaton about the maxmum and mnmum temperature, the ramp-up, ramp-down tmes and the dwell tmes. Cycle countng algorthms dentfy the cycles based on a gven temperature profle. Cycle countng methods are used to transform a tme hstory consstng of several reversals (peaks and valleys) nto an equvalent cyclc hstory. The temperature profle needs to be n the form of a sequence peaks and valleys to be used as nput to the cycle countng algorthms. Vbraton sensor Vbraton Channel 4 Channel 4 T/H channel T/H channel Temperature sensor Fgure 2: Ths pcture shows the data-recordng devce wth the external temperature and vbraton sensor. External temperature and vbraton channels were used to montor the under-hood envronment. Fgure 3: Ths pcture shows the expermental setup where the test board s mounted n the underhood envronment of a car. The vbraton sensor was glued near the clampng pont of the board and the temperature sensors were taped to the board. 138

4 Temperature data collected by the sensors s a random varaton of temperature and does not follow a peak valley sequence. The temperature profle here conssts of two sets of temperature cycles, e.g., temperature cyclng due to ambent temperature change and temperature change due to engne On-Off cycle. The data s converted to a sequence of peaks and valleys usng the ordered overall range (OOR) 2 method [13]. For ths analyss the screenng level was chosen to be %,.e., all the ponts, whch are peaks or valleys, were chosen as nput to the cycle countng algorthm. Fgure 5 shows the acqured temperature data converted to peaks and valleys. The sequence of peaks and valleys (temperature tme hstory) are converted to temperature cycles usng 2 Temperature ( o C) Tme (hrs.) Fgure 4: Ths pcture shows the temperature profle on the test board n the under-hood envronment, as recorded by the data-recordng devce. Temperature ( o C) Tme (hrs.) Fgure 5: Ths pcture shows the envronmental temperature profle converted to the peaks and valleys usng the Ordered Overall Range (OOR) method. The set of peaks and valleys were used to dentfy the number of temperature cycles. The ordered overall method (OOR) s a data smplfcaton method, whch allows the user to convert an rregular hstory nto a regular sequence of peaks and valleys (whch s essental for fatgue analyss), and also specfy the range (.e., upper lmt lower lmt) of the reversals to be elmnated. the ranflow cycle countng method [14], [15]. The ranflow cycle countng method fnds the cycles and necessary nformaton (e.g., maxmum, mnmum temperature and the tme ranges). 3.2 Lfe Cycle Envronment - Vbraton Vbraton that excted the prnted crcut board s measured by the accelerometer n the form of acceleraton (g vales). Hence the data recorded by the data-recordng devce s n the tme doman 3. But the physcs-of-falure relablty assessment models requre nformaton about vbraton n frequency doman, whch s typcally represented as power spectral densty (PSD) as a functon of frequency. The power spectral densty s calculated from the sampled data (.e., the type of data recorded by SAVER) usng the Cooley-Tukey method, whch s based on fast fourer transform (FFT) of the orgnal sampled acceleraton data [16]. Fgure 6 shows the PSD vs. frequency of the vbraton. Ths vbraton data was used for vbraton analyss. Power Spectral Densty (g 2 /Hz.) 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-6 1.E-7 1.E-8 1.E+ 1.E+1 1.E+2 1.E+3 Frequency (Hz.) Fgure 6: Ths pcture shows the Power Spectral Densty (PSD) vs. frequency plot for the clampng ponts of the board. Ths was the vbraton that excted the board. The dsplacement of each component was estmated through numercal analyss usng cacepwa 4. Fgure 6 shows the estmated dsplacement of the board caused by vbraton. From the dsplacement nformaton, radus of curvature of the board was estmated to be almost the same. 3.3 Lfe Cycle Envronment Shock Durng the experment the car faced an accdent, where t was ht from the back by another car. Ths resulted n two shock (vbraton) profles subjected to the board for small perods of tme (n the order of mll-seconds). A shock s dfferent from vbraton n a sense that the 3 Sgnals can be analyzed n several domans, such as the frequency, tme, and ampltude domans. Translaton of nformaton from one doman to another may often be requred to get more nformaton from the sgnal. 4 CalcePWA s a vrtual qualfcaton tool developed by CALCE Electronc Products and Systems Center, Unversty of Maryland, College Park. 139

5 acceleraton values are very hgh compared (at least hgher by an order) to the vbraton envronment and t acts over a very small perod of tme. Fgure 8 shows the recorded shock at the nstant of crash. In ths case the maxmum value of acceleraton s 23g (n both drectons) as compared to 2g n case of recorded normal engne vbraton. Fgure 9 shows the shock profle caused durng ds-engagement of the cars, whch was after approxmately mnutes of the frst shock. Clampng Ponts Fgure 7: Ths pcture shows board dsplacement estmated by calcepwa caused by the vbraton profle. Falure due to shock s consdered to be an overstress mechansm and overstress models are usually used for vbratonal shocks to fnd out whether the board can sustan the mpact or not. But for lfe consumpton montorng we requre to estmate the accumulated damage. For ths purpose the acceleraton data was converted to frequency doman. An overstress analyss was also conducted for both the shock profles wth the maxmum acceleraton values, whch showed no overstress falure. Acceleraton (g) Tme (m. sec.) Fgure 8: Ths pcture shows the shock profle that the board was subjected at the nstant of the accdent. The acceleraton values were as hgh as +/- 23 g. 3.4 Physcs-of-falure Analyss The physcs-of-falure approach of relablty predcton s based on the fact that fundamental mechancal, electrcal, thermal, and chemcal processes govern falure mechansms. The objectve of a physcs-of-falure analyss n the lfe consumpton montorng methodology s to determne when a specfc falure mechansm wll occur for a product n a gven envronment n terms of tme or number of cycles. A physcs-of-falure analyss conssts of the three steps,.e., desgn capture, dentfcaton of potental falure modes, mechansms, stes and relablty assessment. Acceleraton (g) Tme (m. sec.) Fgure 9: Ths pcture shows the shock profle that the board was subjected to durng ds-engagement of the cars. Desgn capture s the process of collectng geometrcal (dmensonal) and materal nformaton about a product to generate a model of the product. Ths step nvolves characterzng the product at all levels,.e., parts, crcut cards, as well as physcal nterfaces. The potental falure mode dentfcaton step nvolves usng the geometry and materal propertes of the product together wth the measured lfe cycle loads actng on the product to dentfy the potental falure mechansms, falure stes (e.g., part nterconnects, board metallzaton, and external connectons), and falure modes (e.g., electrcal shorts or opens) n the product. Ths task s best performed through vrtual qualfcaton, whch s a smulaton-based methodology used to dentfy and rank the potental falure mechansms. Relablty assessment step nvolves dentfcaton of approprate physcs-of-falure models for the dentfed falure mechansms. A load-stress analyss s conducted usng materal propertes, product geometry, and the lfe cycle loads. Wth the computed stresses, and the falure models, an analyss s conducted to determne the cycles to falure and then the accumulated damage s estmated usng a damage model Damage Accumulaton Damage s defned as the extent of a part or product s degradaton or devaton from ts normal operatng state. The am of damage assessment s to convert the number of cycles to falure values obtaned from the physcs-offalure analyss nto a metrc for lfe consumpton. Many models have been proposed for quantfyng damage caused by operaton at a gven stress level and for addng damage ncrements to predct falure under mult-loadng condtons. The Palmgren-Mner cumulatve damage theory, whch s a lnear damage theory, was used for 14

6 analyss. It was proposed by Palmgren n 1924 and later developed by Mner n 1945 [17]. The term lnear refers to the algebrac addton of the fractons of the total consumed lfe and the exponent of unty used for the damage fracton, and not to the lnearty of the damage process. The Palmgren-Mner hypothess states that the damage fracton (D ) at any stress level S s lnearly proportonal to the rato of the number of cycles of operaton (n ) to the total number of cycles that would produce falure ( ) at that stress level. In other words, and falure s predcted to occur f Accumulated damage at the end of each day of experment was estmated usng the physcs-of-falure models and Palmgren-Mner theory 5. The results obtaned are shown n the form of a bar chart (see Fgure ). 7%, 61% and 16% damage accumulaton was estmated because of temperature, vbraton and shock respectvely. Accumulated Damage (%) D = (1) j= 1 n n j j 1 Tme n Use (days) Damage due to temperature Damage due to shock Damage due to vbraton (2) Fgure : Ths pcture shows the accumulated damage estmated usng calcepwa and Mner s rule. The damage of the solder jonts was tracked expermentally n terms of resstance ncrease of the jonts. The resstances of the jonts were measured everyday durng the experment. The measurements were done when the car s off. An event detector crcut was put n seres wth the components (lead less nductors) to track any abrupt change n resstance. The event detector recorded four events, where the resstances of the crcut ncreased by 5% of the ntal value. Fgure 11 shows the resstance change of the crcut wth tme. The pcture 5 Estmated damage of % damage corresponds to the predcted end-of-lfe of the board. also shows the tme where there were changes n resstance for a short duraton of tme (n the order of seconds). Ths data was collected from the transstorrelay crcut placed to montor sudden change n resstance. Resstance (ohms) (28 o C) Resstance across the solder jonts ncreased by 5% (26 o C) (15 o C) (22 o C) (24 o C) (25 o C) (13 o C) (22 o C) (23 o C) (28 o C) (24 o C) Tme n Use (days) Fgure 11: Ths pcture shows the resstance values of the solder jonts. The fgures n brackets denote the temperatures at whch the measurement was done Remanng Lfe Predcton Remanng lfe predcton s the process of estmatng the remanng lfe (e.g., the tme n days, dstance n mles) through whch the product can functon relably, based on the damage accumulaton nformaton. Two dfferent methods can be used to estmate the remanng lfe of a system (tme n days s consdered as the unts for ths experment). The total lfe of the system under the gven lfe cycle envronment can be calculated drectly usng the accumulated damage fracton (calculated usng Mnor rule) at any pont of tme. It s obtaned smply by dvdng the number of days n the lfe cycle envronment wth the accumulated damage fracton. If the number of days n the lfe cycle envronment s one, then the nverse of accumulated damage fracton gves the total lfe. umber of days n the lfe cycle envronment s then subtracted form the total lfe to get the remanng lfe. Thus the followng equaton can be used to get the remanng lfe at any pont: RL 1 = ADR where RL s the predcted remanng lfe at the end of th day and ADR s the accumulated damage raton tll day. If there s a wde varaton n system usage, undesred fluctuatons n predcted remanng lfe may occur by usng the equaton shown n equaton 3. We may see an ncrease n remanng lfe, whch s many tmes confusng. Increase n remanng lfe occurs n the calculaton when the usage on a partcular day s much below the usual value there by brngng down the average damage per day. (3) 141

7 The remanng lfe at the end of a partcular day can also be estmated by subtractng the lfe consumed on that day from the predcted remanng lfe on the prevous day. Ths approach makes the use of an teratve formula to fnd out the remanng lfe. For calculaton on a partcular day the total lfetme s assumed to be same as that of the prevous day. where RL s the remanng lfe at the end of day, TL s predcted total lfe at the end of day and DR s the damage rato accumulated at the end of day. The teratve method (equaton 4) can be used n cases where the system usage s wdely dfferent. Fgure 12 shows the estmated remanng lfe for the experment usng the teratve method. We only need the remanng lfe at the end of prevous day nstead of all the data, whch decreases the requred storng space. The rest data can ether be erased or kept n back up memory. Predcted Remanng Lfe (days) 5 4 RL (4) = RL 1 DR * TL 1 Car Accdent Tme n Use (days) Fgure 12: Ths pcture shows the predcted remanng lfe as a functon of tme. The remanng lfe predcton was done usng the teratve method 4. Summary Ths paper demonstrates a practcal lfe consumpton montorng methodology appled to an automoble envronment. A test board was subjected to the under the hood envronment (temperature, vbraton and shock) of an automoble. The collected data was made compatble wth physcs-of-falure models. Damage accumulaton was calculated usng Mner s rule, to calculate the remanng lfe of the test board. The method for remanng lfe estmaton has been dscussed n the paper. 5. Acknowledgement The research for ths paper was performed at the CALCE Electronc Products and Systems Center of the Unversty of Maryland. The Center provdes a knowledge and resource base to support the development of compettve electronc components, products and systems. The Center s supported by more than electronc products and systems companes from all sectors, ncludng telecommuncatons, computer, avoncs, automotve, and mltary manufacturers. 6. References [1] IEEE Relablty Socety, IEEE Std 1413 IEEE Standard Methodology for Relablty Predcton and Assessment for Electronc Systems and Equpment, ew York, January [2] Ramakrshnan, A., Syrus, T., and M. Pecht, Electronc Hardware Relablty, The Modern Mcrowave and RF Handbook, pp. 3-2 to 3-121, CRC Press, Boca Raton,. [3] Beder, S., Makng Engneerng Desgn Sustanable, Transactons of Mult-Dscplnary Engneerng Australa, pp , Vol. GE17, o. 1, June [4] Lall, P., Pecht, M., and E. Hakm, Deratng Gudelnes for Temperature-Tolerant Desgn of Mcroelectroncs, 4th European Symposum on Relablty of Electron Devces, Falure Physcs and Analyss, Bordeaux, France, October 4-7, [5] Kelkar,., Dasgupta, D., Pecht, M., Knowles, I., Hawley, M. and D. Jennngs, Smart Electronc Systems for Condton-Based Health Management, Qualty and Relablty Engneerng Internatonal, Vol. 13, pp. 3-7, [6] Rao, B.K.., Handbook of Condton Montorng, pp. 1-12, Elsever Scence Publshers Ltd., Oxford, [7] Mobley, R.K., An Introducton to Preventve Mantenance, pp. 1, Van ostrand Renhold, ew York, 199. [8] The Boeng Company, ETOPS Mantenance, Aero Magazne, o. 7, July [9] M. Pecht, M. Dube, M. atshan, and I. Knowles, An Evaluaton of Bult-In Test, IEEE Transactons on Aerospace and Electronc Systems, Vol. 37, o. 1, pp , January 1. [] Ramakrshnan and M. Pecht, Implementng a Lfe Consumpton Montorng Process for Electronc Product, CALCE EPSC nternal publcaton, 1. [11] Dallas Instruments, SAVER User s Manual, Dallas, Texas, February. [12] Fuchs, H.O., elson, D.V., Burke, M.A., and T.L. Toomay, Shortcuts n Cumulatve Damage Analyss, SAE atonal Automoble Engneerng Meetng, Detrot, [13] Wetzel, R.M., Fatgue Under Complex Loadng: Analyses and Experments, The Socety of Automotve Engneers, Inc., Warrendale, [14] Collns, J., Falure of Materals n Mechancal Desgn, John Wley & Sons, ew York, [15] Anza, H., Algorthm of the Ranflow Method, pp. 11-, The Ranflow Method n Fatgue, Butterworth-Henemann, Oxford, [16] Bendat, S.J. and A.G. Persol, Random Data: Analyss and Measurement Procedures, Wley- Interscence, ew York, [17] Mner, M.A., Cumulatve Damage n Fatgue, Journal of Appled Mechancs, pp. A-159 to A-164, September