modelling of predictive maintenance for a periodically inspected system

Available online at www.sciencedirect.com ScienceDirect Procedia CIRP 59 (2017) 95 – 101 The 5th International Conference on Through-life Engineering Services (TESConf 2016) Modelling of predictive maintenance for a periodically inspected system Ahmed Razaa, Vladimir Ulanskyb,* Department of the President’s Affairs, Overseas Projects and Maintenance, P.O Box: 372, Abu Dhabi, UAE b National Aviation University, Kosmonavta Komarova Avenue, Kiev 03058, Ukraine a * Corresponding author Tel.: +38-0632754982 E-mail address: vladimir_ulansky@nau.edu.ua Abstract Predictive maintenance includes condition monitoring and prognosis of future system condition where maintenance decision-making is based on the results of prediction In this paper, the modelling of predictive maintenance is conducted It is assumed that the system is periodically checked by using imperfect measuring equipment The decision rule for the predictive checking is formulated and the probabilities of correct and incorrect decisions are derived The effectiveness of the predictive maintenance is evaluated by the average availability and downtime cost per unit time The mathematical models are proposed to calculate the maintenance indicators for an arbitrary distribution of time to failure The proposed approach is illustrated by determining the optimal number of predictive checks for a specific stochastic deterioration process Numerical example illustrates the advantage of the predictive maintenance compared to the corrective maintenance 2016The The Authors Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license ©2016 © Authors Published by Elsevier B.V This Peer-review under responsibility of the Programme Committee of the 5th International Conference on Through-life Engineering Services (http://creativecommons.org/licenses/by-nc-nd/4.0/) (TESConfunder 2016) Peer-review responsibility of the scientific committee of the The 5th International Conference on Through-life Engineering Services (TESConf 2016) Keywords: Availability; Corrective maintenance; Decision rule; False failure; Predictive checking; Prognostics; Remaining useful life; Undetective failure Introduction Currently, the most promising strategy of maintenance for various technical systems and production lines is the predictive maintenance (PM), which can be applied to any system if there is a deteriorating physical parameter like vibration, pressure, voltage, or current that can be measured This allows to recognize approaching troubles, to predict wear or accelerating aging and to prevent failure through the repair or replacement of the affected component Predictive maintenance is based on the prognostic and health management technology, which supposes that the remaining useful life of equipment can be predicted However, due to uncertainty of prognostics there could be wrong decisions regarding the remaining time to failure The growing interest to PM is evident from the large number of publications related to various mathematical models and implementation techniques Let us consider some references related to the modelling of the PM In [1], a PM policy for a continuously deteriorating system subject to stress is developed Condition-based maintenance policy is used to inspect and replace the system according to the observed deterioration level A mathematical model for the maintained system cost is derived In [2], the predictable reactive maintenance policies are studied based on a fatigue crack propagation model of the wind turbine blade considering random shocks and dynamic covariates In [3], a PM method is developed to determine the most effective time to apply maintenance to equipment and study its application to a real semiconductor etching chamber The PM decision is based on the likelihood of the predicted health condition, which exceeds a certain maintenance threshold In [4], the costs model is analysed where the costs include small repair cost, PM cost and productive loss An optimal model of PM strategy is further proposed to overcome the shortcoming of PM model with identical period In [5], a PM structure for a gradually deteriorating single-unit system is considered The decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon In [6], a data-driven machine prognostics approach is considered to predict machine’s health condition and describe machine degradation A PM model is constructed to decide machine’s optimal maintenance threshold and 2212-8271 © 2016 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the The 5th International Conference on Through-life Engineering Services (TESConf 2016) doi:10.1016/j.procir.2016.09.032 96 Ahmed Raza and Vladimir Ulansky / Procedia CIRP 59 (2017) 95 – 101 maintenance cycles In [7], a PM model for the deteriorating system with semi-Markov process is proposed A method to determine the best inspection and maintenance policy is developed In [8], a discriminant function is developed on the basis of the representation of the observed system degradation process as a discrete parameter Markov chain In [9], a multiple classifier machine learning methodology for PM is considered The proposed PM methodology applies dynamical decision rules to maintenance management It should be noted that all considered models of PM not take into account the probabilities of the correct and incorrect decisions made by the results of the predictive checks (PCs) In this paper, a new PM model is developed for determining optimal periodicity of PCs A decision rule is proposed for inspecting the system condition, which is based on the evaluation of the remaining time to failure Based on this decision rule, general expressions are derived for calculating the probabilities of correct and incorrect decisions made by the results of the PCs The effectiveness of the PM is evaluated by such indicators as average availability and average downtime cost per unit time (k+1)τ, the system is judged as unsuitable for operation in the time interval [kτ, (k+1)τ] By the results of the PC at time kτ the following decisions are made: to allow the j-th system to be used until the next PC at the instant (k + 1)τ if ξj,k ≥ (k+1)τ; to restore the j-th system if ξj,k < (k+1)τ The mismatch between the solutions of (2) and (3) results in the appearance of one of the following mutually exclusive events by the results of the PC at the instant kτ: Nomenclature ­° h kW ®kW  ; d k  1W ¯° PC PDF PM predictive check probability distribution function predictive maintenance Decision rule Assume that the state of a system is completely determined by the value of the parameter X (t), which is a non-stationary random process with continuous time The system should operate over a finite horizon T and is checked with prediction of condition at discrete time kτ (݇ ൌ തതതതത ͳǡ ܰ) When the system state parameter exceeds threshold FF, the system passes into the failed state The measured value of X(t) at time kτ is expressed as follows: Z kW X kW  Y kW , (1) where Y(kτ) is the measurement error of the system state parameter at time kτ Assume that random variable Ξ (Ξ ≥ 0) denotes the failure time of a system with probability distribution function (PDF) ω(ξ) Let Ξk be a random assessment of Ξ based on the results of the PC at time kτ Random variables Ξ and Ξk are the smallest roots of the following stochastic equations: X t  FF Z kW  FF (2) (3) Let ξj,k be the realisation of Ξk for the j-th system Then, when carrying out the PC at the instant kτ the following decision rule is used: if ξj,k ≥ (k+1)τ, the system is judged to be suitable for operation in the time interval [kτ, (k+1)τ]; if ξj,k < ­ h1 kW ®; ! k  1W ¯ ­ h2 kW ®; ! k  1W Đ k Ãẵ ă ;i ! i  1W ắ âi ê k 1 ẵ ô ;i ! i  1W ằ ắ (5) ¼¿ ; k d k  1W ­ h3 kW ®kW  ; d k  1W ¯ (4) § k Ãẵ ă ;i ! i  1W ắ ©i ¹¿ ; k d k  1W (6) ê k 1 ẵ ô ; i ! i  1W ằ ắ (7) ẳ h5 kW đ; d kW êk ẵ ô ;i ! i  1W ằ ắ ẳ h6 kW ®; d kW ¯ ; k d k  1W (8) ê k 1 ẵ ô ;i ! i  1W ằ ắ (9) ẳ Events h1(kτ), h4(kτ) and h6(kτ) correspond to the correct decisions by the results of the PC at time kτ Event h2(kτ) is the joint occurrence of two events: the system is suitable for use over the interval [kτ, (k+1)τ] and by the results of the PC it is judged as unsuitable We define event h2(kτ) as a ‘false failure’ Events h3(kτ) and h5(kτ) we define as ‘undetected failure 1’ and ‘undetected failure 2’, respectively System states Let us consider the stochastic process S(t), which characterizes the state of the system at an arbitrary instant of time t: S1, if at time t, the system is used as intended and is in the operable state; S2, if at time t, the system is used as intended and is in an inoperable state (unrevealed failure); S3, if at time t, the system is not used for its intended purpose because the PC is carried out; S4, if at time t, the system is not used for its intended purpose because event h2 has occurred and a ‘false corrective repair’ is performed; S5, if at time t, the system is not used for its intended purpose because either h3 or h6 event has occurred and a ‘true corrective repair’ is performed Further we assume that process S(t) is the regenerative stochastic process When determining maintenance efficiency indicators we use a well-known property of the regenerative stochastic processes [10], which is based on the fact that the 97 Ahmed Raza and Vladimir Ulansky / Procedia CIRP 59 (2017) 95 – 101 fraction of time for which the system is in the state Si (݅ ൌ തതതതത ͳǡ ͷ) is equal to the ratio of the average time spent in the state Si per regeneration cycle to the average cycle duration We designate Ti as the time spent by the system in the state Si ( ݅ ൌ തതതത ͳǡͷ ) Obviously, Ti is a random variable with the expected mean time M[Ti] The average duration of the regeneration cycle is given by M >T0 @ ¦ M >T @ (10) i i Probabilities of correct and incorrect decisions Let us define the conditional probabilities of correct and incorrect decisions made at carrying out the PC under the assumption that failure of the system occurs at time ξ and kτ  ξ d k  τ, k =1, N , T N  1W (11) The conditional probability of a ‘false failure’ by the results of carrying out the PC at time ντ (ߥ ൌ തതതതതതതതതത ͳǡ ݇ െ ͳ) is formulated as follows: PU S τ,(ν  1)τ ;ντ ξ ­ ν 1 P ® ; i ! i  τ ¯i ½ ; ν d ν  τ ; ξ ¾ (12) ¿ The conditional probability of the event ‘operable system is correctly judged unsuitable’ by the results of carrying out the PC at time kτ (݇ ൌ തതതതത ͳǡ ܰ) is formulated as follows: PU O τ,(k  1)τ ; k τ ξ ­ k 1 P ® ; ν ! ν  τ ¯ν ½ ; k d k  τ ; ξ ¾ (13) ¿ The conditional probability of the event ‘undetected failure 1’ by the results of carrying out the PC at time kτ is formulated as follows: PS O τ,(k  1)τ ; k ưk ẵ P đ ; ! ν  τ ; ξ ¾ ¯ν ¿ ẵ P đ ;i ! i  τ ; ξ ¾ ¯i ¿ (15) ­ j 1 P ® ; i ! i  τ ¯i ½ ; j d j  ; ắ (16) ưN ẵ P ® ;i ! i  1W ; ξ ¾ ¯i ¿ (17) To determine the probabilities (12)-(17), we introduce the തതതതതതത conditional joint PDF of random variablesȩ ଵ ǡ ȩ௞ , under the condition that Ξ = ξ, which we denote as ȳ଴ ሺɌതതതതതത ଵ ǡ Ɍ௞ ‫ פ‬Ɍሻ As can be seen from (3), Ξk is a function of random variables Ξ and Y(kτ) The presence of Y(kτ) in (3) results in appearing a random measurement error Λi with respect to the time to failure Ξ at time point iτ, which is defined as follows: /i ;i  ;, i 1, k (18) Between random variables Ξ (0 T3 @ W pc Ư j ³ ³ ³ f a , a | ξ da da f (35) f ª N 1 W pc ôƯ kPU S ,(k  1) ; kτ -  NPS S τ,( N  2)τ ;( N  1) NW k ằẳ u Z - d- , (36) A similar change of variables in (20)-(24) results in ( k 1)τ-ξ f PU O τ,(k  1)τ ; k τ ξ PS O τ,(k  1)τ ; k τ ξ f ³ ³ ³ f a , a | ξ da da / f kτ-ξ 2τ-ξ f f f / f k (29) k (30) k ³ ³ ³ f a , a | ξ da da ( k 1)τ-ξ kτ-ξ PS S τ,(ν  1)τ ; ντ ξ 1 k 2τ-ξ f where τpc is the mean time of a PC The mean time of staying the system in the state S4 is ª N ( k 1)W k 1 M >T4 @ W fr ôƯ Ư PU S ,(  1) ; - Z - d-  ôơ k kW Q f ³ ³ ³ f a , a | ξ da da / (ν 1)τ-ξ ντ-ξ ν 1 ν (31) 2τ-ξ º f N ³ ¦ P τ,(k  1)τ ; kτ - Z - d- »¼ , (37) US T k PU I τ,( j  1)τ ; jτ ξ PS I W , N  1W ; Nτ ξ ( j 1)τ-ξ f f ³ ³ ³ f jτ-ξ 2τ-ξ f f f f / a1 , a j | ξ da1da j (32) ³ ³ ³ f a , a | ξ da da / ( N 1)τ-ξ N τ-ξ 1 N N (33) 2τ-ξ The mean time of staying the system in the state S1 is determined as follows: N ª k ¬ ( k 1)W k 1 ντP τ,(ν  1)τ ; ντ -  kW P τ,(k  1)τ ; k -  Ư ôô Ư W Q US k UO f ª - PS O τ,(k  1)τ ; k τ ξ º Z - d-  ôƯ kPU S ,(k  1) ; k -  ẳ ơk N T TPS S τ,( N  1)τ ; Nτ - º Z - dẳ (34) M >T2 @ ê N Ư ô Ư j  - PU I τ,( j  1)τ ; jτ -  T  - u k kW ¬ j k 1 T º ³ Z - d- »¼ , PS I W , N  1W ; Nτ ξ º Z - d-  ³ T  - PS O τ,( N  1)τ ; N τ - u ¼ NW (38) where τtr is the mean time of a ‘true corrective repair’ Indicators of maintenance efficiency തതതതതതതതതതതതതതതത When the mean times ‫ܯ‬ሾܶ ଵ ሿǡ ‫ܯ‬ሾܶହ ሿ are known we can identify any of the maintenance efficiency indicators Let us consider some of indicators Average availability is one of the key performance indicators used in nuclear power plants [11], aviation and military systems [12] For this model the average availability is A M [T1 ] M [T0 ] The mean time spent by the system in the state S2 is N 1 ( k 1)W ª N ( k 1)W M >T5 @ W tr ôƯ ³ PS S τ,(k  2)τ ;(k  1)τ - Z - d-  ôơ k kW W Expected up and down times M >T1 @ where τfr is the mean time of a ‘false corrective repair’ The mean time of staying the system in the state S4 is (39) Average total down time (TDT) can be defined as M [TDT ] T ^M [T0 ]  M [T1 ]` M [T0 ] Average downtime cost per unit time is expressed as (40) 99 Ahmed Raza and Vladimir Ulansky / Procedia CIRP 59 (2017) 95 – 101 M >C @ ¦ C M >T @ i M [T0 ] i (41) i Designating Yi = Y(iτ) (i = 1, 2, ), we solve the stochastic equations A0  A1Ξ FF Optimal number of predictive checks The problem of determining the optimal number of the PC Nopt depends on the selected optimization criterion By the criterion of maximum average availability Nopt is determined by solving the following problem: A0  A1Ξi +Yi FF  A0 Nopt M êơC N ẳ (43) N /i A0  A1t , (44) where A0 is the random initial value of X(t) and A1 is the random rate of parameter deterioration defined in the interval from to Ğ It should be noted that a linear model of a stochastic deterioration process was used in many previous studies for describing real physical deterioration processes For example, the linear regressive model studied in [13] describes a change in radar output voltage with time, and a linear model was used to represent a corrosion state function in [14] Let us determine the conditional PDF ݂ஃ ൫ɉതതതതതതത ଵ ǡ ɉ௞ ‫ פ‬Ɍ൯ for the stochastic process given by (44) If തതതതതതതതതതതതതതത ܻሺ߬ሻǡ ܻሺ݇߬ሻ are independent random variables, then f f / λ1 , λ k ξ ³ f a ω ξ a êơ FF  a ẳ 0 k u ` (45) PDF of the random variable Y(iτ), and ω ξ a0 is the conditional PDF of the random variable Ξ under the condition that A0 = a0 Let us prove relation (45) Since തതതതതതതതതതതതതതത ܻሺ߬ሻǡ ܻሺ݇߬ሻ are independent, then for the stochastic process (44) we can write ; (52) Yi ; FF  A0 /i (53) For any values Yi = yi, A0 = a0 and Ξ = ξ, the random variable Λi with a probability of has only one value Therefore, conditional PDF of random variables തതതതതതതത Ȧଵ ǡ Ȧ௞ with respect to തതതതതതത ଵ ǡ ௞ , A0 and Ξ is the Dirac delta function: f λ1 ,λ k y1 , yk ,, a0 k êơ   y ξ FF  a º¼ i (54) i i Using the multiplication theorem of PDFs, we find the joint PDF of the random variables തതതതതതതത Ȧଵ ǡ Ȧ௞ , തതതതതതത ଵ ǡ ௞ , Ξ and A0 f y , y ,ξ, a f λ ,λ k y1 , yk ,ξ, a0 k (55) Taking into account (54), expression (55) is converted to  FF ξ º¼ λi da0 ω ξ , f λ1 , λ k | ξ, a0 FF  A0 f λ1 ,λ k , y1 , yk ,ξ, a0 where f(a0) is the PDF of the random variable A0, ψ(yi) is the (51) Substituting (52) to (51), we get i (50)  Yi A1 A1 Assume that the deterioration process of a one-parameter system is described by the monotonic stochastic function A1 Solving (47) in respect to A1 gives 8.1 Deterioration process modelling k (49) By substitution of (49) and (50) into (18) we obtain Example ^êơ a A1 FF  A0  Yi ;i If the criterion of the minimum average downtime cost per unit time is used, then (48) (42) N X t FF in respect to Ξ and Ξi ; Nopt Ÿ max A N (47) i 1 k i i i Since random variables തതതതതതത ଵ ǡ ௞ are assumed to be independent and not dependent on Ξ and A0 then f y1 , yk ,ξ, a0 k ω ξ, a0 – ψ yi (57) i Substituting (57) into (56), we obtain k – f λi | ξ, a0 f y , y ,, a êơ  y ξ FF  a º¼ (56) k f λ1 ,λ k , y1 , yk ,ξ, a0 (46) f λ1 ,λ k , y1 , yk ,ξ, a0 k Z ξ, a0 – ψ yi δ êơ i  yi FF  a0 ẳ (58) i 100 Ahmed Raza and Vladimir Ulansky / Procedia CIRP 59 (2017) 95 – 101 Integrating (58) by the independent variables തതതതതതത ଵ ǡ ௞ , we get f λ1 ,λ k ,ξ, a0 k f ω ξ, a0 ui êơ i  ui ξ FF  a0 º¼ dui (59) i f We represent the joint PDF of the random variables Ξ and A0 as follows: f a0 ω ξ a0 ω ξ, a0 (60) Taking into account (60), expression (59) takes the form f λ1 ,λ k ,ξ, a0 f k f a0 ω ξ a0 – ³ ψ ui u Assume T = 3000 h, τpc = τfr = h, τtr = 10 h, m1 = 0.002 kV/h, σ1 = 0.00085 kV/h, a0 = 16 kV, and σy = 0.25 kV Let us now find the optimal number of PCs Nopt that maximizes the system’s average availability Figure shows the average availability versus number of checks for two different types of maintenance Curve corresponds to the PM with Nopt = 3, τopt = 750 h and A(Nopt) = 0.989 Curve corresponds to the maintenance based on the periodic operability checking This type of maintenance can be classified as corrective maintenance Here, Nopt = 16, τopt = 176.5 h and A(Nopt) = 0.923 Thus, the use of the PM instead of the corrective maintenance results in increasing average availability and decreasing the number of optimal checks i f (61) êơ i  ui ξ FF  a0 º¼ dui Consider the integral standing under the sign of the product in (61) Given the properties of the delta function, we can write f u êơ  u FF  a ẳ du i i i i f Đ FF  a0 à êĐ a0  FF à ă ôă i ằ (62) â ơâ ẳ Substituting (62) into (61) gives f λ1 ,λ k ,ξ, a0 § FF  a0 à f a0 a0 ă â k k êĐ a0  FF à i ằ (63) ơâ ẳ ôă i Integrating the PDF (63) over the variable a0, we determine f λ1 ,λ k ,ξ f § FF  a0 · ³0 f a0 a0 ăâ áạ k êĐ a  FF à ôă i ằda0 (64) ẳ i ơâ k Using the multiplication theorem of PDFs, we find f / λ1 ,λ k ξ f λ1 ,λ k ,ξ ω ξ (65) Finally, by substitution of (64) to (65) we obtain (45) 8.2 Numerical calculations As shown in [13], if the output voltage of a certain type of radar transmitter exceeds the threshold FF = 25 kV, it needs maintenance to avoid breakdown Let A1 be a normal random variable and A0 = a0 In this case, the PDF of the random variable Ξ is given by [15] ωt m1σ12t  σ12t FF  a0  m1t 2S σ13t °­ FF  a0  m1t °½ exp đ ắ , (66) 212t where m1 = E[A1] and ߪଵ ൌ ξܸܽ‫ݎ‬ሾ‫ܣ‬ଵ ሿ Fig Average availability versus number of checks: (1) predictive checks; (2) operability checks Conclusions In this paper, we have described a mathematical model of predictive maintenance based on prognostics and health management New approach has been proposed to determining the optimal periodicity of predictive checking, which is based on the use of the PDF of random errors in measurement of remaining useful life New equations have been derived for calculating the probabilities of correct and incorrect decisions made by the results of a predictive checking Mathematical expressions have been derived to determine the mean times spent by the system in various states during operation and maintenance for an arbitrary distribution of time to failure On the example of a linear random process of degradation, the procedure of determining the joint PDF of random errors in the measurement of the remaining useful life has been shown By numerical calculations it has been shown that predictive maintenance is unconditionally more efficient than corrective maintenance because it provides a higher average availability at a smaller number of checks Ahmed Raza and Vladimir Ulansky / Procedia CIRP 59 (2017) 95 – 101 References [1] Deloux E, Castanier B, and B´erenguer C Predictive maintenance policy for a gradually deteriorating system subject to stress Reliab Eng Syst Saf 2009; 94: 418-431 [2] Zhu W, Fouladirad M, and Bérenguer C A Predictive Maintenance Policy Based on the Blade of Offshore Wind Turbine In Proc of 2013 IEEE Reliab and Maintainab Symposium (RAMS) Orlando FL; 2013 p 1-6 [3] Le T, Luo M, Zhou J, and Chan HL Predictive maintenance decision using statistical linear regression and kernel methods In Proc of the 2014 IEEE Emerging Technology and Factory Automation Barcelona; 2014 p 1-6 [4] Zhikun H Predictive maintenance strategy of variable period of power transformer based on reliability and cost In Proc of 25th Chinese Control and Decision Conference (CCDC) Guiyang; 2013 p 4803-4807 [5] Grall A, Dieulle L, Berenguer C, and Roussignol M.Continuous-time predictive-maintenance scheduling for a deteriorating system IEEE Transactions on Reliab, 51(2), 141-150 [6] Liao W and Wang Y Data-driven Machinery Prognostics Approach using in a Predictive Maintenance Model J of Computers 2013; 8(1): 225-231 [7] Wang N, Sun S, Si S, and Li J Research of predictive maintenance for deteriorating system based on semi-markov process In Proc of 16th IEEE Int Conf on Industrial Engineering and Engineering Management Beijing; 2009 p 899-903 [8] Langer Y, Urmanov A, and Bougaev A Predictive maintenance policy optimization by discrimination of marginally distinct signals In Proc of IEEE Conference on Prognostics and Health Management (PHM) Gaithersburg; 2013 p 1-5 [9] Susto GA, Schirru A, Pampuri S, and McLoone S Machine Learning for Predictive Maintenance: A Multiple Classifier Approach IEEE Trans on Industrial Informatics 2014; 11(3): p 812-820 [10] Barlow R and Proshan F Statistical theory of reliability and life testing: probability models New Yourk: Holt, Rinehart and Winston; 1975 [11] Vaisnys P, Contri P, Rieg C, and Bieth M Monitoring the effectiveness of maintenance programs through the use of performance indicators Europian Comission Report: EUR 22602 EN 2006 [12] Enhanced aircraft platform availability through advanced maintenance concepts and technologies NATO RTO tech report TR-AVT-144; 2011 [13] Ma C, Y Shao Y, Ma R Analysis of equipment fault prediction based on metabolism combined model J of Machinery Manufacturing and Automation 2013; 2(3):58–62 [14] Kallen M and Noortwijk J Optimal maintenance decisions under imperfect inspection Reliab Eng Syst Saf 90(2-3): 177-185 [15] Ignatov VA, Ulansky VV, Taisir T Prediction of optimal maintenance of technical systems Kiev: Znanie; 1981 (in Russian) 101 ... probability distribution function predictive maintenance Decision rule Assume that the state of a system is completely determined by the value of the parameter X (t), which is a non-stationary random... inspection and maintenance policy is developed In [8], a discriminant function is developed on the basis of the representation of the observed system degradation process as a discrete parameter Markov... respectively System states Let us consider the stochastic process S(t), which characterizes the state of the system at an arbitrary instant of time t: S1, if at time t, the system is used as intended and