HotSubExpress Case Study: Analyzing Six Sigma Challenges

IE 431 Design for Six Sigma Prof. Harrison Kim Case Study 2 Alejandro Alcoser 664687230 10/16/2023

 DEFINE ‘HotSubExpress’ is a chain of restaurants that offers carry-out hot sandwiches and has its operations centered in the Midwest of the United States. With the implementation of their new promotion: 15 minutes or it is free-guaranteed, the company has started to show financial difficulties. The number of sandwiches given for free is substantially high, which is causing money loss and instability. Because of this, the district manager decided to perform a Six Sigma evaluation on the situation in order to understand the causes of the problem and get to a feasible solution. A variety of data was drawn to perform these studies, and important decisions are now in the hands of the Quality Engineering representatives.  MEASURE The team decided to start by identifying the best fitted type of distribution for the data. As shown in the image below, the normal distribution seems to be the best fit, for which it is going to be used in the rest of the process. Figure 1. Distribution Analysis

The DPM is now calculated using a normal distribution: Figure 2. Capability Analysis CT This resulted in a value of 187129.22 DPM, with a given loss of $3.20 per each defect. It was reported that 1300 out of 14350 sandwiches were given away in the last two weeks. However, using the DPM value, the number of lost sandwiches would go up to 2685.30, following the next calculation: 14350 × 187129.22 1000000 = 2685.30 defects This is twice the value estimated by the managers. This means they are losing around $8.6k every two weeks among the 5 stores, which would represent a value of approximately $860 per working day. It was also observed that the Cpk and Ppk values were 0.32 and 0.30 respectively. These values can be considered low and non-desirable, meaning that the distribution is wide and deviates from the target.

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To analyze the stability of the data, an X-bar chart was performed, which showed that the variable is not stable since some values go over/under the specified limits, as shown in Figure 3. Figure 3. Xbar-R CT It is understood that the output in this scenario is for sandwiches to be cooked in under 15 minutes. To get to that point, the team identified the four main input variables, or causes, for sandwiches taking more than 15 minutes. These causes are described as follows: - Overcooking hot sandwiches: New employees without proper training overcook the product, which takes more time. - Standard oven controls: Subjectivity in setting oven controls because of variations among different stores.

- Oven power level: Differences in cooking power between different stores, which slow down the process. - Manager’s experience: Managers not properly trained to supervise the stores, causing delays and misunderstandings.  ANALYZE In order to evaluate the cooking time stratified by store and shift, a comparative box plot is going to be performed, as well as its respective statistics. Figure 4. Box plot CT

Table 1. Statistics CT Based on the graph and data, the first thing that can be evidenced is Store A’s inconsistency between its two shifts. It can be seen that in their second shift, Store A goes over the 15-minute mark on various occasions, even having a mean value of 15.576, which is totally different from what is seen in shift 1 where the values are much lower. A considerable number of outliers can also be identified in Store A’s second shift, which matches with the cause of implementing two new cooks to the store. Additionally, Store E has cooking times of over 15 minutes in both shifts, which indicates a problem in its management. A difference in standard deviation can also be seen in Store B, which could be due to a new cook being hired for shift 1. The rest of the stores seem to be able to cook their sandwiches in less than 15 minutes and have a good performance. Evaluating new improvements

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In order to evaluate the effectiveness of the new improvements due to special causes, two new box plots are going to be performed indicating the cooking time of each store before and after the improvements, based on the data given. Figure 5. Box plots CT and CT improved An ANOVA is also going to be performed in order to observe the variances between the two cases. ANOVA before improvement Table 2. ANOVA CT ANOVA after improvement

Table 3. ANOVA CT improved A new Capability Analysis was also performed considering the data after the improvements, which is shown below. Figure 6. Capability Analysis CT improved It’s important to note that after these changes, the DPM went from 187129.22 to 50268.77, which is a reduction of less than a third from the original value, revealing that these improvements are actually taking effect. On the other hand, the ANOVA showed a P-value of 0 in both cases, which means that H0 is rejected and not all means are equal.

Based on the tests performed, an evaluation of the specified special causes is going to be made: 1. Overcooking hot sandwiches: This is due to new untrained cooks in stores A, B, and C. By investing in training, the mean value of Store A, which initially had the most outliers and higher values, decreases significantly (from 13.33 to 9.83), while the other two stores remain similar. This suggests that the investment of $900 for training was justified. 2. Standard oven controls: By changing the manual controls of the oven in Store D to electronic ones, the company is investing $500. Based on the standard deviation values of Store D before and after the improvement, it can be said that said improvement is justified since the new value is half the previous one. 3. Oven power level. An investment of $2500 was made in order to install a 220V power service in Store E. As discussed previously, Store E has initially the second highest mean value (almost 13 minutes), and some of its cooking times are even going over the 15- minute mark. After the improvement, a mean drop of 2 minutes can be evidenced, for which the investment, although expensive, is justified since this store was causing direct money loss alongside store A. 4. Manager experience: It was identified that the manager in Store B doesn’t have as much experience as managers in the other stores, for which a value of $240 was invested in his/her training. However, it is shown that Store B has the lowest mean value and second lowest standard deviation among all stores before the investment, for which the investment is probably not justified since it didn’t seem to be a specific problem in that store in the first place.  IMPROVE It was informed that the team is still not satisfied with the results. Because of this, they’ve brainstormed two improvement options to apply to the company. Both options are going to be analyzed in the following pages in order to decide which one is a better fit for HotSubExpress. Option 1: Purchase new ovens

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By purchasing new ovens for the 5 stores, the company would invest a total of $100k. However, the cooking time is expected to decrease in 0.4 minutes per sandwich. New graphs and statistics were made showing these changes and are shown as follows. Table 4. ANOVA new ovens Figure 7. Capability Analysis new ovens

Figure 8. Xbar-R new ovens In the first place, it can be seen that the DPM is reduced even more, to 35723.21. Also, the values of Ppk and Cpk are very similar and are higher than before. The Xbar-R graph also demonstrates that the data is now in control since no value is over any of the limits. The ANOVA shows the same R squared and P-value, but all the means seem to be lower with no exceptions. This all suggests that buying new ovens is an investment that will most likely result in a positive outcome for the company. Option 2: Optimize the cooking process It was brought up that there could exist a difference between cooking the sandwiches in the center of the oven vs on the outside of the oven. Two Capability Analysis were created to observe the difference between the cooking placements.

Figure 9. Capability Analysis Outside Oven Figure 10. . Capability Analysis Center Oven

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Table 5. Statistics Center vs Outside Figure 11. I-MR Center vs Outside Evidently, there is a considerable difference between the two DPM values, going from 37839.78 with an outside cooking strategy vs 19834.34 with a center one. The means and standard deviation are also smaller in the case of the center placement of the sandwiches, and the I-MR graph shows a more controlled data. This suggests that cooking the sandwiches in the center of the oven does in fact reduce the time in which they are cooked. Therefore, based on the DPM values from both approaches as well as their stability, and considering the fact that it doesn’t involve any additional investment, it is recommended that the company follows option 2 to achieve the best results.  CONTROL It is stated that the promotion ’15 or it is free – guaranteed’ raised the annual net income by 150k, excluding the cost of free sandwiches. With the results obtained in the previous analysis, the costs of the different improvements can be calculated in order to evaluate the effectiveness of the promotion.

Before any improvement, the DPM value was 187129.22, with a given loss of $3.20 per defect. Knowing that the stores operate 343 days per year, and they serve a mean of 200 sandwiches per store per day, the cost of defects per year would be: [ ( 187129.22 1000000 ) × 200 × 5 × 343 ] ×$ 3.2 = $ 205393.03 Subtracting the additional annual net income with the annual cost of defects would give a value of $55393 in money lost. The company is losing all $150k additional profit from the promotion plus $55393 without the improvements. However, after the improvements already made, and after applying option 2, the DPM value would decrease to 19834.34. Performing the same calculations, the cost of defects per year would be: [ ( 19834.34 1000000 ) × 200 × 5 × 343 ] ×$ 3.2 = $ 21770.17 Therefore, the profit of the first year would be  $150000 - $4140 - $21770.17 = $124089.83. The profit of the second year after paying the initial improvements would be  $150000 - $21770.17 = $128229.83. These improvements would make the company lose only around 20k yearly in comparison to the 205k they were losing before the changes. If they make sure all the new standards are consistently followed, it can be concluded that the promotion was worth it to the company, and that it will help increase their annual profit considerably.

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Case 2 Alejandro Alcoser

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