First let me define the term RPM being used in this paper. RPM in the remaining lines stands for Revolution Per Minute and refers to the speed of an electric motor which drives a machine. Sewing machines use electric motors set a a specific RPM among other settings to produce the garment. Most factories in this type of business possess thousands of such machines, and therefore at least the same amount of electric motors. Hence in the basic concepts and understanding of six sigma tells us that we should expect among such a large population of machines a great deal of variation of RPMs among the motors.

It does not matter if your sewing facility is in Latin America, Asia, Africa, or even Europe or North America, the effects of machines RPM on productivity and quality are not random effects in the plant, will no spare your plant, and most of the time act behind-the-scene and thus is not taken into account in strategic planning, decisions taking or cost drivers understanding. That is why we consider RPM effects in the garment industry in particular and in the fashion industry in general, which includes leather type products (shoes, handbags etc.), a hidden critical-to-quality (CTQ) and critical-to-process (CTP) factor with a lethal weapon on cost. At this stage I would like to replace the term critical-to-process, CTP, by critical-to-value stream, CTV. And in the following lines it will be cleared why substituting CTP by CTV, but for now let's just say that one of the major effect is on value-flow through the unbalanced time it creates.

This in fact is where I would like to start the details explanation of those effects, using as much as possible a true data, a real case study, to illustrate the concept.

### Cycle Time variations and the setting of machines speed.

It all initiates with the cycle time of the operation. Cycle times are usually set as an average time resulting from a time study taken directly on site. In sewing this current cycle time of an operation is often compared to standard time established from GSD (General Sewing Data) methodology, to decide on the amount of variance and improvement to make. It is also used to establish incentive plans.

However it is usually forgotten that making decisions, especially numerical decisions, based on mean only, is not very statistically savvy, given the fact that central tendency and central theorem are fundamental concepts of statistics. Also as the cycle time study is made at a predetermined station, it usually has a preset machine speed or RPM depending in some cases on recommended values from the machine operating manual, and in other cases on empirical knowledge of the lines, but rarely on scientifically calculated from operators skills and efficiency. Therefore to start with we are in the presence of a combined issue: operator's cycle time improperly set because of unconsidered variations within the times in the study itself, and RPM not a function of that operator's cycle time.

The real issue to be resolved is threefold:

- Why the operator's cycle time resulting from the study does not match the mathematical value corresponding to the preset RPM of the machine?
- How much impact the variance accounts for in productivity?
- What would be an effective "productivity at the source" solution to prevent this first effect.

In order to correctly answer the first question, first the distribution of the time study must be analyzed and understood. A good study will include different times of the day, say at least morning and afternoon, different levels of operators (slow, medium, and fast) for the same operation, and about 10 parts each time. Therefore the study generates at least 60 data, enough to define a distribution, which not necessarily is a normal distribution and hence statistical mean or average may not be representative.

#### Case Study Part 1-

The following study was realized in a sewing plant with slightly over 800 machines. The study was performed according to the minimum requirements mentioned above and 60 data were recorded.

Average cycle time from the study is 18.92 seconds. But is it really a fact, when you have time as much as 27.68 seconds, more than 46% higher, or as low as 12 seconds or 36.5% lower? Using 18.92 seconds as cycle time which would be the tendency of most factories, would be a gigantic mistake and any plan made on this number, incentives, customer delivery dates, and even product cost and gross margin, would be at very high risk.

This study presents the following distribution, in which it can be observed that in spite of being a normal distribution (p-value =0.0516), because of the dispersion between time samples the mean is no significant for the production process.

Time studies in any industry have three important characteristics that must be looked at: skewness, kurtosis and coefficient of variation, and specially in the fashion industry using sewing RPM, as all three of them will have an effect on RPM. In our particular case study it is observed

- a slightly skewed distribution to the right (0.52) meaning that there exists a bit more frequent repetitions of times lower than the mathematical mean. The higher the skewness value, the more disqualified would be the average time, the mean, to be used as cycle time of the operation.
- a negative kurtosis (using a software which in turn uses the G2 formula with a correction factor of -3 for excess kurtosis, so that a normal distribution would have a kurtosis of zero) meaning that the distribution is platykurtic (flat and dispersed). The more platykurtic is the time study, the higher the uncertainty of meeting production goals would be using the average time as cycle time
- a coefficient of variation relatively high, 19%. This is basically a summary of the amount of variation present in the distribution. In this case study it tells us on the volatility of productivity. Productivity can "evaporate" at a rate of 19%. This is a high risk for cost.

Understanding the distribution (in plain language the behavior) of the time study is thus a first and important step in any process balancing in any type of industry and even service. But in sewing what is its relation with RPM? Logically speaking one cannot operate any machine faster than the maximum machine speed itself, which is given by the motor driving the speed. Therefore it is evident that there exists a regression formula which correlates both factors: RPM and cycle time. The given formula is:

Machine RPM = (SPI X loop length X 60)/cycle time

where the loop length is the length of the part to be sewn, and SPI is stitches per inch. This equation expressed in term of cycle time is:

Cycle time = (SPI X loop length X 60)/Machine RPM

At the time of the study, the machine had a preset speed. Hence it can be calculated mathematically what the expected cycle time should be; and vice versa given the cycle time from the time study it can be calculated what is the corresponding machine speed. In either case, the difference between the theoretical expected value and the actual observed value is the first effect of setting RPM in the garment and fashion industry in general.

In this case study the preset speed is 3550 RPM.The SPI as per customer requirement was set at 12 stitches per inch and the loop length for this sewing section of the garment was 78.74 inches. Given those conditions and the 18.924 seconds average cycle time if used, the expected RPM by mathematics should of been 2996 RPM and not 3550, leading to the conclusion of the negative impact on productivity of -16%

Machine RPM = (12x78.74x60)/18.924 = 2996

% loss = (2996-3550)/3550 = -16%

At the preset speed of the study of 3550 RPM, the operators average cycle time should of been 15.970 seconds instead of 18.920, leading to the -16% loss on productivity.

Cycle time = (12x78.74x60)/3550 = 15.970 seconds

% loss = (15.970-18.924)/18.924 = -16%

The observed operators cycle time does not match the expected cycle time because of a too large gap in skills among the three operators. The Coefficient of Variation was calculated to be 19% and hence the study should of been invalidated. One sure source of the gap in skills is the operators standardization of training, which is a common source in the industry. It goes beyond the garment industry and extends to the fashion industry in general.

Indeed visiting the "sewing academy", an internal preparation school that many factories have to train mostly their new associates, of the garment industry, it is very rare to find lean manufacturing concepts such as standard work combination sheet, TWI training within industry, skills matrix indicators or other effective standardization tools being applied. Therefore methods are strongly taught and above all for the specific purpose of this paper there is no RPM-efficiency learning curve, even though we would think according to what we have been seeing so far that it is a fundamental indicator and training tool to prevent productivity and cost loss in later production. Most of the factories carry over a learning curve. But a learning curve based on time which plots the trainee progress over time. Of course that is important too. But it is much less critical because by human nature a repetitive work will become more efficient over time anyway. But it is not obvious that repetitive work will efficiency increase just from machine speed increase, if it is not properly trained on. One human instinct when machine speed is increased would be to try to hold on the fabrics to compensate for the excess speed, which however will create an elongation of some fabrics because the machine would still try to pull in the fabrics.

One objective of this paper is to set the fundamentals of an RPM-efficiency learning curve (I prefer to call it RPM-Cycle time learning curve), using the case study on hand for true values. For this purpose we will create a table to show on one side different settings of RPM and the corresponding expected cycle times, and on the other the expected cycle times at different coefficient of variation above and below, leaving as fixed values stitches per inch SPI, and loop length for that operation.

- As the preset speed was 3550, let us vary as much as a wide range possible, the RPM. We will use the range from 2000 to 6000 with and increment of 100. This will give a large enough of RPM spectrum.
- For each RPM increment, we calculate from the equation above the expected CT, which we called Standard cycle time below.
- From the descriptive statistics we have a CV of 19%, therefore let us vary over a range of -19% to 19% the CV, to create different scenarios.

The following distribution table is the result.

How de we use the table?

- In the column for expected cycle time (CV std on the table), look for the value closest to the observed average cycle time of the study. In this study case the observed average cycle time is 18.924 seconds and the closest value is 18.898 seconds.
- From this closest Cycle time value, read across the line corresponding expected machine speed RPM. Those steps are shown in blue arrows above. For a CT of 18.898 seconds as the closest value to 18.924, the RPM should of been 3000, which is close enough to the 2996 calculated above.
- Setting the machine RPM at 3000 and taking into account a CV of 19%, one should expect cycle time to be between 15.307 seconds and 22.488 seconds, which are the values within the blue box we used to highlight the example.
- With this table then we can plot a learning curve and use step 3 above to set speed during training.

The following learning curve is the result or the plot of above table distribution with a zoom on step 3.

Using this learning curve for training, shows either by how much should we set RPM for the trainee according to his efficiency performance while in training, or what efficiency should we ask him per out setting of RPM. So the recommended use is to start at a certain RPM as low as possible on the first day of training and keep increasing RPM every time he consistently reach the expected cycle time within the range provided. This way he being trained on faster and faster machine and is expected to math the theoretical value once release to production. This is standardization of speed and cycle at the source, what we previously denominated "productivity at the source" solution.

### Optimizing RPM interactions with other critical-to-process factors

When operators are not well trained within a standard work system in which the pair RPM-Cycle time is critical for continuous flow within the value stream, his natural instinct working on a machine at a higher speed than he is used to, would be to offer some resistance to the natural pulling movement of the mechanics of the machines, trying to hold back by fear of mistakes, which terminates into stretching the fabrics and generating potential failure modes such as misalignment in garment or even over size; and when working on a machine at a lower speed than usual, his tendency would be to push the fabric in, because his frustration makes him want to finish faster, causing the to shrink. Either way not having the proper skill will generate dimensions issues.

We found therefore that it is necessary for the garment industry to also realized some design of experiments,DOE, to capture the impact of setting the machine RPM at a speed greater or lower than the operator acquired skill from the RPM-cycle time learning curve above. A DOE of this type should at the least consider RPM as one of the factor, operator efficiency as a second factor, SPI stiches per inch as a third factor, making it a 2x3 experiment, and if desired the type of fabrics material being sewn as a fourth factor for a 2x4 DOE. And as the interest is on the effect of RPM on quality and productivity the response to look for in the DOE is dimension variation, that is either stretching or shrinking of the fabrics. The industry may also want to study the probability of other quality defects and include in the measure responses potential quality related issues such as missing stitches, potential result from pushing in the fabrics at a low speed by a fast operator, or again defects such as holes from holding back on fabrics at a high speed by a slow operator.

Those are the different effects of RPM that should not be neglected when seeking a productivity improvement in the fashion manufacturing industry.

#### Case study part 2-

The above case study continues with the minimum 2x3 Design of experiment and one response: dimension variation, and 3 repetitions, which implies that each piece of garment of the 24 treatments in that particular production operation shall be measured before sewing and after sewing to record as the DOE response the difference of the measurements. A negative number from the before and after measurement is thus a shrinkage of the fabrics, while a positive difference is a stretch. The factors are as mentioned above and the levels are set to be as followed:

- RPM: low is 3550 and high is 6000
- Operators are chosen from the three who participated in the time study. The slowest is considered low and his cycle time yielded to an hourly capacity of 163, while the fastest is considered as the high level with a capacity of 213 parts per hour.
- Stitches per inch SPI: low is 10 and high is 13

24 treatments are randomly ran and the results in dimension variation is shown on the following table, yellow column. The effect of an appropriate setting of speed relative to operator's skill measure in time (cycle time) is already visible in the results, as predicted above. There are negative numbers meaning shrinkage of the piece of the garment, positive numbers meaning stretching of the piece, and zeros meaning the sewn piece has the same dimension before and after sewing.

To determine whether the difference in settings of the pair (RPM/Operator Capacity) means, is due to random chance or are statistically significantly different, an ANOVA F-test is performed as we recommend to do on any DOE. Any design of experiment implies that one is looking for a model that correlates the individual factors and their combinations to the response recorded. The coefficient of determination R squared is 60% and a sensitive analysis of the residuals allow to conclude that correlation between dimension variation and the factors is good enough. Confirming mathematically the hypothesis of the effect of an inadequate RPM over product dimensions specifications. In fact the ANOVA also shows that operators efficiency and machine speed are quite significant in the model. This can be observed both in the P-values of the parameters and the Pareto Chart of significance.

The F-ratio is equal to the Mean Square of the model divided by the Mean Square error within the model. The Model F-ratio of 3.473 implies the model is significant.The p-value ('Probability of exceeding the observed F-ratio assuming no significant differences among the means') of 0.0186 indicates that there is only a 1.86% probability that a Model F-ratio this large could occur due to noise (random chance) only. In other words, the setting of the factors differs significantly in terms of impact on dimensions or specifications.

An analysis of Main effects and Interactions of the results shows that both independent variables RPM and Operator efficiency have opposite effects on dimension. An increase in machine speed will increase stretching while an increase in operator efficiency will reduce stretching. SPI behaves the same as RPM, but with a lighter slope. As for interactions there are two relevant ones: SPI interacts with both RPM and Operator efficiency

The main purpose of this research paper is to not only establish the probable impact of machine speed, RPM, on quality and cost but also to provide a potential solution or compensation to the effect. Just like the tailored learning curve for RPM-Cycle time derived in part one from the time study, it is fundamental in the design of experiment to be able to extract a guide capable of helping the factory who adopts the principles of RPM effects to optimized the setting of machine speed for the prevention of a later customer satisfaction issue, resulting from dimensions and specifications process related defects. By using a surface and/or contour plot, it is possible to accomplish this objective. Contour plot is a technique consisting of a graphic representation of the relationships among three numeric variables in two dimensions, each variable in the desired range of operation. The two variables are for the X and Y axes, and the third variable Z is for contour levels. The contour levels are plotted as curves and color coded for range of responses. The surface plot is a 3D representation of the contour.

In the particular case study which above results for the DOE, the contour plot is highlighted next and reveals the different options of settings of the machine speed in RPM according to operator efficiency in units per hour for a range of possible responses of variation of the original specifications. As the optimal response would be no stretching, and no shrinking, that is zero elongation, which we have circled in the legend of ranges, what should be the RPM setting for ideally a regular average operator, not fast, not slow? We have marked the answer with the two intersecting lines on the plot. A middle efficiency operator (188 pieces per hour in that particular operation) for the blue range of 0 to 0.01 in of stretch would need an RPM close to 4775. This set guarantees the sustainability of quality specifications over time.

However it is also revealed that RPM and the Operator efficiency has some kind of interaction with SPI, stitch per inches. Therefore setting the RPM of the machine to an average operator or even to a fast or slow operator, requires to go and verify that the setting will not affect in turns the SPI specifications usually given by the customer. For this it is necessary that from a contour plot of Operator efficiency versus SPI or RPM versus SPI, it is verified why is the corresponding Stitches necessary to continue yielding a zero or near zero dimension variation.

This contour plot of our case study is shown next and revealed that SPI can indeed be 12 as originally required by the customer specifications. In case it does not fall within the SPI recommended by customers then it is necessary to discuss options with the customer on the basis of the DOE and share the results so that a consensus can be obtained. However it must be cleared that any consensus reached, it is what it is, a consensus and not the optimum response to minimize RPM effect over dimensions specifications in quality.

### Measuring MTBF originated from RPM to quantify effect on machine stoppages and productivity

What happens when the production floor does not induced, trained and prepared operator to develop efficiency while increasing progressively machine speed, so that he or she develops adequate handling skills at high speed? Not only we shall be at risk for dimension quality errors but as well poor handling may cause minor stoppages due to broken needle, broken thread, unset stitches per inch, looper issues and a few more. Each minor stoppage may look insignificant and because of that supervisors, mechanics, and engineers tend to ignore them. However the sum of it may not be so insignificant and really have a tremendous negative effect on cost. It all depends on the frequency at which stoppages occur, that is Mean Time Between Failure, MTBF. To quantify whether or not the hypothesis of machine failure originated by inadequate RPM versus operator efficiency and skill it is necessary to measure during a representative time period these two basic maintenance indicators MTBF and MTTR Mean Time To Repair.

Such a measurement would require a real-time recording system of when the failure started, when the repair technician arrived, and when the failure was repaired (finish time) and the machine was given back to the operator for full production. We suggest the use of a simple database as the one we developed in our case study to research on the matter.

#### Case Study part 3-

We continue with the same case study as in the prior sections. At this time it is implemented across the entire facility and for all sewing machines a manual system to record times of the day on a form prepared for the purpose. When the machine stops the supervisor calls the technician and punch in a time clock the exact time of the moment. When the technician arrives he would do the same to record his arrival, and when the machine is handed back for production the supervisor and the mechanics would again punch the form. The forms on a daily basis would be entered into the database. It is a simple manual system which only consumes a few seconds of the supervisors and the technicians and no more than 10 minutes of a clerk or anyone to digitally input the data. In our case here one complete month of data was recorded on the following Excel database showing just an extract of the information as 4340 stoppages have been recorded across all 10 lines or areas.

The headline of the database shows the relevant informations to be recollected; the most important being the three times of the day for each minor stoppage, the reason of the stoppage, whether or not the stoppage is originated from a reason related to machine speed versus operator efficiency as this is the main purpose of the study, and on a secondary level of importance the line or area number if we want to go into detailed lines in the future. We could as well record the technician name or employee number for further details in the future, and the machine code for even more details. So far we kept it simple and record the absolute necessary for the main purpose of demonstrating the effect of RPM on MTBF and hence on productivity and cost.

It is important to define and standardize the names of all the potential reasons for stoppages prior to recording, so that data can be filtered if needed. From the data recollected there are three columns which calculate:

- the total downtime from the calling of the technician to handing back of the machine,
- the time it took the technician to arrive or show up at the point of repair
- and the real actual time of repair which is the difference of the above two times.

The results is shown next.

The results shown a negative MTBF which at the a first glance may seems to be a non sense on the basis of the apparent impossibility of having a negative time between two events. However it is not a non sense when your calculations are contemplating a large number of machines and an entire production facility, in the case here 354 machines, because it is perfectly logic that it may occur that a machine breaks down before the technician completes its repair on another machine. In fact the higher the number of machines in the plant, the higher the probability of negative MTBF, when of course there are some serious maintenance issues or inadequate speed adjustment for our particular case study.

Therefore the correct interpretation is that 48 minutes before a machine gets repaired, another breaks down and operator must stop. It is obvious that this will affect the plant productivity even though at this stage we do not yet know by how much. Meanwhile the total time from the calling of the mechanics to the resume time of production is in the average 55 minutes (MTTR) while the real repair time is 36 minutes. This means on the average the technician or mechanics take 19 minutes to arrive at the POS, point of stoppage. expressing the situation in one sentence would be: 48 minutes on the average, before a technician completes his repair work, another machine in the facility will break down and another technician will take 19 minutes to arrive and 36 minutes to repair

The numbers are alarming in this paticular true case study. Other cases may show a healthier MTBF but the principles and the calculations applied here remain the same.

There are calculations that are derived from this data and that are fundamental in the future strategy of the maintenance department. With a total of 21 technicians and a gross day of 576 minutes, the available maintenance time in men-minutes is 21 by 576 or 12,096 minutes-men. From there we can calculate the following:

- Given that it takes 55 minutes of restoration of the function, the maintenance team as a whole has the capacity to attend to 12096/55 = 220 stops per day to be at maximum capacity.
- However, since the technicians must also provide preventive maintenance to the machines, have time for personal needs, and inject holiday factors where the 21 are not present simultaneously, the balancing calculations should only contemplate 50% of the maximum capacity. This 50% would represent 110 stops per day.
- The data show 4340 stops in 48 days, an average of 90 stops per day or 41% of the maximum capacity, but more important 90/110 = 82% of the recommended load for repair. That is to say that sooner than later even 21 technicians will not be enough to attend the machinery.
- The solution is not only in the reduction of the 19 minutes of response time, or in the application of autonomous maintenance checklist of the reasons for stoppages at the beginning of the shift, but above all in an induction program to new operators where speed machine increment is considered progressively with acquired operator s skills.

Taking into account that the working day is 576 minutes, it can be predicted that on average the plant will experience 82 stops during the day (576 / (55-48)). Since each stop takes an average of 55 minutes of repair or average duration to restart its operation, a total of 4510 minutes (82 by 55) of "not working" or stops during the day can be calculated. Assuming that the plant has 354 sewing machines, the total available time is 203,904 minutes (354 by 576 minutes per day). The minimum daily impact on productivity is (4510 / 203,904) is 2.2%

The following table summarize the lost revenues daily impact according to different scenarios of production volume and gross margins per unit.

In general Non adjusted RPM to operators efficiency will also generates Mean time between failures considerable increase and hence have a serious impact on revenues not earned daily. From the number in the case study it can go from only 3.3 dollars a day for an extremely low production and product gross margin, up to 1650 dollars a day for a high volume production and expensive gross margin per product. In this particular plant the production volume is 9000 a day, and on average the gross margin on a product is 1.5 dollars. At the end of the measurement period they had a lost revenues (297 times 48) of US$ 14,256 and in one year the lost revenue would be (297 by 252 days for the year) US$ 74,844

### Conclusion

There is a great effect of machine speed expressed in revolutions per minute, RPM, on productivity, quality, and maintenance, hence on operating cost and lost revenues. Most of the time upper management knows or at least has a feeling for the issue but because they have not put it into equation, it has been difficult for them to take concrete and sustainable decisions. In addition the lack of identification of the most effective solution, that is a different method of training new operators learning curve also contemplate separate curves for machine speed and quality, has prevented upper management in latin america sewing industry to boost revenues, lower cost and be more competitive on the global contract manufacturing market.