Inflation Based replacement model for cutting tools using Markov Stochastic process

Inflation Based replacement model for cutting tools using Markov Stochastic process

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2020 by IJETT Journal
Volume-68 Issue-2
Year of Publication : 2020
Authors : Dr S Gajanana,Yayavaram Revanth Sai, K Rahul, S Rohith Yadav
DOI :  10.14445/22315381/IJETT-V68I2P206

Citation 

MLA Style: Dr S Gajanana,Yayavaram Revanth Sai, K Rahul, S Rohith Yadav  "Inflation Based replacement model for cutting tools using Markov Stochastic process" International Journal of Engineering Trends and Technology 68.2 (2020):29-35.

APA Style:Dr S Gajanana,Yayavaram Revanth Sai, K Rahul, S Rohith Yadav. Inflation Based replacement model for cutting tools using Markov Stochastic process  International Journal of Engineering Trends and Technology, 68(2),29-35.

Abstract
Deterioration of the equipment in any industry is inevitable and is proportional to time. In order to maintain a smooth flow in operations of the machines, it is mandatory to have a continuous monitoring. If there arises a situation where the machine or the equipment requires any kind of repair then it may delay the production. The increase in repairing and the maintenance cost demands the replacement of items. The present paper focuses on three different states of repairs of a single point cutting tool. Markov model, which is a stochastic model used to model randomly changing systems in an assumption that future states depend only on the current state is applied in generating the probabilities of items falling in different states. Based on the average cost the replacement decision is taken considering macroeconomic variable “Inflation.”

Reference

[1] Xitong Zheng & Nasser Fard (1991): “A Maintenance Policy for Repairable Systems based on Opportunistic Failure-rate Tolerance”, IEEE Transactions on Reliability, Vol-40, No.2, June, 1991.
[2] Isha Bagai and Kanchan Jain (1994): “Improvement, Deterioration and Optimal Replacement Under Age-Replacement With Minimal Repair”, IEEE Transactions on Reliability, Vol.43, No.1, P-156 to 162, March, 1994.
[3] Thomas W. Archibald and Rommert Dekker (1996): “Modified Block-Replacement for Multiple-Component Systems”, IEEE Transaction on Reliability, Vol-45, No.1, P-75 to 83, March, 1996.
[4] Nadamuni Reddy. C and C. Uma Sankar (1996): “Markov-Chains in Group replacement decisions”, paper presented at 38th National Convention of Indian Institution of Industrial Engineering, Bombay, December, 1996.
[5] Nadhamuni Reddy.C.(1997): “Block, Combined influence of inflation and cost of money in replacement decisions”, National Conference on Statistical Quality Control, Guntur. India.
[6] Gerry Trodd (1998): “Practical Implementation of Predictive Maintenance”, IEEE Transactions on Semiconductor Manufacturing, P-29 to 37, 1998.
[7] ToyonariShimakage, Kai Wu, Takeyoshi Kato, Tatsuki Okamoto and YasuoSuzuoki (2002): “Economic Evaluation of Cable Replacement Considering Annual Failure Probability”, Conference Record of the 2002, IEEE International Symposium on Electrical Insulation, Boston , MA USA, P-1472 to 475, April, 2002.
[8] Jong Min Lee, Seung-Jong Kim, Chang-Seop Song &Yoha Hwang (2003): “Diagnosis of mechanical fault signals using continuous hidden Markov model” Journal of Sound and Vibration 276 (2004) 1065–1080, Elsevier, August 2003.
[9] S.Gajanana, Dr. G. Krishnaiah& Dr. C.Nadhamuni Reddy (2005): “Prediction of Inflation using Fore casting Techniques for Developing Societies” International conference on Operations Research Applications in Infrastructure Development (ICORAID-2005), IISc, Bangalore, India.
[10] C. Richard Cassady and ErhanKutanoglu (2005): Integrating Preventive Maintenance Planning and Production Scheduling for a Single Machine”, IEEE Transactions on reliability, Vol-54, No.2, June, 2005.
[11] RueyHaueiYeh, Gaung-Chen and Ming-Yuh Chen (2005): "Optimal Age-Replacement Policy for Non repairable Products Under Renewing Free-Replacement Warranty”, IEEE Transactions on Reliability, Vol.54, No.1, P-92 to 97, March 2005.
[12] Antonio G. Vallejo Jr., Juan A. Nolazco-Flores, Rub´en Morales-Men´endez, L. Enrique Sucar&Ciro A. Rodr´?guez (2005): “Tool-Wear Monitoring Based on Continuous Hidden Markov Models” Springer-Verlag Berlin Heidelberg 2005.
[13] S.Gajanana, Dr. G. Krishnaiah& Dr. C.Nadhamuni Reddy (2006): “Development of Mathematical Model For Inflation Prediction Using Forecasting Technique” Industrial Engineering Journal, Vol. XXXV NO.5, May-2006, P-28 to 31.
[14] A. A. Kassim, Zhu Mian&M. A. Mannan : “Tool condition classification using Hidden Markov Model based on fractal analysis of machined surface textures” Machine Vision and Applications (2006) 17:327–336, Springer, July 2006.
[15] S.Gajanana, Dr. G. Krishnaiah& Dr. C.Nadhamuni Reddy (2006): “Development Of Replacement Model Using Predicted Inflation” Indian Journal of Mathematics and Mathematical Sciences.
[16] Tony Boutros, & Ming Liang (2011): “Detection and diagnosis of bearing and cutting tool faults using hidden Markov models” Mechanical Systems and Signal Processing 25 (2011) 2102–2124, Elsevier, February 2011.

Keywords
n = time period
? = inflation
R = real interest rate
i = nominal interest rate
? = present worth factor = 1/(1+i)
C1 = Individual replacement cost per item
C2 = Minor Repair Cost
C3 = Medium Repair Cost
C4 = Major Repair Cost
C5 = Group replacement Cost
XiI = Probability of item in functional state at ith period
XiII = Probability of item in minor repairable state at ith period
XiIII = Probability of item in medium repairable state at ith period
XiIV = Probability of item in major repairable state at ith period
XiV = Probability of item in irreparable state at ith period
M = Transition probability matrix