Restaurant Problem I have recently started five fast food restaurants throughout Texas. My concern is that my stores are taking too long to process orders in the drive-through, so I've instructed the store managers to collect drive-through order processing times for a two hour period during the day. These data are shown below (values are in minutes). It is assumed that this data represents a typical two hour time period for the restaurants. Order # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Restaurant 1 Restaurant 2 Restaurant 3 Restaurant 4 Restaurant 5 1.99 1.52 1.47 1.72 1.45 1.85 1.53 1.42 1.77 1.69 1.94 1.41 1.60 1.55 1.50 1.38 1.47 1.60 1.35 1.42 1.70 1.68 1.81 1.56 1.66 1.81 1.86 1.90 1.63 1.64 1.75 1.67 1.37 1.53 1.58 1.80 1.81 1.43 1.90 1.47 1.56 1.61 1.52 1.51 2.06 1.83 1.27 1.42 1.58 1.75 1.43 1.80 1.27 1.49 1.73 1.84 1.50 1.74 1.56 1.94 1.76 1.47 1.86 1.75 1.75 1.83 1.26 1.56 1.27 1.54 1.85 1.65 1.71 1.64 2.27 1.31 2.09 1.73 0.85 2.26 1.43 1.94 1.68 2.51 2.07 1.17 1.83 1.88 1.62 2.41 1.12 1.68 1.64 1.69 2.19 1.08 2.33 0.70 0.91 2.29 2.07 1.35 1.56 1.56 1.49 1.27 1.67 1.61 1.96 2.58 1.49 1.80 1.69 1.88 1.78 1.76 2.10 1.81 1.69 1.77 1.83 1.60 1.74 1.85 1.88 1.68 1.61 1.93 1.82 1.93 1.97 1.46 1.92 1.66 1.72 1.96 1.64 1.74 1.87 1.63 1.61 1.72 1.83 1.62 1.65 1.63 1.66 1.95 1.96 1.62 1.67 1.96 2.07 2.27 1.55 1.85 1.45 1.75 1.90 1.75 1.44 1.78 1.74 1.96 2.15 1.92 1.81 1.75 2.11 1.90 1.48 1.44 1.64 1.99 1.72 1.61 1.50 1.93 1.48 1.67 2.03 1.76 1.59 1.80 2.21 Page 1 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 1.80 1.97 1.59 1.68 1.92 1.57 1.52 1.62 1.70 1.71 1.65 1.48 1.58 1.51 1.55 1.88 1.77 1.91 1.39 1.74 1.78 1.81 1.28 1.53 1.61 1.46 1.67 1.61 1.91 1.64 1.55 1.45 1.64 1.27 1.17 1.70 1.93 1.71 1.52 1.72 1.81 1.53 1.84 2.04 1.73 2.05 1.75 1.47 1.43 1.56 1.62 1.34 1.65 1.42 1.80 1.41 1.37 2.11 1.46 1.86 1.73 1.69 1.36 1.67 1.32 1.75 1.52 1.47 1.60 1.62 1.62 1.65 2.68 1.81 1.57 1.66 2.29 1.52 2.03 1.97 2.09 2.06 2.22 2.05 1.85 1.73 2.68 2.58 1.80 2.06 2.06 1.86 1.57 1.10 1.60 1.46 1.78 1.79 1.75 1.57 2.10 1.78 1.83 1.90 1.47 1.79 1.78 1.60 1.72 1.72 1.52 1.79 1.73 1.52 1.96 1.63 1.98 1.61 1.84 1.68 1.56 1.80 1.69 1.67 1.51 1.74 1.87 1.81 1.71 1.75 1.40 1.71 1.77 1.75 1.97 1.70 1.82 1.68 2.23 1.60 2.20 1.73 1.94 1.74 1.84 1.64 1.63 2.21 1.95 1.76 1.68 1.52 1.31 1.69 1.84 1.80 1.86 1.89 1.52 1.82 1.70 1.80 I have a requirement of order times less than 2 minutes. Any order taking longer than 2 minutes is considered unacceptable. Unstable processes are also unacceptable. I am considering two options for drive-through ordering process improvement: 1) implementation of a voice recognition software-based automatic order taker and 2) retraining of the staff. The voice recognition software system costs $5,000 per restaurant and cuts variation in order time in half (assume you can estimate \"after install\" data by reducing the distance from the average time to the data point in half). Re-training, on the other hand, costs $5,000 per restaurant and reduces the average drive-through order time by 15 seconds. Remember that process improvements also potentially translate to Page 2 38 increased productivity as the average order time may be reduced (enabling more orders to be processed during the day). Which restaurant sites, if any, would you recommend installing the system(s) in? Which restaurants should be prioritized? Keep in mind that I have a low budget and I am not interested in wasting money on unnecessary systems. I value an order above 2 minutes as costing $0.50 in lost business, so that any savings represents a profit of $0.50. I am not interested in any investment that does not pay for itself within a year. Finally, in the spirit of process improvement, I believe in rewarding those that are successful. I plan on giving a $10,000 bonus to the \"best\" of my five restaurants. Make a recommendation as to which restaurant should receive the money based on current performance. Explain your analysis to me in a short formal report, including statistical and quality techniques used for the analysis, your assumptions, calculations, tables and figures (with labels), and references as necessary. Make sure you include a summary of your recommendation. Determine the: 1. Rational Subgrouping 2. Xbar - R Chart 3. P Chart 4. C Chart 5. Cp/Cpk Index