To Find the Alternate Formula for Production Rate Trends to Design for Un-Paced Production Line When Unbalancing the Workloads

INTRODUCTION

In Un-paced production line there are prediction of production line rate to calculate develop the mathematical (Jamali, 2002. Ziaulhaq, et. al., 2015) formula. There are for 2 station the formula for production rate calculated manually the formula (Jamali, 2002) are when we solve the equation when we found these 3equation through exponential distribution strategy to solve the un-paced line for steady state. Solving the three algebraic equations is easy task but for developing 5 station production line found the 55 algebraic equations we found solving it a difficult task therefore we solve it by C programing (Jamali, 2002. Ziaulhaq, et. al., 2015). There for 2 station un-paced production line the formula are given below We know that αi = mean operation rate at station i Where αi = 1/μi Where μi ( mu) = mean operation time at station i : i=1,2 Where R= production rate of the line R =α1Xα2(α1+α2)/( α12+ α22+ α1Xα2) In for designing un-paced production line more than 7 station large algebraic equation generate this is not easy solve to find the production rate of line. Therefore from result of 5-station production we gave an alternate formula to find out the trends of effective ness in this formula to 5 station line. We found it the trends is effective when we see the graphs of un-paced line rate and the alternate formula production line.

Many Researchers Find the Optimal Bowl distribution of workload (Hiller, and So, 1993) and degree of closeness (Jamali, 2016) or when the optimal bowl is unknown (Jamali & Suhail, 2016) to the 5-station to the bowel phenol menon.in 5 station un-paced production line with exponentially distributed operation time. From the bowel phenomenon we see that in the μi (mui) = mean operation time at station i: (i=1,2,3,4,5) If we use only last and first operation station time behavior of worker in the line we say that the two station time is important for designing the Un-paced production line other station behavior is less impact on the un-paced production line. Therefore for calculation this production line is called as Alternate formula for calculating the rate. To find the alternate production rate we take the formula as fallows Alternate formula Rate = (μ1 + μ 5)/total time in production line In table for μ1= Mu1; μ2= Mu2; μ3= Mu3; μ4= Mu4; μ5= Mu5

formula given in tables. We see the trends in graphs developed in to serial number VS production rate (R) and alternate formula production rate (AFR) from different outcomes of workloads distribution linearly and randomly from different data set. We found that for different values of degree of imbalance D (the difference between highest operation times to the lowest operation time) Example for table 1 (D= μ5 – μ4: D= 1.9- 0.1 = 1.8) In Table one the degree of imbalance is D= 1.8 Here highest work load on work station 5 is 1.9 and lowest workload on station 4 is 0.1 Therefore the degree of imbalance is equal to D=1.8

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

Graph For series 1 Rate(R) , For series 2 Alternate Formula rate ( AFR) For S. No. 1 to 60 in table is mention as 1 to 14 in graph in horizontal

Alternate production rate is same as the trends in production rate. 2. For unbalancing the line D= 1.8 linear distribution of workloads in station or D=1.9 random distribution or higher the value of imbalance like D=1.2 or D=1 in linear or random distribution of workload distribution the graph nature of alternate formula of production rate is same as the production rate formula 3. For Low degree of imbalance like D= 0.4 to 0.3 for linear or random values the alternate formula the curve or graph is above to the production rate formula

From the above results we say that the alternate formula is effective for designing the bigger assembly line without using the computer or software. It is easy and designer who know the assembly line/ production line arrange the work-station easily according to the work.

1. This formula is checked for designing the robotic assembly line for practical uses of the work load distribution when the work process done by the expert operator by manually. 2. Also find out the production rate of the assembly line/ production line when the batch size, operation time, setup time know for any products assembly. 3. We also estimate the cost of production to develop the software

1. Mohammad Tarique Jamali (2002). ―The effect of performance of imbalance on the performance of Unpaced production line‖ M.Tech dissertation, AMU Aligarh, India 2. 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 3. Hiller, F.S. and K.C. So (1993). Some data for applying the bowel phenomenon to large 4. M. T. Jamali, Prof. Arif Suhail (2016). ―The Effect of Imbalance on the Performance of Un-paced Production line when the optimal bowel known‖ www. academia.com‖ 5. 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 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

Research Scholar, Young Scientist University, USA (IMA-INT-17-19 ADC-271051)