Optimization Model for Lathe Management (Paper)

International Journal of Engineering & Technology IJET-IJENS Vol: 11 No: 04 1

112504-0909 IJET-IJENS @ August 2011 IJENS I J E N S

Abstract This paper discusses the optimization model for

automatic lathe continuous process periodic inspection and replacement of the cutting tool. One of the problems is to reduces the management costs by integrate theory with probability statistical method and establish a regular inspection that would provides adjustment to the average management cost. By using optimization model to perform computer simulation in order to solve the process efficiency in term of finding the best period for cutting tool replacement and also for running inspection for the machine. Furthermore, with the use of probability adjustment on the inspection interval, and enables the computing of the average downtime loss caused during inspection time interval to establish an objective function that capable to provide the best design processes and tool replacement period for inspection intervals. This model is design to effectively reduce the downtime losses and improve process efficiency. Finally, based on the proposed model evaluation, some suggestion on improving the management efficiency and reducing costs are provided at the end section of this paper.

Index TermsOptimization, modeling, lathe management, cost function

I. INTRODUCTION N industry, production costs are often lowered by reducing manufacturing times. Along with such objective, the machine tools are also continually being improved in term

of speed, acceleration and force. However, this process is also continually undergoing optimization. The problem arises when the machine operates particularly fast but it does not meet the requirement in terms of quality and tools have shorter service lives. Thus, to enhance the quality of product as well as to reduce the management costs in term of periodic inspection and replacement of cutting tool, an optimization model developed to fulfill such requirement. Recently, Brecher et al. [1] has study the interaction between manufacturing process and machine tool service lives to improve the efficiency of production system. However, this model is mainly focus on the process-machine interactions instead of reducing the management costs which is the main interest for industry. Neugebauer et al. [2] reported his review on machine tools that would increase efficiency of

Manuscript received July 1, 2011. Lim Eng Aik is with Institut Matematik Kejuruteraan, Universiti Malaysia

Perlis, 02000 Kuala Perlis, Perlis, Malaysia (Phone: 604-985-5485; fax: 604-985-5432; e-mail: ealim@ unimap.edu.my).

Syamir Alihan was with School of Manufacturing Engineering, Universiti Malaysia Perlis, Ulu Pauh, 02600 Arau, Perlis, Malaysia.

Tan Wee Choon is with School of Mechatronic Engineering, Universiti Malaysia Perlis, Ulu Pauh, 02600 Arau, Perlis, Malaysia (E-mail: [email protected]).

manufacturing production and quality. The review place a lot of comment on cutting tools technology that capable to increase the output and reduce the loss on defective product, but lack of discussion on the cost such advance tool and it effect to small industry. Lately, Mativenga and Rajemi [3] have introduced an optimum cutting parameters using minimum energy footprint. This model aim to reduce the energy consumption of lathe machine and thus, reducing the production cost. Rajemi et al. [4] reported on their work in modeling the optimum tool life for minimum energy footprint. This model enables users to select their corresponding cutting conditions that can contribute to longer tool life and reduce tool replacement costs. Finally, a critical review on metal cutting modeling and optimization techniques is performs by Mukherjee and Ray [5]. They revealed the some process parameter relationship modeling condition that improves the manufacturing operation process.

Obviously, all the mentioned works are lack of the focus on cost management that involves a continuous process periodic inspection cost along with cutting tool replacement cost. This paper is mainly focus on building an optimization model for lathe management for industry cost saving purposes. The outline of this paper is as follows: in Section 2 gives a brief explanation on the problem statement that become the main motivation for building the model; the model description and the symbol conventions are provided in Section 3; Section 4 shows the development of the optimization model along with suggestion to optimize the production process; finally, we conclude our finding in Section 5.

II. PROBLEM STATEMENT Process to produce the products can be measured in some

units. In order to maintain the normal process, it is necessary to conduct a regular inspections of the during whole production process. This inspection process is part of the procedure to maintain the quality of product which is also part of industry production process implementation. If the inspection is performs too often, then the production process surely performs in normal state processes and tremendously reduce the number of defective product. However, excessive inspection consumes high cost and increase the diagnosis time interval. Although the diagnosis cost can be reduce by the industry management, but the risk may result in a large number of defective products being produce which increases the cost of defective losses. Therefore, this optimization

Optimization Model for Lathe Management Lim Eng Aik, Syamir Alihan, and Tan Wee Choon

I



model are tends to seek the best inspection time interval in term of hour which able to minimize average industry management cost.

III. MODEL DESCRIPTION To setup our model, we placed a few assumptions as

follows: 1. Process failure is completely random and the occurrence

of 2. these failures has the same probabilities; 3. The accumulated record of 100 tool failure is the count

for a tool that has complete each task and found to produce a defective product during the process;

4. There are sufficient tool for replacement; 5. Each defective product produced during failure period is

count as cost losses per product; 6. During the inspection process, the production does not

stop. During this period, there a part being produced. Along with the assumption, we also include the symbol conventions involved in this paper: f Failure resulting defective loss of each product cost, f = 93 Ringgit / piece t The cost of each inspection, t = 5 Ringgit / times; d Cost of recovering the process failure to normal, d = 1400 Ringgit / times; k Cost of replacing new tool before failure, k = 470 Ringgit / times; L Average management cost for fix period of inspection on single part; n Time taken for each inspection (each inspection done based on number of the product produce); Average failure time interval; * Average failure time interval for fix period cutting tool replacement; ' Average time interval for tool replacement; set Average failure time interval for fix period cutting tool replacement with taking consideration on other factor;

Other Average failure time interval produce by other factor; l Number of product produce during inspection period; p ' Ratio for cases where cutting tool life that less than the average failure time interval; p1 Ratio for losses cause by other factor (not include cutting tool failure).

IV. MODEL DEVELOPMENT Based on statistical analysis for 100 sets of experimental

data, we obtained the normal distribution for this model using 2 test as N(280,91.05).

The average management cost for fix period of inspection on single part, L, consists of the following four components: I = average inspection fee for individual part; II = average diagnosis costs for individual parts; III = average loss generated by checking failure; IV = average loss caused defective products during the inspection time interval.

The inspection is performs for every n-parts, therefore, the inspection cost for each part are divided into t / n, which yield I = t / n As they only perform diagnosis after inspected failure in the process, while at average, there will be one failure for each part. Therefore, the diagnosis fees for each part is divided into II = d /

For III, due to the production process still continues during the inspection execution and to carry out such inspection also require a fix amount of time. Suppose that during the inspection of a part there were products that have been produced. Therefore, for every delay cause by inspection process is defined as l f, then the cost of losses cause by inspection delay is defined as l / , ultimately makes III = l /

Finally, to analyze IV, note that the inspection is perform once for every n-part, if there are defective product found in some part during the inspection period, in general, there are at least more than one defective product, then the detail can be illustrated as in Fig. 1. Note that "0" represents part of the qualified product while x correspond to defective product produce from failure part.

For situation (1) in Fig. 1, just a check point process is abnormal, and other in front is normal, meaning there only have one defective product; For (2), there is a checkpoint in previous part which the beginning of not normal process. Hence, there are two defective products. Lastly, for (n) is the previous checkpoint, the process is not normal, so there are n defective products. Therefore, the average defective product found during the inspection time interval at the check point

part are 1 2 ... 1

2

n n

n

. The resulting loss for this cause

Fig. 1. Inspection checkpoint for failure part.



can be define as 1

2

nf

, and with average of one failure for

each part, so losses fro each part are 12

n fu

, which yield,

IV = 1

2

n fu

In summary, the fix inspection time intervals can be derived into the following equation for calculating the average management cost as in Eq. (1).

1

2

t d l f n fL

n u u u

(1) The best inspection time interval, even L approach the

smallest n on both sides, we obtained:

2

1'

2

t fL

n u

For order = 0, we obtain:

2t un

f

(2) By considering the diagnosis on the fault location, we can

be set the most appropriate inspection time interval n with the corrected formula as:

2( )

/

l u tn

f d u

(3) As for the inspection delay that cause the production of l defective product, l = 1 that produce a defective products will identify the process is not normal.

By using Eq. (1) to reduce management costs, this allow the average failure time interval increases, this means by regularly replacing the tool enable average failure time interval increases, but as a result of fix periodic replacement of cutting tools, the tool costs will also increase which ultimately increase the management fee. Therefore, a computation is performs to verify this approach is cost-effective or not.

As the process fault losses are mainly cause by the cutting tool, specifically: (1) Failure probability cause by other reasons is p1 = 0.05; (2) The average number of recovering parts during tool failure period is less than ' piece along with it probability as p'.

After some explanation on the average failure time interval for fix period cutting tool replacement with coefficient *, then by placing it into Eq. (1) we obtain Eq. (4) as follow:

1*

' * * 2 *

k t d l f n fL

u n u u u

(4) While for * it can be calculated as follows:

Number of Produced Product*

Number of Failure Product

a u uu

a p p

In addition, the probability for process failure that caused

by other reasons is as low as 5%, but it should also be taken into account. Hence, the average failure time interval is otheru is given by:

Number of Produced Product

Number of Failure Product

Number of Produced Product total number of occur faults

total number of occur faults Number of Failure Product

1

otheru

up

Periodic replacement during the average failure time interval set, substitute for *u , making otheru obtain the harmonic mean define as follow:

11 1

*

set

other

u

u u

Therefore the optimization model can be summarizing as follow:

1

Min2set set set set

k t d l f n fL

u n u u u

(5)

Let Lset= 0 provide the most suitable inspection time intervals to be:

2 u tn

f

(6) And the correction formula is:

2( )

/set

set

u l tn

f d u

(7)

The model can be solved through computer programming to achieve one-dimensional search, the results are as follows: the most suitable inspection intervals n = 15 (cases), the best tool change intervals ' = 365 (cases), the smallest unit for average management cost for fix period of inspection on single part, L = 4.65 (Ringgit).

Assume that industry installing automatic inspection systems on the lathe machine. Therefore, inspection on each part fee is consider as zero. With the automatic inspection systems can avoid losses arising from man make inspection downtime, thus reducing the average management cost.

Set n as the inspection statistics value, where the number represent the system sequentially inspection for n-parts that appears to have m defective product. With the establishment of dynamic inspection mode, the inspection system will automatically record the inspection on k parts during normal process. The following are four the possible cases: 1. Statistics order of n-parts, with defective probability of

less than 2%, then the process consider normal to continue production;

2. Statistics order of n-parts, with defective probability at 2% but less than 60%, with all inspected parts consists of defective probability of less than 2%, then the process consider normal to continue production;

3. Statistics order of n-parts, with defective probability is higher than 60%, with all inspected parts consists of defective probability of less than 2%, then the process consider normal to continue production;



4. Statistics order of n-parts, defective rate at 2% less than 60%, with all inspected parts consists of defective probability at 2%, then the process consider fail and the system will automatically send a signal to perform inspection and diagnosis.

V. CONCLUSIONS From the proposed model, we can infer that the model is

easy to operate and has a wide range of application. Furthermore, this model provides the average management cost that capable of solving for the optimum values with the aids of computer programming. The results show a strong stability and the solution obtained is consistent with the actual situation. This proposed mathematical optimization model are build using the statistical data established and it provided long term value for guiding the production process and minimize the management cost. This proposed model still consist spaces for future improvement. One of the studies that could be included in this model is the impact of the cutting tool life which certainly improves the practicality of the model. The other studies is the consideration on parts of the production process that still lack of continuity in current model which will help improve the better scalability to the model. Both the mentioned improvement are for future work.

REFERENCES [1] C. Brecher, M. Esser, S. Witt, Interaction of manufacturing process and

machine tool, in CIRP ANNALS Manufacturing Technology 58, 2009, pp. 588607.

[2] R. Neugebauer, B. Denkena , K. Wegener, Mechatronic systems for machine tools, in CIRP ANNALS Manufacturing Technology 56, 2007, pp. 657686.

[3] P.T. Mativenga, M.F. Rajemi, Calculation of optimum cutting parameters based on minimum energy footprint, in CIRP ANNALS Manufacturing Technology 60, 2011, pp. 149152.

[4] M.F. Rajemi, P.T. Mativenga, A. Aramcharoen, Sustainable machining: selection of optimum turning conditions based on minimum energy considerations, Journal of Cleaner Production, 18, pp. 10591065, 2010.

[5] I. Mukherjee, P.K. Ray, A review of optimization techniques in metal cutting processes, Computer & Industrial Engineering, 50, pp. 1534, 2006.

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Optimization Model for Lathe Management (Paper)