Crusty Do Possibl Liquor Student Competitors Competitors Store Size Seating License Population within 2 Miles within 5 Miles s = small Y = yes Y = yes Number Number Number M = medium N = No N = No L = Large VL = Very Large Store store ID Store 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 Store Size L M L M M VL VL VL M M VL VL M VL VL L M L M M L M S VL M VL L L M Seating Y N Y N N Y Y Y N N Y Y N Y Y Y N Y N N Y N N Y N Y Y Y N Liquor License No Yes No No Yes Yes Yes Yes Yes Yes Yes No Yes No Yes Yes Yes Yes No No Yes No No Yes No Yes Yes Yes Yes Student Competitors Competitors Population within 2 Miles within 5 Miles 12712 3 7 9582 2 3 12424 3 3 5429 1 1 7856 2 6 19057 3 5 20961 3 7 19493 3 7 8044 2 5 7352 0 1 15812 4 7 18316 3 5 7784 3 7 18353 3 3 19740 5 9 13396 4 5 6818 0 0 13586 3 3 8261 4 4 8685 3 7 10884 3 6 5896 2 6 3349 3 7 16141 3 4 7807 3 6 21664 5 8 14613 4 7 13537 3 7 7667 2 3 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 S VL L M VL VL S S VL M L VL VL L L VL L M M M VL S VL L M L L VL VL M VL N Y Y N Y Y N N Y N Y Y Y Y Y Y Y N N N Y N Y Y N Y Y Y Y N Y Yes Yes No Yes Yes Yes No No Yes Yes No Yes Yes No Yes Yes No No Yes Yes No Yes No Yes No No Yes Yes No No Yes 3317 17513 14080 6626 18261 15023 3560 4082 15254 7113 12482 19178 18757 13908 10667 16093 10418 8181 7334 7117 15061 4619 18659 14958 5909 13187 10576 17733 17922 6974 16789 2 4 4 1 3 5 3 2 5 0 2 5 3 3 4 3 2 4 1 1 3 2 5 2 1 3 3 5 4 3 3 4 5 7 5 5 9 4 4 9 2 6 7 4 3 6 4 4 7 1 5 6 5 9 3 3 6 3 9 4 3 6 Crusty Dough Pizza Company Possible values for each variable Competitors within 15 Monthly Miles Profit Number Dollars Competitors within 15 Miles 11 7 7 7 10 8 10 11 8 1 12 10 17 7 21 12 8 12 10 17 9 15 17 12 17 16 12 12 6 Population Pizza within 20 Do they Varieties miles Delivery Order Options Number Number Y = yes T = Twitter N= No W = Website F=Fax T&W = Twitter and Website All = all three Population Monthly Pizza within 20 Do they Profit Varieties miles Delivery $9,348 23 188779 Yes $15,008 23 389047 Yes $8,471 30 394410 Yes $8,295 16 81974 No $13,976 29 183635 Yes $32,213 36 169629 Yes $30,751 33 246213 Yes $30,629 21 466299 No $9,767 15 428605 No $25,698 31 230856 Yes $10,831 35 140680 Yes $27,532 49 264170 Yes $4,861 36 221521 Yes $28,449 22 359655 Yes $22,015 31 392558 Yes $10,341 22 472788 Yes $22,927 40 281573 Yes $19,029 26 163719 Yes -$7,239 25 287663 Yes -$402 50 92523 No $7,599 45 352856 Yes $1,908 41 218415 No -$9,104 25 375979 Yes $20,182 49 423080 Yes $5,170 41 403347 Yes $25,368 34 448382 Yes $15,652 28 415007 Yes $17,207 18 457680 No $9,814 49 192841 No Order Options All All F All T&W T&W All T&W All All T&W T All T&W All T F T&W F T All T&W T&W All T&W All All All T 9 11 19 11 9 17 15 12 15 9 8 20 9 7 16 9 11 11 8 11 12 14 20 13 12 14 10 17 8 6 12 $1,202 $14,345 $10,102 $18,478 $24,062 $16,091 -$6,358 $3,112 $11,114 $24,097 $16,215 $5,711 $26,954 $9,064 $8,778 $24,545 $12,712 -$9,738 $17,696 $18,100 $20,357 $6,141 $11,321 $25,939 $10,206 $17,535 $13,046 $9,770 $12,795 -$7,077 $26,241 31 41 31 25 42 17 26 21 32 40 40 32 45 31 23 48 48 43 45 28 39 43 26 28 30 37 28 16 24 30 20 364810 274841 136701 505370 535476 495098 104935 505480 255847 249909 214788 214908 240588 137808 468688 290875 407155 234949 291526 283128 330264 265576 224022 249881 312422 522331 369701 498515 98219 239568 401750 No Yes Yes Yes No Yes Yes Yes Yes Yes No No Yes No Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes T&W F T&W T&W F All All T&W F T F T F T T All All T&W All T T All F All T F All T&W T&W F F Review in Monthly Offer Pizza local Advertising by the Parking newspaper expenditure Slice Spots Positive Dollars Y = Yes Number Negative N = No Review in local newspaper Negative Positive Positive Positive Positive Positive Positive Positive Positive Positive Negative Positive Negative Positive Positive Positive Positive Positive Positive Positive Negative Positive Positive Positive Positive Negative Positive Positive Positive Monthly Offer Pizza Advertising by the Parking expenditure Slice Spots 1250 Yes 56 2342 No 39 972 Yes 83 890 No 26 2308 Yes 60 2929 No 141 2621 Yes 69 2728 No 116 1251 Yes 31 2467 Yes 48 2334 Yes 66 2809 Yes 71 887 Yes 19 2000 No 86 2206 Yes 94 1973 No 42 1692 Yes 53 2155 No 61 1248 Yes 56 1182 Yes 33 1250 No 67 1081 No 53 813 No 14 2036 Yes 113 1000 Yes 37 3155 No 81 1714 Yes 61 2169 No 77 1142 Yes 44 Buffet on Weekends Yes No Buffet on Weekends No No No No No Yes No No No No Yes No No Yes No Yes No Yes No No Yes No No No No No No Yes No Negative Positive Positive Positive Positive Negative Positive Positive Negative Positive Positive Positive Positive Positive Negative Negative Negative Positive Positive Positive Negative Negative Negative Positive Positive Positive Negative Positive Positive Positive Positive 1309 2109 1836 2351 2146 2118 1016 1031 2054 2069 1679 1026 2032 1267 929 1999 2384 882 1855 1964 2094 806 1916 2188 1941 2321 1935 846 1980 1080 2997 Yes No No Yes Yes Yes Yes Yes Yes No No No No No No No Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes No Yes Yes 21 136 52 48 189 141 46 55 95 40 48 167 108 86 88 167 86 29 49 24 79 36 120 62 60 89 61 190 53 34 79 No Yes No No Yes No No No No No No No Yes Yes Yes Yes Yes No No No Yes No No No No Yes No Yes Yes No No Crusty Do Possible Store store ID Store A B C D E F G H I J K L M N O P Q R S T Store Size s = small M = medium L = Large VL = Very Large Store Size M S L L VL S L M L VL S L L L VL M S VL VL M Liquor Student Seating License Population Y = yes Y = yes Number N = No N = No Seating N N Y Y Y N Y N Y Y N Y Y Y Y N N Y Y N Liquor License No Yes No Yes Yes No No Yes No Yes No Yes No Yes Yes No No No No No Student Population 5772 4725 14138 12533 16616 3733 14233 7753 12734 18665 4270 12522 13997 10925 17747 7258 3733 15478 21091 9058 Competitors Competitors within 2 within 5 Miles Miles Number Number Competitors Competitors within 2 within 5 Miles Miles 0 1 3 3 2 6 2 6 3 6 1 4 3 4 0 4 3 4 3 4 3 5 4 7 4 4 4 5 3 3 2 5 1 3 3 6 5 5 3 6 Crusty Dough Pizza Company Possible values for each variable Competitors within 15 Monthly Miles Profit Number Dollars Population Pizza within 20 Do they Varieties miles Delivery Order Options Number Number Y = yes T = Twitter N= No W = Website F=Fax T&W = Twitter and Website All = all three Competitors within 15 Miles 9 6 14 10 15 8 7 9 11 9 16 12 8 12 11 11 6 11 16 10 Population Pizza within 20 Do they Varieties miles Delivery 18 262617 Yes 35 221002 Yes 38 473391 Yes 46 454977 No 42 268351 No 23 432209 Yes 38 375508 Yes 28 104017 No 26 456295 Yes 24 99219 No 30 139461 Yes 24 447048 Yes 41 515330 No 31 212929 Yes 23 460884 Yes 21 439550 Yes 40 106690 No 45 226014 No 24 489921 Yes 25 173841 Yes Monthly Profit ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Order Options F All All T F W T&W T&W W All T F T F All F T&W All T&W W Review in local newspaper Positive Negative Review in local newspaper Positive Positive Negative Negative Positive Positive Positive Positive Positive Negative Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Monthly Offer Pizza Advertising by the Parking expenditure Slice Spots Dollars Y = Yes Number N = No Buffet on Weekends Yes No Monthly Offer Pizza Advertising by the Parking expenditure Slice Spots 2289 Yes 21 1015 Yes 35 1678 No 76 1882 No 40 1765 Yes 119 874 Yes 25 1862 Yes 90 1776 Yes 45 921 Yes 59 3451 No 157 890 Yes 24 1250 Yes 79 978 Yes 70 1082 Yes 40 2261 No 92 886 Yes 51 977 Yes 23 2389 No 176 2000 Yes 140 909 Yes 42 Buffet on Weekends No No No Yes Yes No No No No No No No Yes No Yes No No No No No Use this table to create p-charts fo statistical control? Why? To answer behavior of pizza weights at each s Use this table to create c-charts for the 5 stores. Which ones are in statistical control? Why? To answer, evaluate the patterns and behavior of daily complaints. Number of Complaints per day by store Day B1 B2 B3 1 3 16 23 2 1 4 12 3 3 13 11 4 4 3 13 5 2 1 15 6 9 1 21 7 6 8 12 8 5 7 10 9 7 0 15 10 1 3 14 11 8 7 17 12 7 5 22 13 5 7 15 14 10 5 10 15 9 1 12 16 4 2 11 17 0 3 20 18 8 10 11 19 4 0 13 20 7 1 10 21 3 9 11 22 9 4 22 23 4 14 13 24 4 2 12 25 6 10 11 26 9 0 15 27 7 7 11 28 6 3 13 29 9 2 18 30 5 2 15 31 1 10 11 32 1 6 18 33 10 3 19 34 4 6 13 35 9 0 12 36 10 5 14 37 10 4 10 38 6 2 11 39 6 9 14 40 9 0 20 B4 15 8 4 14 1 12 9 4 10 10 10 15 2 1 4 7 6 4 14 8 17 6 0 17 12 5 18 11 20 12 7 15 2 7 2 1 11 16 3 0 B5 5 0 3 0 4 5 6 5 4 2 0 4 4 0 8 5 1 1 6 1 0 1 3 2 4 3 0 5 1 1 0 5 5 2 8 4 6 2 6 5 Each Day's sample size Pizza weight (number over or und Day 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 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9 2 5 9 5 3 5 5 10 12 6 7 2 0 8 3 7 2 4 0 1 5 10 8 5 3 7 2 7 1 2 6 2 9 7 0 6 4 0 9 13 11 14 15 12 10 15 14 12 10 13 10 14 14 13 15 13 13 22 12 7 8 12 8 12 15 3 12 9 4 11 9 13 10 6 13 2 7 20 15 5 1 1 6 3 6 4 3 5 0 5 6 6 3 0 0 3 5 4 0 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Each Day's sample size se this table to create p-charts for the 5 stores. Which ones are in tatistical control? Why? To answer, evaluate the patterns and ehavior of pizza weights at each store. 100 100 100 izza weight (number over or under wgt) B1 B2 B3 5 5 5 5 3 5 4 7 3 4 4 5 5 3 5 4 4 3 7 5 15 14 3 5 3 5 3 14 5 4 3 5 5 5 5 4 3 3 5 4 4 15 3 4 4 3 5 5 3 4 5 3 5 5 3 6 3 5 5 8 5 7 8 4 3 3 4 4 5 4 10 4 5 4 4 3 4 3 5 7 3 4 11 15 7 8 14 5 4 11 3 3 3 4 5 11 5 4 3 4 3 4 3 4 5 3 5 4 4 5 3 5 4 14 12 10 5 3 5 3 100 B4 11 4 5 9 4 3 10 5 11 5 10 3 3 5 9 3 10 5 9 5 6 4 5 3 4 4 5 5 4 5 9 3 4 11 9 5 3 5 4 7 100 B5 10 15 9 13 18 15 12 9 36 11 9 23 14 15 14 9 23 10 15 15 12 8 24 9 9 27 13 13 16 12 34 11 8 14 10 13 14 17 14 15 Delivery times for store B1 Day customer1 customer2 1 24.07 26.93 2 21.20 20.78 3 20.03 15.40 4 23.07 32.90 5 18.02 29.92 6 30.03 27.75 7 25.50 21.70 8 28.38 24.03 9 19.95 28.32 10 28.29 31.43 11 27.13 25.78 12 20.27 19.32 13 29.76 19.66 14 19.49 25.34 15 27.27 25.65 16 26.08 16.69 17 23.52 28.38 18 23.47 24.12 19 27.67 28.19 20 25.90 32.51 21 31.72 33.69 22 28.99 31.81 23 17.27 26.52 24 20.76 31.18 25 22.02 16.40 26 24.88 20.90 27 29.97 25.97 28 31.06 20.33 29 26.99 31.39 30 29.10 25.85 3 3 4 4 5 4 7 3 5 3 8 5 4 4 3 5 4 4 10 4 5 7 9 5 4 5 10 5 3 5 4 4 3 3 3 7 5 3 8 5 13 9 3 4 5 3 3 14 3 6 4 5 3 3 5 5 4 3 4 5 4 5 4 5 4 3 4 5 5 3 3 3 5 5 5 4 5 5 9 9 15 14 8 8 19 11 10 13 13 30 15 9 13 10 12 11 15 11 8 14 100 100 100 100 100 Use the data for store B1 (this table) and for store B2 (next table) to create X-b Comment on statistical control of delivery times for ea To answer, evaluate the patterns and behavior of pizza delivery ti e B1 customer3 customer4 customer5 customer6 customer7 customer8 customer9 customer10 21.53 28.04 22.93 18.85 20.96 29.34 21.24 37.36 21.25 21.84 30.19 22.65 23.20 31.36 32.34 24.06 22.22 25.13 27.10 25.22 27.34 24.82 23.82 19.36 30.71 30.68 26.29 28.26 25.19 24.74 28.90 25.15 33.55 26.77 27.78 25.10 22.86 27.41 31.35 29.25 20.52 16.37 25.62 31.39 25.57 36.26 26.84 31.29 25.47 29.87 38.16 10.80 26.65 33.11 24.84 27.26 26.68 32.61 23.16 31.01 24.79 31.50 29.45 39.06 22.23 23.57 23.72 19.06 23.44 21.85 25.82 34.06 21.68 27.08 29.47 21.60 26.38 19.62 33.15 19.99 26.72 29.31 18.23 20.29 37.94 25.72 28.30 18.89 23.31 32.86 31.09 27.04 20.93 35.84 23.81 31.03 26.71 28.17 22.93 7.62 18.67 31.28 17.12 27.17 26.62 34.09 25.85 24.33 18.67 26.25 29.76 21.24 23.47 18.54 31.80 23.77 29.69 19.83 25.71 24.58 22.42 34.63 25.69 23.97 23.72 18.77 18.68 28.52 19.52 21.23 20.36 34.67 23.71 23.61 23.00 28.80 33.85 15.97 29.30 23.79 25.27 16.97 31.10 23.12 23.78 27.50 25.32 12.73 20.40 26.74 30.72 28.03 18.39 32.75 22.73 19.10 28.73 25.16 30.54 21.88 21.54 27.39 27.47 19.44 19.68 30.41 20.99 25.69 29.34 21.62 21.09 16.93 26.23 25.69 27.16 28.06 24.19 22.83 32.61 30.44 24.50 27.49 28.78 21.85 28.75 22.12 23.18 22.30 22.70 26.73 23.24 32.05 29.78 29.76 29.81 21.10 25.11 28.43 31.70 27.64 27.40 30.11 16.65 26.58 26.56 26.89 17.41 24.48 20.85 17.99 28.36 24.02 29.98 29.85 28.06 27.38 20.63 24.15 26.74 16.98 27.72 23.12 26.83 23.12 27.82 25.59 31.24 21.58 22.28 32.78 30.62 29.90 34.13 20.89 28.78 29.10 20.69 31.99 17.70 11.45 store B2 (next table) to create X-bar and R-charts for each store. l control of delivery times for each store. and behavior of pizza delivery times for each store. Delivery times for store B2 Day customer1 customer2 customer3 customer4 customer5 customer6 customer7 customer8 1 36.67 35.43 18.45 13.59 18.52 34.04 30.07 35.15 2 33.11 41.02 34.61 36.77 22.63 32.64 7.66 18.61 3 30.39 36.30 22.27 29.82 29.50 23.98 30.55 14.25 4 5.08 24.12 31.51 31.52 13.79 24.84 14.87 8.09 5 37.12 22.33 33.95 9.03 41.29 18.28 10.17 21.19 6 28.86 18.35 16.16 -1.61 31.14 26.14 24.55 17.97 7 57.22 24.96 24.13 48.64 26.20 27.49 36.94 30.65 8 30.20 31.29 21.40 21.40 40.57 17.97 33.86 17.33 9 33.05 18.39 25.62 31.30 20.03 26.32 30.20 14.34 10 17.26 26.45 12.53 23.28 21.63 31.65 23.65 37.03 11 18.40 29.79 30.06 33.40 13.68 33.03 44.01 15.96 12 14.97 14.77 17.86 26.23 24.45 24.83 25.46 27.43 13 10.07 13.04 17.19 29.69 37.62 47.81 32.65 22.54 14 15.51 22.65 32.64 44.83 40.46 7.83 20.42 30.34 15 23.48 26.21 20.17 13.50 22.10 17.09 27.20 31.97 16 19.95 9.12 33.13 8.43 38.05 29.35 7.55 18.04 17 37.19 31.81 30.57 30.16 31.40 43.96 27.90 16.00 18 43.29 36.20 36.91 28.93 19.78 27.31 23.30 15.65 19 21.02 19.63 39.53 24.97 37.68 25.97 16.42 29.60 20 29.35 24.24 31.53 25.14 23.13 28.63 11.72 21.96 21 22.84 27.51 22.05 31.54 19.95 32.62 44.38 11.33 22 34.99 29.86 11.52 38.34 3.25 25.72 29.86 21.39 23 28.17 14.27 49.38 41.47 19.41 25.95 27.23 25.23 24 30.55 17.09 19.16 32.84 31.87 26.84 27.53 19.23 25 -0.09 24.14 46.67 21.96 24.79 24.57 22.16 26.90 26 24.56 17.38 20.00 22.08 19.18 26.16 24.18 39.99 27 35.97 13.48 23.02 21.08 19.65 20.16 26.69 25.27 28 10.70 19.29 23.69 16.08 20.28 29.30 26.55 14.62 29 24.27 24.71 24.88 21.54 23.24 19.61 20.64 25.20 30 14.16 46.17 21.06 36.36 31.83 16.17 20.29 19.73 customer9 customer10 12.01 18.18 31.26 17.79 24.24 20.08 10.92 33.54 35.07 21.14 11.12 12.13 24.49 42.04 14.57 26.61 25.05 17.37 16.35 25.93 35.08 16.77 46.74 20.74 46.51 0.23 25.02 48.78 14.23 13.87 38.91 38.21 20.29 11.31 12.83 19.12 30.78 6.64 32.05 -7.66 16.32 35.72 43.01 42.33 26.85 44.97 25.08 19.51 32.50 23.82 24.35 22.85 20.11 28.18 25.07 32.64 12.99 9.60 38.66 34.46 Case study: Quality Control Charting 1 Case study: Quality Control Charting Aaron Kurtzer Bellevue University Case study: Quality Control Charting 2 Case 2: Quality Control Charting a) C Chart for the number of complaints. To investigate the process stability, the company assessed the number of complains about their daily performance. In order to achieve the survey target, a 60 days random sampling was carried out. The number of complains per day for each store was recorded to aid in investigating the process stability. In our case study, the process was said to be stable. The above process is under statistical control. This is because all the number of complains reported per day in each store are within the \"Upper\" and \"Lower\" control limits. None of the 8 tests are violated by the number of complains registered by every store. There is more than fourteen points shifting up and down the center line of the control chart. This is an implication that the store management is done by different people. However, there is no shift in the process mean as the number of daily complains alternate with respect to the average line. Case study: Quality Control Charting 3 14 12.672 12.672 12 10 8 B1 - B5 (STORES) 6 5.583 5.583 4 2 0 C chart Figure 1: C- Chart (store B1-B5) b) P- chart for Pizza weight A review of the pizza weights for stores B1, B2, B3, B4 and B5 was used to monitor pizza production weights within a 60-day time limit. Nearly all the stores' performances are out of statistical control. This is evident in the control chart which shows a total of 19 points above and below the control limits (UCL = 1.0000, CL = 0.9373, LCL=0.6802). The p-control chart below described a possible known source of variation. With alternating pizza weights below and above the central limit (CL), the statistical process depicts shifting average. For example, between days 4 to day 8, pizza weight records had a constant positive increase pattern. Similarly, the process has a pattern of more than fourteen points alternating below and above the central limit line. Case study: Quality Control Charting 4 Production of Pizza product by the stores B1 to B5 is running out of statistical control. A total of 25 points are beyond the control limits of the p-chart. The production process of pizza by the company runs out of control on days 5, 2, 8, 10, 22, 26, 24, 28, 30, 33, 34, 38, 39, 46, 50, 53, 54, 55, 59, and 60 respectively. Production of pizza is not consistent. It is not predictable as the process stability has a greater variation from the moving average. The process managers therefore need to formulate production and management methods to eliminate the variations. Figure 2 below is a p- chart for pizza production within a sample time frame of 60 days. B1 / B5(STORES) p Chart for Pizza production 5.000 4.500 1.0000 1.0000 4.000 3.500 0.6802 3.000 B1 - B5(STORES) 2.500 0.5174 2.000 1.500 1.0000.9373 0.9373 0.500 0.000 1234567891011 213141516171819202122 324252627282930313233 435363738394041424344 546474849505152535455 657585960 Day Figure 2: P-chart (pizza weights) c) X-Bar-R charts Case study: Quality Control Charting 5 In determining the stability of five different stores in a production company, the X-Bar-R chart below was used. As per the research study sampling results, the corresponding X-bar and R charts are as in figure 3 and 4 respectively for store B1 and B2. The production process for delivery times for pizza is said to be under statistical control. Not a single point plot is outside the control limit range of (UCL= 30.423, CL = 25.542, LCL= 20.661) for B1 X-bar chart and (UCL= 28.160, CL= 15.847, LCL= 3. 534) for the B1 R-chart. The process variability is therefore stable and predictable. Similarly, store B2 is within control as all the range and mean plots lie within the described process control limits. (UCL= 34.368, CL=25.155, LCL=15.943) and (UCL= 53.153, CL=29.910, LCL=6.670) for X-bar and R-bar respectively. The variability of store B2 is stable. X customer1 - customer10 (B1) 31.00 30.423 30.423 27.00 20.661 25.542 25.00 20.661 25.542 29.00 Average 23.00 21.00 19.00 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 Day Figure 3:X-bar chart for store B1 Case study: Quality Control Charting 6 R customer1 - customer10 (B1) Range 28.160 30.00 28.160 25.00 20.00 15.847 15.847 15.00 10.00 3.534 5.00 3.534 0.00 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 Day Figure 4:R-bar chart for store B1 X customer1 - customer10(B2) 37.85 34.368 34.368 27.85 25.155 15.943 22.85 25.155 15.943 32.85 Average 17.85 12.85 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 Day Figure 5: X-bar chart for store B2 Case study: Quality Control Charting 7 R customer1 - customer10(B2) 50.00 53.150 40.00 29.910 30.00 Range 53.150 29.910 20.00 10.00 6.670 0.00 6.670 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 Day Figure 6: R-bar chart for store B2 Case Statements, Due Dates, and Instructions Case 1: Descriptive Summaries Due: 11 a.m., May 15, 2016 Key Objective: You are tasked with identifying and discussing what makes a Crusty Pizza Company restaurant successful and, conversely, unsuccessful. Use: The data for the 60 stores in worksheet \"Descriptive\" to prepare your report. Summary tools of chapters 2 and 3 to perform the analysis and explore relationship between each variable and profit Up to 8 pages for the body of report, plus a cover page, and any appendixes. Your guiding light and focus to plan the analysis and organize your report must be the Key Objective mentioned above. Use summaries that you believe best allow you to accomplish the task. In all comparisons, you must comment on your results and interpret findings as they pertain to the Key Objective. Case 2: Quality Control Charting Due: 11 a.m., June 19, 2016 Key Objective: You are tasked with analyzing data to create center-line, UCL, and LCL for c-charts, p-charts, X charts, and R charts. You must also plot the data points and interpret patterns present in each chart to decide whether any assignable causes of variation are visible, and whether each process is in statistical control. Use the data in worksheet \"Quality Control\" to perform the analysis. You may use up to 8 pages for the body of your report, plus a cover page, and any appendixes. Case 3: Forecasting with Regression Due: 11 a.m., June 26, 2016 Key Objective: Crusty Pizza executives are considering opening several new stores and they would like a forecast of monthly profit for each store. a) Use the data in worksheet \"Descriptive\". Perform simple linear regression on the key variables to address the key objective for this case. b) Comment on goodness of fit and discuss which variables would be good indicators of profit, and explain why. c) Use results from parts \"a\" and \"b\" above, along with data in Worksheet \"Regression\" to predict monthly profit for each of the 20 stores in that worksheet (i.e., stores A through T). d) Identify the top 5, and bottom 5 locations you would recommend to Crusty Pizza Company to open and explain why. e) You may use up to 5 pages for the body of report, plus a cover page, and any appendixes. 1 Store B1 LCL: 0 Center: 5.58 UCL: 12.67 The chart for store B1 is in control as can be seen in Figure CB 1. All data points are within the LCL and the UCL with no obvious trends. B1 C Chart for # of Complaints B1 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 1 Store B2 LCL: 0 Center: 4.82 UCL: 11.40 The chart for store B2 is out of control as can be seen in Figure CB 2. There are 3 data points that are above the UCL. Days 1,3, and 23 have to be researched and investigated to see why there were so many complaints. Do they have one employee working all those three days? B2 C Chart for # of Complaints B2 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 2 Store B3 LCL: 2.73 Center: 13.92 UCL: 25.11 The chart for store B2 is in control with no obvious trends or patterns. As can be seen in Figure CB 3, data points are all within the LCL and UCL. B3 C Chart for # of Complaints B3 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 3 Store B4 LCL: 0 Center: 8.93 UCL: 17.90 The chart for store B4 is out of control as can be seen in Figure CB 4. There are 2 data points that are above the UCL. Days 29 and 59 have to be researched and investigated to see why there were so many complaints. B4 C Chart for # of Complaints B4 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 4 Store B5 LCL: 0 Center: 3.22 UCL: 8.60 The chart for store B5 is in control as can be seen in Figure CB 5. All data points are within the LCL and UCL with no obvious patterns or trends. B5 C Chart for # of Complaints B5 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 5 All C Charts were formatted with the number of complaints zero to 30 so it looks obvious when comparing the charts that store B5 has the lowest average complaints. Store B3 has the largest average complaints. Administration should analyze why store B5 has such a low level compared to the other stores and try to implement some changes to other stores based on their findings. Store B1 LCL: 0% Center: 5% UCL: 11% The control chart for Store B1 shows a process that is out of control as can be seen in Figure PB 1. There are special cause variations (3 separate points) above the UCL. Management needs to determine the root cause for the 3 special cause variations and then take corrective action. Store B1: p Chart for Nonconforming Pizza Weight 16% 14% 12% 10% 8% Percentage of Pizzas under/over weight 6% 4% 2% 0% 0 10 20 30 40 50 60 70 Days p LCL Center UCL Figure PB 1 Store B2 LCL: 0% Center: 5% UCL: 12% The control chart for Store B2 shows a process that is in a state of statistical control as can be seen in Figure PB 2. All the points are within the control limits. Only common cause variation is seen here with no apparent pattern in values or time. Store B2: p Chart for Nonconforming Pizza Weights 14% 12% 10% 8% Percentage of pizzas under/over weight 6% 4% 2% 0% 0 10 20 30 Days p Figure PB 2 LCL Center UCL 40 50 60 70 Store B3 LCL: 0% Center: 6% UCL: 13% The control chart for Store B3 shows a process that is out of control as can be seen in Figure PB 3. There are special cause variations (7 separate points) above the UCL. Most of the points fall below the center line of 6% and above 3% which is satisfactory. Management needs to determine the root cause for the special cause variations. They should also see if there is a way to modify the process to help keep the points below the center line (as according to this p Chart it seems quite achievable). Store B3: p Chart for Nonconforming Pizza Weight 16% 14% 12% 10% Percentage of Pizzas under/over weight 8% 6% 4% 2% 0% 0 10 20 30 40 50 60 70 Days p LCL Center UCL Figure PB 3 Store B4 LCL: 0% Center: 5% UCL: 12% The control chart for store B4 shows an out of control process even though all points fall between the UCL and LCL. This is because there are many consecutive points below the center (mean) line of 5%. Since the consecutive points are below the center line, this means that more pizzas are within the acceptable weight defined by Operations. Being below the center line increases quality and therefore management should investigate these consecutive points to incorporate change into the process. Store 4: p Chart for Nonconforming Pizza Weight 14% 12% 10% 8% Percentage of Pizzas under/over Weight 6% 4% 2% 0% 0 10 20 30 Days p Figure PB 4 LCL Center UCL 40 50 60 70 Store B5 LCL: 4% Center: 14% UCL: 25% The control chart for store B5 is out of control as can be seen in Figure PB 5. The four points above the UCL are special cause variations. Management needs to investigate and analyze why these variations are occurring and corrective action must be taken. Store B5: p Chart for Nonconforming Pizza Weight 40% 35% 30% 25% Percentage of Pizzas under/over Weight 20% 15% 10% 5% 0% 0 10 20 30 Days p Figure PB 5 LCL Center UCL 40 50 60 70 Store B1 LCL: 0 Center: 5.58 UCL: 12.67 The chart for store B1 is in control as can be seen in Figure CB 1. All data points are within the LCL and the UCL with no obvious trends. B1 C Chart for # of Complaints B1 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 1 Store B2 LCL: 0 Center: 4.82 UCL: 11.40 The chart for store B2 is out of control as can be seen in Figure CB 2. There are 3 data points that are above the UCL. Days 1,3, and 23 have to be researched and investigated to see why there were so many complaints. Do they have one employee working all those three days? B2 C Chart for # of Complaints B2 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 2 Store B3 LCL: 2.73 Center: 13.92 UCL: 25.11 The chart for store B2 is in control with no obvious trends or patterns. As can be seen in Figure CB 3, data points are all within the LCL and UCL. B3 C Chart for # of Complaints B3 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 3 Store B4 LCL: 0 Center: 8.93 UCL: 17.90 The chart for store B4 is out of control as can be seen in Figure CB 4. There are 2 data points that are above the UCL. Days 29 and 59 have to be researched and investigated to see why there were so many complaints. B4 C Chart for # of Complaints B4 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 4 Store B5 LCL: 0 Center: 3.22 UCL: 8.60 The chart for store B5 is in control as can be seen in Figure CB 5. All data points are within the LCL and UCL with no obvious patterns or trends. B5 C Chart for # of Complaints B5 LCL Center UCL 30 25 20 Number of Complaints 15 10 5 0 Days Figure CB 5 All C Charts were formatted with the number of complaints zero to 30 so it looks obvious when comparing the charts that store B5 has the lowest average complaints. Store B3 has the largest average complaints. Administration should analyze why store B5 has such a low level compared to the other stores and try to implement some changes to other stores based on their findings. Store B1 LCL: 0% Center: 5% UCL: 11% The control chart for Store B1 shows a process that is out of control as can be seen in Figure PB 1. There are special cause variations (3 separate points) above the UCL. Management needs to determine the root cause for the 3 special cause variations and then take corrective action. Store B1: p Chart for Nonconforming Pizza Weight 16% 14% 12% 10% 8% Percentage of Pizzas under/over weight 6% 4% 2% 0% 0 10 20 30 40 50 60 70 Days p LCL Center UCL Figure PB 1 Store B2 LCL: 0% Center: 5% UCL: 12% The control chart for Store B2 shows a process that is in a state of statistical control as can be seen in Figure PB 2. All the points are within the control limits. Only common cause variation is seen here with no apparent pattern in values or time. Store B2: p Chart for Nonconforming Pizza Weights 14% 12% 10% 8% Percentage of pizzas under/over weight 6% 4% 2% 0% 0 10 20 30 Days p Figure PB 2 LCL Center UCL 40 50 60 70 Store B3 LCL: 0% Center: 6% UCL: 13% The control chart for Store B3 shows a process that is out of control as can be seen in Figure PB 3. There are special cause variations (7 separate points) above the UCL. Most of the points fall below the center line of 6% and above 3% which is satisfactory. Management needs to determine the root cause for the special cause variations. They should also see if there is a way to modify the process to help keep the points below the center line (as according to this p Chart it seems quite achievable). Store B3: p Chart for Nonconforming Pizza Weight 16% 14% 12% 10% Percentage of Pizzas under/over weight 8% 6% 4% 2% 0% 0 10 20 30 40 50 60 70 Days p LCL Center UCL Figure PB 3 Store B4 LCL: 0% Center: 5% UCL: 12% The control chart for store B4 shows an out of control process even though all points fall between the UCL and LCL. This is because there are many consecutive points below the center (mean) line of 5%. Since the consecutive points are below the center line, this means that more pizzas are within the acceptable weight defined by Operations. Being below the center line increases quality and therefore management should investigate these consecutive points to incorporate change into the process. Store 4: p Chart for Nonconforming Pizza Weight 14% 12% 10% 8% Percentage of Pizzas under/over Weight 6% 4% 2% 0% 0 10 20 30 Days p Figure PB 4 LCL Center UCL 40 50 60 70 Store B5 LCL: 4% Center: 14% UCL: 25% The control chart for store B5 is out of control as can be seen in Figure PB 5. The four points above the UCL are special cause variations. Management needs to investigate and analyze why these variations are occurring and corrective action must be taken. Store B5: p Chart for Nonconforming Pizza Weight 40% 35% 30% 25% Percentage of Pizzas under/over Weight 20% 15% 10% 5% 0% 0 10 20 30 Days p Figure PB 5 LCL Center UCL 40 50 60 70