Managing System Reliability and                    Maintenance under Performance                    Maintenance nder Perfo...
ASQ Reliability Division                 ASQ Reliability Division                Chinese Webinar Series                Chi...
Managing Reliability andMaintenance under Performance-        Based Contract        Tongdan Jin (金彤丹), Ph.D.          Ingr...
Contents• Introduction to Performance-Based Contract  (PBC)• Five Overarching Performance Measures• Multi-Criteria Approac...
Topic OneIntroduction to Performance-  Based Contracting (PBC)                               3
4 Characteristics of Capital Equipment• Capital-intensive• Long service time• Prohibitive downtime cost• Expensive in main...
5  Overview of Maintenance/Service Business     • Representing 8-10% of GDP in the US.     • US airline industry is $45B o...
Challenges in Material-Based Contract (MBC)  • Local or sub-optimal decision-making on    maintenance.  • Disintegration o...
The Goal of Performance-Based Contracting   Lifecyle Cost ($)                                        30-40%               ...
PBC and The Technology Suite                                   PBC         PBD                     PBMfg                  ...
Existing Maintenance/Sustainment Strategy     • Corrective Maintenance           * Run-to-failure     • Preventive Mainten...
Evolution of Maintenance Strategy                                    Evolution of Asset Management Strategy               ...
Topic TwoDesign, Implement, and Monitor         PBC Programs                                 11
Logistics & Supply Chain (MBC vs. PBC)                            New System Shipping/Installation                        ...
13                A 4-Step Process to PBC   Step 1            Step 2           Step 3             Step 4Performance       ...
US DoD’s Overarching Performance Measures  • Operational availability (OA)  • System reliability/Mission reliability (MR) ...
Operational Availability                            MTBF          CM         Ao                           MTBF  MDT     ...
Performance Measures and Drivers             Inherent system                Reliability                                  M...
17      Availability and Variable Fleet Size                                                                              ...
Operational Availability under CM Policy                                                                                  ...
19           Operational Availability under PM Policy                                                                     ...
Topic ThreeMulti-Criteria Approach to      PBC Planning                             20
21Reliability Optimization and Spare Parts Logistics       Reliability Optimization                                   Spar...
22    Performance Based Logistics/ContractNew Features:•  Integrating reliability management with spares provisioning•  Fo...
Generic Decision Model for PBCObjective Functions:     Max: Service profit (OEM and 3PL)     Min: Cost per unit usage (cus...
Total Lifecycle Cost Management                 Fleet Costs:                            C ( , s )  D( )  nc ( )  I (...
Design and Manufacturing Cost                              Design Cost                                                    ...
26    Spares Inventory and Repair Cost                                       m    I ( , s)  smc( )  mc1  mc2   c3 s...
Linear and Exponential Reward Model                • Cost Plus Fixed Fee (CPFF)                • Cost Plus Award Fee (CPAF...
28                    Profit-Centric Servitization Maximize:                                          K                   ...
Numerical Example-Wind Turbine       Index              i=1             i=2             i=3    subsystem            Blade ...
30                          Results Comparison             =5 years, Amin=0.97, =1, and n=50 systemsOption            Li...
Topic FourPotential Research Thrusts    under PBC Theme                             31
Reliability Growth and Increased Install Base                   MTBF Run Chart and Cumulative Field Systems               ...
(Q, r) Spare Parts Inventory Control                                                          Inventory                   ...
A Lifecycle Approach to Spares Provisioning                 Ramp-up               Mature   Phase out                    In...
35Lifecycle for Major USA Aircraft Systems                                                                                ...
Conclusion1. PBM represents a new paradigm in designing,   marketing, and operating capital-intensive equipment.2. PBM mer...
Key Terminologies1.    Original equipment manufacturer (OEM)2.    3rd party logistics (3PL) supplier3.    Maintenance, rep...
Selected ReferencesReliability Modeling   1.   D.W. Coit, “System reliability confidence intervals for complex systems wit...
Thanks   &Questions            39
Upcoming SlideShare
Loading in …5
×

Managing system reliability and maintenance under performance based contract 15 jul2012_rev1

1,920 views
1,701 views

Published on

Performance based contracting (PBC) emerged as a new service model which is reshaping the acquisition, operation and maintenance of capital equipment. PBC is often referred to as performance based logistics in defense industry, or is called as power-by-the-hour in the airline industry. The focus of PBC is on the outcome of the system reliability performance, not materials and labors involved in the maintenance. This presentation introduces a novel quantitative approach to planning performance-based contracts in the presence of system usage uncertainty. We develop an analytical model to characterize the system availability by comprehending five key performance drivers: failure rate, usage variability, spare parts inventory, repair turn-around time, and system fleet population. This analytical insight into the system performance allows us to estimate the lifecycle cost by taking into account the design, manufacturing, maintenance and repair across the system lifetime. Two types of contracting schemes are examined under the cost minimization and the profit maximization. This presentation aims to provide theoretical guidance to facilitate the paradigm change as it shits from material based services to performance based contracting.

Published in: Technology, Business
1 Comment
3 Likes
Statistics
Notes
No Downloads
Views
Total views
1,920
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
58
Comments
1
Likes
3
Embeds 0
No embeds

No notes for slide

Managing system reliability and maintenance under performance based contract 15 jul2012_rev1

  1. 1. Managing System Reliability and  Maintenance under Performance  Maintenance nder Performance Based Contract (面向综合表现合 同的系统可靠性和维修性管理) 同的系统可靠性和维修性管理 Dr. Tongdan Jin (金彤丹博士) ,  Assistant Professor of Industrial Engineering, Texas State  A i t tP f fI d t i lE i i T St t University (德克萨斯州立大学工业工程系助理教授) ©2012 ASQ & Presentation Jin Presented live on Jul 15th, 2012http://reliabilitycalendar.org/The_Reliability_Calendar/Webinars_liability Calendar/Webinars ‐_Chinese/Webinars_‐_Chinese.html
  2. 2. ASQ Reliability Division  ASQ Reliability Division Chinese Webinar Series Chinese Webinar Series One of the monthly webinars  One of the monthly webinars on topics of interest to  reliability engineers. To view recorded webinar (available to ASQ Reliability  Division members only) visit asq.org/reliability ) / To sign up for the free and available to anyone live  webinars visit reliabilitycalendar.org and select English  Webinars to find links to register for upcoming eventshttp://reliabilitycalendar.org/The_Reliability_Calendar/Webinars_liability Calendar/Webinars ‐_Chinese/Webinars_‐_Chinese.html
  3. 3. Managing Reliability andMaintenance under Performance- Based Contract Tongdan Jin (金彤丹), Ph.D. Ingram School of Engineering Texas State University, TX 78666, USA ASQ Webinar Series July 14, 2012 (US Time) 1
  4. 4. Contents• Introduction to Performance-Based Contract (PBC)• Five Overarching Performance Measures• Multi-Criteria Approach to PBC• Application to Wind Power Industry• Future Study and Conclusion 2
  5. 5. Topic OneIntroduction to Performance- Based Contracting (PBC) 3
  6. 6. 4 Characteristics of Capital Equipment• Capital-intensive• Long service time• Prohibitive downtime cost• Expensive in maintenance, repair, and overhaul (MRO)• Integrated service and sustainment
  7. 7. 5 Overview of Maintenance/Service Business • Representing 8-10% of GDP in the US. • US airline industry is $45B on MRO in 2008. • US auto industry is $190B and $73B for parts in 2010. • US DoD maintenance budget $125B and $70B inventory with 6,000 suppliers. • Joint Strike Fighter (F-35): $350B for R/D/P, and $600B for after-production O/M for 30 years. • EU Wind turbine service revenue €3B in 2011Reference: 1). Nowicki et al. (2010), 2). Smith and Thompson (2006), 3) http://trade.gov/static/2011Parts.pdf
  8. 8. Challenges in Material-Based Contract (MBC) • Local or sub-optimal decision-making on maintenance. • Disintegration of design, manufacturing and maintenance/sustainment. • Lack of reliability commitment from OEM. • Profit-driven by the OEM or 3rd party logistics supply. 6
  9. 9. The Goal of Performance-Based Contracting Lifecyle Cost ($) 30-40% 50-60% 10-20% 5% Research Manufacturing Operation and Support Retirement Development Performance based contracting (PBC) aims to reduce the cost ownership while ensuring the reliability goals. 7Ref: DoD 5000, University of Tennessee
  10. 10. PBC and The Technology Suite PBC PBD PBMfg PBM Reliability Reliability, quality, warranty, maintenance and functions and time-to-market schedule, spares, operational availability PBD=performance-based design PBMfg=performance-based manufacturing PBM=performance-based maintenanceNote: In military, PBC is also called Performance based logistics (PBL), In airline industry, PBC is referred as Power-by-hour (PBH). 8
  11. 11. Existing Maintenance/Sustainment Strategy • Corrective Maintenance * Run-to-failure • Preventive Maintenance * Age-based maintenance * Block replacement • Condition-based Maintenance (Monitoring) * Remaining useful lifetimeRef: E. Elsayed (1996), Reliability Engineering, H.-Z. Wang (2002) “A survey of maintenance policies of deteriorating systems,” Si X.S., et al. “Remaining useful life estimation-A review on the statistical data driven approaches”. 9
  12. 12. Evolution of Maintenance Strategy Evolution of Asset Management Strategy CM=Corrective Maintenance PM=Preventive Maintenance Lifecycle Cost CBM=Condition-Based Maintenance PBM=Performance-Based Maintenance CM PM CBM PBMSource: T. Jin, Y. Ding, H. Guo,N. Nalajala “Managing wind turbine reliability and maintenance under performance based contract”IEEE Power and Energy Society General Meeting , July 22-26, 2012 (accepted). 10
  13. 13. Topic TwoDesign, Implement, and Monitor PBC Programs 11
  14. 14. Logistics & Supply Chain (MBC vs. PBC) New System Shipping/Installation Replenish Repair by inventory replacement OEM for In-service Repair Center Spares design and Fleet with n M/G/ Inventory production Systems OEM Customer New System Shipping/Installation Replenish Repair by inventory replacement OEM for In-service Repair Center Spares design and Fleet with n M/G/ Inventory production Systems 12 OEM Customer
  15. 15. 13 A 4-Step Process to PBC Step 1 Step 2 Step 3 Step 4Performance Performance Performance Performance Outcome Measures Criteria Compensation System System Mini Cost plus readiness, availability, availability, incentive fee, operational MTBF, max failure cost plus reliability, MTTR, Mean rate, max award fee,assurance of downtime, repair waiting linear reward, spare parts logistics time, max cost exponential supply response time per unit time reward
  16. 16. US DoD’s Overarching Performance Measures • Operational availability (OA) • System reliability/Mission reliability (MR) • Logistics response time (LRT) • Logistics footprint (LF) • Cost per unit usage (CUU) Mission Reliability Operational Logistics Cost Per Unit Availability Footprint Usage Logistics Response Time 14
  17. 17. Operational Availability MTBF CM Ao  MTBF  MDT MTBR PM and Ao  CBM MTBR  MDTMTBF=Mean time between failuresMTBR=mean time between replacementsMDT=mean down time 15
  18. 18. Performance Measures and Drivers Inherent system Reliability MTBF OEM MaintenanceControlled Schedule () Operational MTTR Availability (Ao) Logistics Support (s, ts, tp , tr) MLDTCustomer Fleet size (n)Controlled System usage () 16
  19. 19. 17 Availability and Variable Fleet Size Variable Fleet Size• Availability Figure 1: System Reliability and Fleet Size MTBF A 2,000 1000 Semiconductor Industry MTBF MTBF  MDT 1,600 800 Cumulative Fleet Size MTBF(hours) 1,200 600 System Population 800 400 400 200• MTBF=100 hours, MDT=5 hours 0 0 105 120 135 15 30 45 60 75 90 1 100 A  0.95 Weeks 100  5 160,000 Cumulative Installed WT (1998 to 2030) 150,000 140,000 1.5 MW (2010-2014 ) Wind Power Industry 2.0 MW (2015-2020) 120,000 Installed WT Population 2.5 MW (2020-2025) 100,000 3.0 MW (2025-2030)• MTBF=200 hours, MDT=10 hours 80,000 60,000 200 40,000 22,500 A  0.95 20,000 200  10 0 98-99 02-03 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 2026 2028 2030
  20. 20. Operational Availability under CM Policy 1 Ao ( , s,  , n, t r )   s ( n t ) x e  n t r  1  t s  t r 1    x 0 r    x!   =system or subsystem inherent failure rate s =base stock level for spares β =usage rate, and 0β1 n =system fleet size tr =defective part repair turn-around time ts =time for conducting repair-by-replacementRef: Jin, Wang, “Planning performance based contracts considering reliability and uncertaint system usage,” Journal of the 18Operational Research Society , 2012
  21. 21. 19 Operational Availability under PM Policy  A0 ( s, , t p , t r )   0 R(t )dt R(t )dt  t s  t p R( )  t r F ( ) Pr{O  s}  0 R(t) =reliability function O =spares demand, a random variable s =base stock level tp =parts reconditioning turn-around time tr =defective repair turn-around time ts =hands-on repair-by-replacement timeRef: Jin, Tian, Xie, “A Multi-Criteria Approach to Performance-Based Service with Variable System Usage,” Texas State University Working paper (2012).
  22. 22. Topic ThreeMulti-Criteria Approach to PBC Planning 20
  23. 23. 21Reliability Optimization and Spare Parts Logistics Reliability Optimization Spare Parts Logistics r5 (t) s32 Fleet 1 r1(t) s21 r6(t) r8(t) s s32 Fleet 2 r2(t) r4(t) s22 r7(t) s3,n-1 Fleet n-1 s3,n max E[ Rsys (r(t ), n)] Fleet n min var Rsys (r(t ), n)  max Ap (s, x) min Cost r(t ), n  min Cost (s, x), EBO (s, x) • Tillman et al. (1977) • Scherbrooke (1968, 1992) • Kuo et al. (1987) • Muckstadt (1973) • Chen (1992) • Graves (1985) • Jin & Coit (2001) • Lee (1987) • Levitin & Lisnianski (2001) • Cohen et al. (1990) • Coit et al. (2004) • Diaz & Fu (1996) • Ramirez-Marquez et al. (2004) • Alfredsson (1997) • Marseguerra et al. (2005) • Zamperini & Freimer (2005) • Jin & Ozalp (2009) • Lau & Song (2008) • Ramirez-Marquez & Rocco (2010) • Kutanoglu et al. (2009) • More ..... • More .....
  24. 24. 22 Performance Based Logistics/ContractNew Features:• Integrating reliability management with spares provisioning• Focus on system performance outcome• Lifecycle cost analysis• Variable installed base and uncertain usage• Profit-centric decision making• Kim, Cohen, Netessine (2007) Operation Availability• Nowicki et al. (2008)• Jin and Liao (2009) MTBF Ao • Jeet, Kutanoglu, Partani (2009) MTBF  MTTR  MLDT• Kang & McDonald (2010)• Oner et al. (2010) MTBF=mean time between failures• Jalil et al. (2011) MTTR=mean time to repair• Mirzahosseinian & Piplani (2011) MLDT=mean logistics delay time• Jin & Wang (2012)• Jin & Tian (2012) Ref: Jin & Wang (2011)
  25. 25. Generic Decision Model for PBCObjective Functions: Max: Service profit (OEM and 3PL) Min: Cost per unit usage (customer)Subject to: System Operational Available>A(min) System Reliability>MTBF(min) Logistics Response Time<Time(min) Logistics Footprint<Cost(min) 23
  26. 26. Total Lifecycle Cost Management Fleet Costs: C ( , s )  D( )  nc ( )  I ( , s )  max    D( )  B1 exp       Design Costs:  min   1 1  Mfg. Costs: c( )  B2  B3       max    Spares/Repair (1   )  1 I ( , s)  sc ( )  c r n Logistics Costs:  (1   )1. K.B. Öner, G.P. Kiesmüller, G.J. van Houtum (2010) in European Journal of Operational Research, vol. 205, no. 3, 2010, pp. 615-624.2. H.Z. Huang, Z.J. Liu, D.N.P. Murthy (2007) in IIE Transactions, vol. 39, no. 8, 2007, pp. 819-827.3. T. Jin, P. Wang (2012) in Journal of the Operational Research Society, 2012, doi:10.1057/jors.2011.144, (forthcoming). 24
  27. 27. Design and Manufacturing Cost Design Cost   max    D( )  B1 exp k       min Unit Production Cost c( )  B3 ( A)  B2 (  v   max ) v Design Cost vs. Reliability Manufacturing Cost vs. Reliability 2.0 600,000 B1=$1106 B2=$1105 Cost ($) (106) 1.8 500,000 =0.05 B3=$2,000 =0.6 400,000 1.6 Cost($) 300,000 1.4 =0.5 200,000 1.2 =0.02 100,000 =0.4 1.0 0 20000 24000 28000 32000 36000 40000 20,000 25,000 30,000 35,000 40,000 1/ 1/ References: 1) A. Mettas (2000), RAMS 2) H.-Z. Huang, H.J. Liu, D.N.P. Murthy (2007), IIE Transactions 3) A.G. Loerch (1999), Naval Research Logistics 25
  28. 28. 26 Spares Inventory and Repair Cost m I ( , s)  smc( )  mc1  mc2   c3 si  R( , s) i 1 Repair costCapital Cost Cost for Holding cost parameter updating Order cost Ref: Jin et al. 2011, ICRMS 2011
  29. 29. Linear and Exponential Reward Model • Cost Plus Fixed Fee (CPFF) • Cost Plus Award Fee (CPAF) • Cost Plus Incentive Fee (CPIF) * linear incentive a  b( A  Amin ) A  Amin R( A)   a A  Amin * exponential incentive exp   ( A  Amin )  A  Amin R( A)   a A  Amin 27Ref: Nowicki et al. (2008)
  30. 30. 28 Profit-Centric Servitization Maximize: K K KE [ P(λ, s;  )]  R( As (λ, s;  ))   Di (i )  B1,i   n mi ci (i )  B2,i    I i (i , si ;  ) i 1 i 1 i 1 Subject to: min,iimax,i for i=1, 2, …., K mi   K As (λ, s;  )   Ai (i , si ;   Amin i 1 1 1 1 2 K
  31. 31. Numerical Example-Wind Turbine Index i=1 i=2 i=3 subsystem Blade Mainshaft/Bearing Gearbox mi 3 1 1 max(faults/year) 0.2898 0.0312 0.1306 min(faults/year) 0.1560 0.0168 0.0703 B1($) 3,330,000 675,000 1,936,500 B2($) 333,000 67,500 193,650 B3($) 20,000 7,000 12,000  0.02 0.02 0.02  0.6 0.6 0.6cr ($/defective part) 40,000 50,000 60,000 tr (days) 45 90 120 ts (days) 3 4 6 29
  32. 32. 30 Results Comparison =5 years, Amin=0.97, =1, and n=50 systemsOption Linear Exponential i 1 2 3 1 2 3 mi 3 1 1 3 1 1Name Blade MS/B GX Blade MS/B GX  0.180 0.031 0.120 0.179 0.031 0.119 5-Year s 7 0 5 7 0 5 contract Asub 0.9981 0.9972 0.9974 0.9981 0.9972 0.9975Acluster 0.9942 0.9972 0.9974 0.9943 0.9972 0.9975 Asys 0.9889 0.9890Profit $25.06M $24.78M =10 years, Amin=0.97, =1, and n=50 systems Optio Linear Exponential n i 1 2 3 1 2 3 mi 3 1 1 3 1 1 Name Blade MS/B GX Blade MS/B GX 10-Year  0.172 0.025 0.103 0.172 0.024 0.0990 s 8 0 5 8 0 5 Contract Asub 0.9985 0.9981 0.9980 0.9985 0.9982 0.9982 Acluster 0.9954 0.9981 0.9980 0.9954 0.9982 0.9982 Asys 0.9916 0.9918 profit $57.59M $57.11M
  33. 33. Topic FourPotential Research Thrusts under PBC Theme 31
  34. 34. Reliability Growth and Increased Install Base MTBF Run Chart and Cumulative Field Systems Reliability and Field Shipment for a Type ATE Equipment 1,600 800 Installed Systems 1,200 MTBF 600 Cum Systems MTBF(hours) 800 400 400 200 0 0 15 30 60 90 45 75 105 135 120 1 Weeks 32
  35. 35. (Q, r) Spare Parts Inventory Control Inventory Basic model q Q qQ r l Time t Multi-resolution (s, s-1) model L for i=1 L for i=2 i=3 q2 q1 r2 r1 0 t11 t12 t13 t21 t22 t23 t24 t31 time 33Ref: Jin and Liao 2009 , Computer and Industrial Engineering
  36. 36. A Lifecycle Approach to Spares Provisioning Ramp-up Mature Phase out Installed base Spare parts Quantity demand New Shipment Time 34Ref. Inderfurth and Mukherjee (2008)
  37. 37. 35Lifecycle for Major USA Aircraft Systems Planned Phase Out Development Start (Last Model) 1946 B-52 94 1954 KC-135 86 1953 AIM-9 72 1970 SSN-688 56 1969 F-15 51 1955 UH-1 49 1969 F-14 41 0 10 20 30 40 50 60 70 80 90 100 Years Reference : Timothy Smith, “Reliability Growth Planning Under Performance Based Logistics” Master Thesis, Texas Tech University, 2003.
  38. 38. Conclusion1. PBM represents a new paradigm in designing, marketing, and operating capital-intensive equipment.2. PBM merges two distinct bodies of literature: reliability optimization and spares supply management.3. PBM is a lifecycle approach to system reliability commitment involving the users and the suppliers.4. A long-term PBM contract drives the reliability growth. 36
  39. 39. Key Terminologies1. Original equipment manufacturer (OEM)2. 3rd party logistics (3PL) supplier3. Maintenance, repair and overhaul (MRO)4. Material-based contract (MBC)5. Performance based logistics/contracting/maintenance6. Power-by-hour (PBH)7. Servitization8. Lifecycle cost analysis9. Operational availability10. Mean-time-between-replacements (MTBR)11. Mean downtime (MDT)12. Mean-time-to-repair (MTTR)13. Mean logistics delay time (MLDT)14. Mean-time-between-failures (MTBF)15. Performance measures16. Spare/service parts logistics (SPL)17. Multi-criteria optimization18. Multi-echelon, multi-item repairable inventory19. Reliability allocation/optimization 37
  40. 40. Selected ReferencesReliability Modeling 1. D.W. Coit, “System reliability confidence intervals for complex systems with estimated component reliability,” IEEE Transactions on Reliability, vol. 46, no. 4, 1997, pp. 487-493. 2. J.E. Ramirez-Marquez, and W. Jiang, “An improved confidence bounds for system reliability,” IEEE Transactions on Reliability, vol. 55, no. 1, 2006, pp. 26-36. 3. E. Borgonov, “A new uncertainty measure”, Reliability Engineering and System Safety, vo;. 92, pp. 771- 784, 2007. 4. T. Jin, D. Coit, "Unbiased variance estimates for system reliability estimate using block decompositions," IEEE Transactions on Reliability , vol. 57, 2008, pp.458-464. 5. H. Guo, T. Jin, A. Mettas, “Designing reliability demonstration test for one-shot systems under zero component failures," IEEE Transactions on Reliability , vol. 60, no. 1, 2011, pp. 286-294Reliability, Maintenance, and Spares Logistics Management 1. H.-Z. Huang, H.J. Liu, D.N.P. Murthy. 2007. Optimal reliability, warranty and price for new products. IIE Transactions, vol. 39, no. 8, pp. 819-827. 2. K. Kang, M. McDonald. 2010. Impact of logistics on readiness and life cycle cost: a design of experiments approach, Proceedings of Winter Simulation Conference. pp. 1336-1346. 3. S.H. Kim, M.A. Cohen, S. Netessine. 2007. Performance contracting in after-sales service supply chains. Management Science, vol. 53, pp. 1843-1858. 4. D. Nowicki, U.D. Kumar, H.J. Steudel, D. Verma. 2008. Spares provisioning under performance-based logistics contract: profit-centric approach. Journal of the Operational Research Society. vol. 59, no. 3, 2008, pp. 342-352. 5. K.B. Öner, G.P. Kiesmüller, G.J. van Houtum. 2010. Optimization of component reliability in the design phase of capital goods. European Journal of Operational Research, vol. 205, no. 3, pp. 615-624. 6. T. Jin, P. Wang, “Planning performance based contracts considering reliability and uncertain system usage,” Journal of the Operational Research Society , 2012 (forthcoming) 7. T. Jin, Y. Tian, “Optimizing reliability and service parts logistics for a time-varying installed base,” European Journal of Operational Research, vol. 218, no. 1, 2012, pp. 152-162 38
  41. 41. Thanks &Questions 39

×