A DETRMINISTIC RELIABILITY BASED MODEL FOR PROCESS CONTROL

Transcription

1 Intenational Jounal Jounal of Poduction of Poduction Technology Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 pp IAEME IJPTM I A E M E A DETRMINISTIC RELIABILITY BASED MODEL FOR ABSTRACT PROCESS CONTROL Jose K Jacob Ph.D Reseach Schola Anna Univesity Coimbatoe Tamilnadu jjsolutions@yahoo.com D. Shoui P.V. Dept. of Mechanical Engineeing Model Engineeing College Cochin Keala pvshoui@yahoo.com Reliability of pocess plants is assuming moe impotance than eve befoe fo impoving the effectiveness of the poduction pocess to meet the eve inceasing demands of the society. Pocess eliability and availability study gives us the necessay infomation fo impoving the poduction and optimizing the cost of poduction and maintenance. The eliability of a pocess unit is the pobability that the pocess pefoms its equied function in tems of quality and quantity fo a given time peiod unde given conditions. Pocess eliability analysis can povide a tue indication of the pocess potential and can also bing out vaious aspects of design that equie moe attention. Statistical contol chats is widely used pocess monitoing tool in the manufactuing industy. An algoithm to develop a contol chat is pesented in this pape. A case study based on Chocolate manufactuing company is also pesented. Key wods : Pocess eliability Availability Mean Time Between Failue ( Contol chat Failue ate 32

2 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME. INTRODUCTION. Reliability and Availability Reliability is the pobability of the equipment o pocess functioning without failue when opeated as pescibed fo a given inteval of time unde stated conditions [Kuma et al992]. High costs motivate seeing engineeing solutions to eliability poblems fo educing financial expenditues enhancing eliability satisfying customes with on-time deliveies though inceased equipment availability and by educing costs and poblems aising fom poducts that fail easily [Bainge2]. Reliability in powe plants is affected by opeating peiods i.e. between scheduled outages; budget peiods; and pea-poduction peiods [Wabuton998]. Measuing the eliabilities of plant and equipment by quantifying the annual cost of uneliability incued by the facility puts eliability into a business context. Highe-plant eliability educes equipment failue costs. Failue deceases poduction and limits goss pofits [Wabuton 998]. Failue is a loss of function when that function is needed paticulaly fo meeting finance goals. Failue equies a clea definition fo oganizations stiving to mae eliability impovements [Bainge 2]. Impoving eliability involves educing the fequency of failue. Reliability is a measue of the pobability fo failue-fee opeation i.e. it is often expessed as: t R( t exp exp( λt ( Long failue-fee peiods esult in inceased poductivity; fewe spae pats need to be stoced and less manpowe employed in maintenance activities and hence lowe costs. To the supplie of a poduct high eliability is ealized by completing a failue-fee waanty peiod unde specified opeating condition with few failues duing the subsequent design life of the poduct [Bainge & Webe 996]. Inceased availability deceased down-time smalle maintenance costs and lowe seconday-failue expenditues esult in bigge pofits. While geneal calculations of eliability ae based on consideations of the initial failue-mode which may be temed infant motality (deceasing failue ates then with time o wea-out mode (i.e. inceasing failue ates then with time. Key paametes descibing eliability ae mean time to failue mean time between/befoe epais mean 33

3 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME life of components failue ate and the maximum numbe of failues in a specific timeinteval. eliabilit y + uneliability (2 Weibull Distibution Exponential Distibution.2 Contol Chat Figue Bath Tub Cuve The main pupose statistical pocess contol is to impove quality and poductivity. One of the instument that fom quality tool set is the contol chat. Contol chats ae efficient instuments fo checing the changes o vaiations in the pocess. Though out this tool it is intended to get a model which detects bette the vaiations in the aveage when it is necessay to contol moe sensitive pocess. Failue pocess monitoing is an impotant issue fo complex o epaiable systems. It is also a common poblem fo a fleet of systems such as equipment o vehicles of the same type in a company. Statistical contol chat is a widely used pocess monitoing tool in the manufactuing industy; and it can be used in this type of failue pocess monitoing. This is usually done by plotting the numbe of failues o beadowns pe unit time such as wee o month. Standad c-chat o u-chat which is fo the monitoing of the numbe of defects in a sample can then be used fo this pupose. Howeve this pocedue equies a 34

4 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME lage numbe of failues and it is not appopiate fo application to a highly eliable system When thee is an excessive numbe of a failue the chat will signal in such an out-of-contol situations. Although the anticipated false alam pobability the pobability that the pocess is not changed when the plot shows an alam is.27% by a taditional chat it could be much highe because when the numbe of failues is Poisson distibuted nomal distibution which is used is not a good appoximation when the aveage numbe of failues is small. Moeove the lowe contol limit (LCL is usually set at zeo which is not useful because then pocess impovement cannot be detected. Chan et al. [] ecently poposed a pocedue based on the monitoing of cumulative poduction quantity between the obsevations of two defects in a manufactuing pocess. This appoach has shown to have a numbe of advantages: it does not involve the choice of a subjective sample size; it aises fewe false alams; it can be used in any envionment iespective of whethe the pocess is of high quality; and it can detect futhe pocess impovement. Since the quantity poduced between the obsevations of two defects is elated to the time between failues in eliability study this appoach can be eadily adopted fo pocess monitoing in eliability and maintenance. The use of cumulative quality is a diffeent and new appoach which is of paticula advantage in eliability and maintenance engineeing. We futhe extend the pocedue to the case when cumulative time to the th failue is used to monito the failue pocess. The implementation and intepetations ae povided and numeical examples ae used to illustate the application pocedue. 2. METHODOLOGY 2. t- Chat Fo a system in nomal opeation failues ae andom event caused by fo example sudden incease of stess and human eo. The failue occuence pocess can usually be modeled by a homogeneous Poisson pocess with a cetain intensity. Hence ou aim hee is to monito the failue pocess and detect any change of the intensity paamete. The pocedue in Ref. [] is based on the monitoing of the cumulative poduction quantity between obseving two defects in a manufactuing pocess. This 35

5 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME cumulative Poduction quantity is an exponential andom vaiable that descibes the length till the occuence of next defects in a Poisson pocess. When pocess failues can be descibed by a Poisson pocess the time between failues will be exponential and the same pocedue can be used in eliability monitoing. Hee we biefly descibe the pocedue fo eliability monitoing. Since time is ou peliminay concen the contol chat will be temed t-chat in this pape. The distibution function of exponential distibution with paamete λ is given by Ft e t t (3 The distibution function of Weibull distibution is (4 Whee: and: β is the shape paamete also nown as the Weibull slope η is the scale paamete γ is the location paamete The contol limits fo t-chat ae defined in such a manne that the pocess is consideed to be out of contol when the time to obseve exactly one failue is less than LCL T L o geate than uppe contol limit (UCL T U. When the pocess is nomal thee is a chance fo this to happen and it is commonly nown as false alam. The taditional false alam pobability is set to be.27% although any othe false alam pobability α can be used. 36

6 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME Figue 2 Nomal Distibution Cuve The actual acceptable false alam pobability should in fact depend on the actual poduct o pocess. Assuming an acceptable pobability of false alam of α the contol limits can be obtained as: T L ln α / 2 and T U ln( 2 /α (5 The median of the distibution is usually called the cente line (CL T C and it can be computed as T C ln (6 These contol limits can then be utilized to monito the failue times of components. Afte each failue the time can be plotted on the chat. If the plotted point falls between the calculated contol limits it indicates that the pocess is in the state of 37

7 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME statistical contol and no action is waanted. If the point falls above the UCL it indicates that the pocess aveage o the failue occuence ate may have deceased which esulted in an incease in the time between failues. This is an impotant indication of possible pocess impovement. If this happens the management should loo fo possible causes fo this impovement and if the causes ae discoveed then action should be taen to maintain them. If the plotted point falls below the LCL it indicates that the pocess aveage o the failue occuence ate may have inceased which esulted in a decease in the failue time. This means that pocess may have deteioated and thus actions should be taen to identify and emove them. In eithe case the people involved can now when the eliability of the system is changed and by a pope follow up they can maintain and impove the eliability. Anothe advantage of using the contol chat is that it infoms the maintenance cew when to leave the pocess alone thus saving time and esouces. It can be noted hee that the paamete λ should nomally be estimated with the data fom the failue pocess. 2.2 t Chat Monitoing the failue occuence pocess using the t chat is staightfowad. Howeve since the decision is based on only one obsevation it may cause many false alams o it is insensitive to pocess shift if the contol limits ae wide (with small value of a. To deal with this poblem we can monito using the time between failues. Denote the time to obseving the th failue by t. To monito the system based on the time between the occuences of failues we need a distibution to model the cumulative time till the th failue t : It is well nown that the sum of exponentially distibuted andom vaiables is the Elang distibution. An Elang andom vaiable is defined as the length until the occuence of defects (failues in a Poisson pocess. Then the pobability density function of T is given as: ft t exp t (! (7 38

8 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME Ft The cumulative Elang distibution is ( t exp t! (8 To calculate the contol limits of the t -chat the exact pobability limits will be used. If α is the accepted false alam is then the uppe contol limit UCL the cente line CL and the lowe contol limit LCL can be easily calculated by using Eq. (67&8 in the following manne: FUCL ( UCL! exp UCL α / 2 (9 F( CL CL exp CL.5 ( F LCL ( LCL! exp LCL α / 2 ( The decision-maing pocedue fo the t -chat emains same as the t-chat. A point plotted below the LCL signifies deteioation of pocess and waants coective action while a point plotted above the UCL denoted pocess impovement and action should be taen to identify the cause of impovement and to maintain it. Fom eliability point of view a point plotted below the contol limit points out that the time between failues may have deceased while a point plotted above the contol limit indicates that the time between failues may have inceased. 3. ALGORITHM FOR CONTROL CHART DEVELOPMENT Steps. Daw Reliability Bloc Diagam (RBD 2. Measue of each component. 39

9 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME 4 3. Calculate steady state availability of each component using the fomula MTTR A i + 4. Calculate unavailability of each component using the fomula i i A U 5. Calculate pecentage unavailability of each component. 6. Identify the citical component one which has the maximum% of unavailability. Contol chat is to be pepaed fo the citical component. 7. Calculate LCL CL and UCL fo t chat using t e t F 2 / ln α T L ( 2 /α ln T U.693 ln 2 T C 8. Calculate LCL CL and UCL fo t -chat using t t t F exp! ( 2 / exp! ( α UCL UCL UCL F.5 exp ( CL CL CL F 2 / exp! ( α LCL LCL LCL F 9. Ma LCL CL and UCL and plot the time between failues on the chat. 4. MODEL APPLIED IN A PROCESS INDUSTRY Table shows the mean time between failues of a citical component of a chocolate manufactuing company. Fist 4 ae the values ae befoe modification

10 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME and the second 4 values ae that afte modification. Figue 3 4 & 5 shows the t chat t 2 chat and t 3 chat espectively. Table Failue Data Befoe Modification Afte Modification Failue no. Figue 3 t Chat 4

11 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME LCL 4 CL 453 UCL 245 Befoe Modification Afte Modification Cumulative failue(2 failues no. Figue 4 t 2 Chat LCL 57.2 CL 7.83 UCL Befoe Modification Afte Modification Cumulative failue(3 failue no. 5. CONCLUSIONS Figue 5 t 3 Chat Until now statistical contol chats have been mostly used to monito poduction pocesses. Although eliability monitoing especially that fo complex equipment o fleet of systems is an impotant subject. In this study the focus was on the use of contol chating technique to monito the failue of components. To deal with the poblems suffeed by conventional quality contol chats the monitoing pocedue specifically based on exponential distibution was used. A new pocedue based on the monitoing of time to obseve failues efeed to as t chat was poposed and it can be moe appopiate fo eliability monitoing. The t chat diffes fom the t chat in the sense that it plots the cumulative time until obseving failues. This pocedue is useful and moe 42

12 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME sensitive when compaed with the t-chat although it will wait until failues fo a decision. These chats can be egaded as poweful tools fo eliability monitoing. t gives moe accuate esults than t chat. The contol chat fo Weibull distibution can also be established in the same way and can be used fo monitoing the ealy life and wea out life time of the pocess. Befoe conducting the modifications the changes can be simulated to analyze the failue patten so that appopiate decisions egading plant modifications can be made. REFERENCES []. Chan L.Y Xie M Goe TN. Cumulative contol chats fo monitoing poduction pocess. Int J Pod Res 2; 38(2: [2]. Goel H.D. Gievin J. Hetde.P Weijnen M.P.C. Integating eliability optimization into chemical pocess Reliability engineeing and system safety 78 ( [3]. Patic D.T.O Conno Pactical eliability engineeing John Wiley & Sons (Asia Pte. Ltd. 24. [4]. L.S.Sinath Reliability Engineeing Affiliated East-West Pess Pvt. Ltd. 99. [5]. Dale H Bestefield Quality contol Pentice Hall Inc 99. [6]. William J Kolai Ceating Quality concepts systems stategies and tools McGRAW- HILLINC 995 [7]. Shoui PV and Seejith PS. Impotance of pumping eliability in system valuation. Poceedings of the Intenational Confeence & Exhibition on Fluid Powe Technology- EMCHAFT Novembe 25 Chennai India. pp 265. [8]. Shoui PV and Seejith PS.Algoithm fo Beaeven Reliability Allocation in System Modification AIMTDR-26 IIT Rooee Decembe [9]. Cassay C.R Bowden Rao Liew L Pohl E. A. Combining peventive maintenance and statistical pocess contol: a peliminay investigation. IIE Tans2: 32:47-8 []. Kuma D Klefsjo B Kuna U. Reliability analysis of powe-tansmission cables of electic loades using a popotional-hazad model. Reliab Eng Syst Safety 992;37:

13 Intenational Jounal of Poduction Technology and Management (IJPTM ISSN (Pint ISSN (Online Volume Numbe July - Aug (2 IAEME []. Bainge PE. Reliability engineeing pinciples. Bainge & Associates Humble TX hpaul@bainge.com 2. [2]. Wabuton D Stutt JE Allsop K. Reliability-pediction pocedues fo mechanical components at design stage. Poc Inst Mech Eng 998;22(Pat E: [3]. Bainge PE Webe PD. Life-cycle cost. In: Fifth intenational confeence on pocess-plant eliabilitymaaiost Houston Westside Houston Texas Octobe 2 4;