### OPTIMAL PERIODIC REPLACEMENT USING ACCELERATED LIFE TESTING FOR INVERTED WEIBULL DISTRIBUTION

Osama H Mahmoud Hassan 1 ; Eman A El-Dessouky Nassef 2
1 Vice Presidency for Graduate Studies and Scientific Research, Department of Mathematics, Statistics and Insurance, King Faisal University, Sadat Academy for Management Sciences, Al-Ahsa, Saudi Arabia, Egypt.
2 Department of Statistics, Faculty of Commerce, Al- Azhar University, Egypt.

Article Id - IJARET_12_03_056, Pages : 613-625

Scopedatabase Link : https://scopedatabase.com/Document/document_search?title=OPTIMAL PERIODIC REPLACEMENT USING ACCELERATED LIFE TESTING FOR INVERTED WEIBULL DISTRIBUTION&type=1

### Abstract

Planned maintenance of facilities, equipment, and systems with periodic replacements is designed to improve equipment life and avoid any unplanned maintenance activities, helping to reduce equipment downtime and reduce the number of major repairs, reduce overtime costs and safety and quality conditions are improved for all. In this paper, we estimate the optimal periodic replacement for repairable and non-repairable products that minimize the total replacement cost and replacement cost rate. The investigations concern the estimation of parameters. Inverted Weibull distribution using the power rule model for constant stress in accelerated life tests. The maximum likelihood method is used to estimate the model and life distribution parameters from the test data when Type II censoring is applied. The confidence interval for the model parameters is constructed using the normal approximation and the bootstrap method. We use the estimated parameters to achieve optimal periodic replacement of repairable and non-repairable products, which minimizes the total cost of replacement. Finally, some numerical illustrations are provided. We find the confidence interval length for the estimated parameters in bootstrap method for the shape parameter of IW distribution greater than it in normal approximation while for scale parameter is vice verse. Furthermore, the optimal periodical replacement for nonrepairable or repairable products is increasing as increasing the values of the estimated parameters.

### Keywords

Accelerated Life Testing, Inverted Weibull Distribution, Maintenance, Constant Stress, Power Rule Model, Optimal Periodic Replacement, Expected Replacement Cost, Expected Replacement Cost Rate

Share and Cite:

Osama H Mahmoud Hassan and Eman A. El-Dessouky Nassef, Optimal Periodic Replacement using Accelerated Life Testing for Inverted Weibull Distribution, International Journal of Advanced Research in Engineering and Technology (IJARET), 12(3), 2021, pp. 613-625.

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Once an article has been accepted for publication, any Article Processing Charges on the article become due. The submitting author accepts responsibility for the Article Processing Charges, and will not issue refunds of any kind except those payments made by mistake or in excess of the amount required.

• General Engineering
• Civil and Architecture Engineering
• Chemical Engineering
• Electrical
• Electronics and Computer Engineering
• Information Engineering and Technology
• Automation and Mechatronics Engineering
• Material and Chemical Engineering