To Calculate the Validity of Alternate Formula for Production Rate to Design for Un-Paced Production Line When Unbalancing the Workloads

INTRODUCTION

In the Industry, Now a day Utilize the Computer Integrated Manufacturing (CIM) or flexible Manufacturing System. Therefore we required to design that type of System a production line which production rate is high or suitability of work. This production line is Design according to work (different interval of time) of on each Machine (say work station) in Un-paced line or forced to work for Equal interval of time in Paced production line. In this strategy we use Un-paced production line where the Interval of time for each work station are different. We set time to each work station according to these strategies and find out the production rate. We find the production rate (Jamali, 2015) for 5- work station then we calculate the Alternate formula for Production Rate5 which is simple for designer to calculate the production rate without use of computer. Now we see how much this formula is valid. We check it through correction factor (CF), variance with mean value of Correction Factor and standard deviation. Here we found that our formula is correct if we add the correction factor in this formula for production rate.

Here we Know the interval of time From previously we find out the actual production rate Stretegies (Jamali, 2015. Hiller and So, 1993. Jamali, 2016. Jamali & Suhail, 2016. Jamali, 2002). Know we calculate the Correction Factor, variance with mean value of Correction Factor (Σ CF/n-CFi), standard deviation σ. We define here each function. Here D= Highest work load (Time) distribution in work station – Lowest work load (time) distribution in work station Correction Factor = Production Rate (R) - Alternate formula for Production Rate (AFR) Alternate formula Rate = (μ1 + μ 5)/ total time in production line Here μ1, μ2, μ3, μ4, μ5 is work load (time) distribution on work station (Jamali, 2015. Hiller and So, 1993. Jamali, 2016. Jamali & Suhail, 2016. Jamali, 2002) Mean value of Correction Factor = Σ CF/n

For example , for S. No.1, 3 ,………..30,35…………………………………… 59, 60 means Σ CF/n – CF1, Σ CF/n – CF3, Σ CF/n – CF5……., Σ CF/n – CF30, Σ CF/n – CF35……………….. Σ CF/n – CF55, Σ CF/n – CF60 Where standard deviation σ = Sqrt (Σ (Σ CF/n- CFi)2)/n Here i indicate that S. No. and n =total S.No.= 14 For example, for S. No.1, 3, ………. 30, 35 …………………………………… 59, 60 means Sum (S) =(Σ CF/n- CF1)2 + (Σ CF/n- CF3)2 +………………………+(Σ CF/n- CF30 )2+(Σ CF/n- CF35 )2+………………….(Σ CF/n- CF59 )2+(Σ CF/n- CF60 )2 From these formula we calculated the Alternate formula Production Rate, Correction Factor, Variance with Mean vale Of Correction Factor, Standard deviation and found the graph of each values of variance to S. No. and analyze that our study is correct or not. These values are given in tabulated form given below.

*value of last station and first station are very low therefore the AFR are very low

Variance with Mean vale of Correction Factor (Σ CF/n-CFi) VS S. No. When D= 1.8 linear Variance with Mean vale of Correction Factor (ΣCF/n-CFi) VS S. No. When D= 1.2 linear Variance with Mean vale of Correction Factor (ΣCF/n-CFi) VS S. No. When D= 0.3 linear Variance with Mean vale of Correction Factor (ΣCF/n-CFi) VS S. No. When D= 0.1 linear Variance with Mean vale of Correction Factor (ΣCF/n-CFi) VS S. No. When D= 1.9 Random Variance with Mean vale Of Correction Factor (ΣCF/n-CFi) VS S. No. When D= 0.4 Random

When we analyze the Result From Graph and Table we see that, Variance with Mean vale Of Correction Factor (ΣCF/n-CFi) and standard deviation σ is D=1.8 linear (+0.2397, -0.234) σ=0.0393, D= 1.2 linear(+0.133, -0.116) σ=0.0204, D=0.3linear (+0.037, -0.036) σ=0.0461, D= 0.1linear (+0.011, -0.0134) σ 0.00224, D= 1.9 Random (+0.3914, -0.298) σ = 0.0647 D= 0.4 Random (+0.0256, -0.036) σ=0.0077 When we see the graph of each table, we say that the trends of correction factor to mean value is

the formula is valid and the revised formula is Adding CF to the AFR. Therefore we say that Actual production rate (R) = AFR + CF for Calculation of CF for bigger production line we develop CF= Constant X Standard Deviation

After finding out these results we conclude that 1. Alternate Production Rate formula (AFR) is easy to calculate the production rate for developing the un-paced production line for Industrial Engineer. And the formula is vlaid for 5- Station production rate. 2. They also set the machine in a proper way in Production line when the Emphasis given on best production rate or worst production rate or the according to preference given to the work (load) in production line. 3. We say that these formulas are valid even for calculating higher work station production rate.

This formula is also 1. Useful for Long Un-paced production line like more than 5- station or more like 7-work station. 2. To calculate the exact formulas for Production rate with have very less error from actual production rate. 3. Useful when the set up and operation time we know then we calculate the how much product is produced in assembly line when jobs designs are change.

1. M.T. Jamali, Mohd Ziaulhaq, Dr. A. Suhail, Mohammad Khalid (Jan- Feb. 2015). ―The Effect of Imbalance on the Performance of Un-paced Production Line – A Mathematical Modeling Approach‖, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), PP 14-19, Volume 12, Issue 1 Ver. I, www.iosrjournals.org 2. Hiller, F.S. and K.C. So (1993). Some data for applying the bowel phenomenon to large production line system ―int. J.prod. res., 31, p. 811. bowel known‖ www. academia.com‖ 4. M. T. Jamali, Prof. Arif Suhail (2016). ―THE EFFECT OF IMBALANCE ON THE PERFORMANCE OF UN-PACED PRODUCTION LINE WHEN THE OPTIMAL BOWL UNKNOWN‖ International journal of core Engineering and management (ISSN 2348-9510, vol. 3, issue 8, Nov 2016), www.ijcem.in 5. Mohammad Tarique Jamali (2002). ―To find the alternate formula for production rate trends to design for un-paced production line when unbalancing the workloads.‖ Send to IMA chief academic officer 6. Kunter S. Akbay (1996). ―Using simulation optimization to find the best solution‖, Ind. Engg. Solution 28 No. 5 7. H. A. Beg (1996). ―A study of performance of Production line.‖ M.Tech. Dissertation, AMU Aligarh 8. Mohammad Tarique Jamali (2002). ―The effect of performance of imbalance on the performance of Unpaced production line‖ M.Tech dissertation, AMU Aligarh, India

Research Scholar, Young Scientist University, USA (IMA-INT-17-19 ADC-271051) and Faculty, Department of Industrial Engineering, King Khalid University, Abha, Kingdom of Saudi Arabia