"Why JobshopLean?" This is the original full-length version of the abridged article that appeared in the December 2011 issue of THE FABRICATOR (pages 42-44). Product Mix Segmentation using P-Q-$ Analysis Shahrukh A. Irani Department of Integrated Systems Engineering The Ohio State University Columbus, OH43210 Background Although P-Q Analysis (P= Part, or Product, Q= Quantity, or Production Volume) is a simple and effective method for product mix segmentation, P-Q-$ Analysis ($= Sales, or Profit, or Revenue) simultaneously considers two criteria to rank order and classify products into different segments. P-Q Analysis identifies at most three product segments (High, Medium and Low Volume) in the product mix of a jobshop. Whereas, P-Q-$ Analysis could identify up to four different segments in the same product mix. Ideally, each business segment ought to be served using a different combination of facility layout, manufacturing technology, workforce skills, management strategy, etc.! Justification for this Strategy When implementing Lean in a high-variety low-volume (HVLV) manufacturing facility, especially in a jobshop where small batches of high-priced products are often the norm, we could be erring by focusing on the Value Streams of products that belong in the High-Volume segment that is typically identified by P-Q Analysis. There are two reasons why P-Q Analysis could often select the wrong products to focus on: (i) the High-Volume products do not belong in the High-Revenue segment and (ii) the products in the (LowVolume, High-Revenue) segment that are often profitable are ignored by P-Q Analysis! Cash flow in any business can be improved by (1) completing high-value orders in the shortest period of time and (2) reducing the Seven Types of Waste that decrease margins for the low-volume but high-margin parts. From the perspective of Flow, three types of operational costs – Transportation, WIP (work-in-process inventory) and Queuing – increase manufacturing costs. Two costs – Transportation and Queuing – are heavily dependent on production volumes and container sizes; but, WIP cost is heavily dependent on product value, which is usually reflected in the Sales earned by each product. So, instead of focusing on a sample of products selected using a single criterion – Quantity – the P-Q- Analysis method recommends focusing on a sample of products that is drawn from several segments of the product mix – (High-Volume, High-Revenue), (High-Volume, Low-Revenue) and (Low-Volume, High Revenue). As shown in Figure 1, P-Q-$ Analysis creates a two-dimensional scatterplot for the entire product mix of any jobshop as follows: The horizontal axis (X) represents Quantity (or Volume). The vertical axis (Y) represents Revenue (or Profit Margin). Every point in the scatterplot represents a particular product. Q* is the threshold value of Q that separates Low-Volume products from High-Volume products. Similarly, R* is the threshold value of Sales that separates the Low-Revenue products from the HighRevenue products. There are simple as well as sophisticated methods for choosing the points – Q* and R* – on the two axes. Those methods are beyond the scope of this introductory article. If we draw a vertical line on the X axis at Q* and a horizontal line on the Y axis from R*, then the P-Q-$ scatterplot gets divided into four quadrants. Each product will lie in any one of the four quadrants, depending on its (Q, $) values. The four quadrants are (High-Quantity, High-Revenue), (Low-Quantity, HighRevenue), (Low-Quantity, Low-Revenue) and (High-Quantity, Low-Revenue). Each quadrant defines a product mix “segment” that, ideally, ought to be managed as a separate business and be produced in a separate area of the facility with a suitable layout for that area, manufacturing technology, workforce skills and management strategy! Low High 80000 70000 60000 Revenue 50000 High 40000 30000 20000 R* Low 10000 0 0 2000 4000 6000 Q* 8000 10000 12000 Quantity Figure 1 P-Q-$ Analysis Scatter Plot of the Product Mix in a Hypothetical Jobshop Case Study Table 1 shows the input data from an actual project used for P-Q Analysis (where P= Part or Product and Q= Quantity or Production Volume). Typically, the “Quantity” (# of pieces shipped) and “Revenue” ($ earned) for each part are for a year, or longer production horizon. The “Routing” is the sequence of workcenters that a part must visit ex. Part No. 1 (80-A37353) has the routing: 17→6→2→11→10→29→54→55. Figure 1 and Table 2 are the graphical and tabular versions, respectively, of the P-Q Analysis output that would be used to segment the product mix of any jobshop. In Figure 1 the Parts are sequenced from left-to-right along the X-axis in order of decreasing value of Quantity of each (individual) part; whereas, the Y-axis on the left side of the graph shows the Quantity of each (individual) part and the Y-axis on the right side of the graph shows the Aggregate Quantity for any group of parts. In this particular example, the curve in Figure 1 is “sharp” and the points where the curve has sharp bends are potential cut-off points between different segments of the product mix, such as HighVolume (Runners), Medium-Volume (Repeaters) and Low-Volume (Strangers) segments. In Table 2, where the parts have been sorted in order of decreasing value of Quantity, the Total Aggregate Quantity for a sample of parts comprised of the first 23 parts in the total list of 79 is 1411592 (see Row # 23 in the table) accounts for about 80% of the Total Aggregate Quantity for all 79 parts (which is 1766478). So, using Figure 1 and Table 2, we could segment the product mix into at least two segments, one comprised of the top 23 parts and the other containing the remaining 56 parts. Next, instead of using Q, if we used Sales and did a P-$ Analysis, the Pareto sort of the products would have sequenced them by decreasing value of Sales, as shown in Table 3 and plotted in Figure 2. Are the two samples of parts chosen using either Q (Volume) or $ (Sales) the same? No! So why not enhance the Pareto sorting algorithm to simultaneously incorporate both Q and $? Here is how to do it --Using the columns of data “Part”, “Quantity” and “Revenue” in Table 1, first produce the scatterplot that appears in Figure 3. Even if you did no further analysis and eyeballed Figure 3, you could produce a segmentation of the product mix as shown in Figure 4. In that figure, the scatter plot suggests that the product mix of this jobshop could have three segments – (High-Volume Low-Revenue), (Low-Volume High-Revenue) and (Low-Volume Low-Revenue). So, if we had we relied only on PQ Analysis (Table 2), we would have ignored the products in the High Revenue Low Volume segment. And, if we had relied only on P$ Analysis (Table 3), we would have ignored the products in the Low Revenue High Volume segment. Now, for the purpose of this article, you could do something better than just eyeballing to create a 4quadrant split of the product mix as follows: Locate the point (R*) on the Revenue axis that corresponds to the Revenue value for Part #80-4030007296090 (R*) which is the last part to be included in the Pareto sort to select the P$ Analysis sample. Draw a vertical line through this point. Similarly, on the Quantity axis, locate the point (Q*) that corresponds to the Quantity Value for Part #80-121009-00 which is the last part to be included in the Pareto sort to select the PQ Analysis sample. Draw a horizontal line through this point. Thereby, you will split the PQ$ Analysis scatterplot into four quadrants. If you desire to know the exact PQ$ Analysis results produced by the proprietary algorithm in the PFAST software that we use to implement JobshopLean, please send me an email at [email protected] to request that information. Managing a Jobshop’s Different Product Mix Segments Differently How does one translate the results obtained using this LAT into improvement projects (or kaizen events), management policies, strategic plans, etc.? Here are some examples of the follow-on projects that could be undertaken using the PQ$ Analysis results: Market Diversification: If you study Figure 3, this particular jobshop does not have a single part # in the (High Revenue, High Quantity) quadrant. That figures because a jobshop’s niche is not low-mix highvolume manufacturing! However, creative jobshop owners do not pass up on any opportunity to accept a Long Term Contract from a defense prime or an OEM to supply a single part (or a well-defined part family) that will be ordered on a consistent basis (think takt time!) all through the year, maybe even for a few years! For example, one machine shop set up a stand-alone robotic cell for a single part ordered by a defense prime. Another machine shop installed a dedicated flexible manufacturing cell operated by a single operator to produce a single part for an automotive OEM in their state. Facility Layout, Virtual Cells and Workforce Training (and Compensation too!): A manufacturer of hydraulic pipes and couplings produced 2,000 stock keeping units (SKUs) with 48 hours lead-time customers. The manufacturer was finding it increasingly costly and difficult to consistently achieve this lead-time. Analysis showed over 50% of sales came from only 92 products, or less than 5% of the entire product mix. The other products were ordered infrequently in small quantities, even as single items. Armed with this information, the company decided it needed two types of factory: a high-volume repetitive facility and a flexible job shop. However, it was not cost effective to build two factories. Or even to physically separate the equipment. The company worked out what equipment would be needed for highvolume products in a fixed sequence. This equipment was painted green. Employees for this equipment were selected based on their preference to work routines. They were given green overalls. The remaining equipment was painted beige. Employees were selected on their preference to tackle difficult and complex situations, in their case, lots of setups and unusual machining issues. They were given beige overalls. Although the equipment and staff were totally intermingled on the shop floor, each business operated totally differently. The green factory had fixed hours of work, JIT deliveries and improvement activities focused on achieving faster cycle times and increased productivity. The beige factory had hours of work that varied according to the level of demand each week. Materials were only purchased when required. Improvement activities focused on flexibility and responsiveness. This company succeeded in creating and operating two businesses under the same roof, even each business had different policies, procedures and appropriate performance metrics. For complete details on this eye-opening case study, please read Page 27 “One Business or Two?’ in this book --- Glenday, I. (2005). Breaking Through to Flow: Banish Fire Fighting and Increase Customer Service. Ross-on-Wye, United Kingdom: Lean Enterprise Academy. ISBN 0-9551473-0-1. Vendor Selection, Purchasing Management and Inventory Control: High-volume products, which allow production batch sizes to match a Make-To-Stock inventory policy, also influence how far the suppliers are from the company location, and for FTL (full truck loads) at time of delivery. In contrast, high-revenue orders made from rare metals like titanium (which is not easily available if shipped from, say, China) merit keeping a very close watch on onhand inventory levels, supplier lead times, market price, etc. Priority Scheduling of Orders Loaded on Bottleneck Resources: By knowing which products are of high-value but to be delivered by certain due dates, as opposed which orders are being run to replenish kanban-triggered onhand stock, appropriate inventory control systems can be used for products in different segments. In fact, products in the (High-Volume, Low-Revenue) segment could be outsourced but labeled at the time of shipment by the company selling them to customers. What about shopfloor scheduling? The color of the paperwork, containers, etc. associated with a high-revenue order could be different from the paperwork for the other orders, so everybody on the shop gives a higher priority to minimizing WIP corresponding to that category of orders. Equipment Purchases: The value and volume of production of different products easily influences the flexibility and sophistication of manufacturing equipment. High-volume assembly facilities are increasingly embracing “right-sized automation” i.e. equipment that is designed for producing a welldefined low mix of products in a well-defined range of volumes. On the other hand, most jobshops that I know, who struggle to hire and retain multi-skilled equipment operators, are the first to purchase flexible multi-function single-setup machines, some capable of lights-out operation. About the Next Column In the next column, we will conclude this series on the PQR$T Analysis approach to accurate product mix segmentation as a crucial starting point for jobshops on their Lean journey. In my next column, I will describe PQT Analysis, a method for Product Mix Segmentation that considers both QUANTITY and DEMAND REPEATABILITY for any product to segment the entire product mix of a jobshop, especially when 1000+ routings are involved. PQ Analysis, which is based on the old and obsolete Pareto Law (or 80-20 Rule), fails to consider how many times any product is ordered, the size and variability in order sizes, and the time interval between consecutive orders. Which is why PQT Analysis, instead of PQ Analysis, is a preferred method for identifying the Runners, Repeaters and Strangers in a jobshop’s product mix. Shahrukh Irani, Ph.D., [email protected] is an Associate Professor at The Ohio State University’s Department of Integrated Systems Engineering www.ise.osu.edu, 210 Baker Systems Engineering, 1971 Neil Ave., Columbus, OH 43210-1271, 614-688-4685. His work at The Ohio State University was supported by the Defense Logistics Agency through the cost-shared Forging Advanced Systems and Technologies (FAST) Manufacturing Technology (ManTech) Program. Support is provided by the Defense Logistics Supply Center in Philadelphia, PA, and Headquarters Defense Logistics Agency at Fort Belvoir, VA. The FAST Program focuses on lead-time and cost reduction within forging supply chains through the teamed relationship of Advanced Technology International and the Forging Industry Association. Table 1 Input Data for P-Q Analysis No. 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 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 Part 80-A37353 80-C27416-1 80-C27416-2 80-C46806-1 80-C55581 80-C558-1 80-D8097 80-B113-1001 80-4003111 80-4009121 80-4009262 80-4009263 80-4009270 80-4010346 80-4010348 80-4010349 80-4010350 80-4010351 80-4010352 80-4011714 80-4011725 80-4012169 80-4012174 80-4012179 80-4012212 80-4012213 80-4030339 80-4030341 80-4035144 80-4035149 80-4039260 80-4041707 80-4059989 80-4067179 80-4030011870964 80-150T084LT 80-G121-1002 80-NL150T060LT 80-NL150T072LT 80-NL150T084LT 80-NL150T096LT 80-NL150T120LT 80-3249869 80-121009-00 80-121188-002 80-121189 80-671391 80-121018-00 80-121148 80-121387 80-ULC0200 80-35-B357 80-27750-01 80-37355-1072 80-37355-1084 80-051-1 80-191820 80-522500 80-551500 80-S113-1001 80-S113-1004 80-27708-302UP 80-9033023-303 80-9627712-301UP 80-9627713-301UP 80-9627714-301UP 80-9627715-301UP 80-9627716-301UP 80-3260-041 80-3260-0980 80-3260-503 80-671635-00 80-4030007296089 80-4030007296090 80-4030007296091 80-4030007296094 80-27377 80-921790 80-W101-2006 Quantity 728 1456 5614 4354 1750 1526 756 48132 4900 30800 5600 39886 32900 117614 21000 12600 38500 19600 7000 28000 16800 33362 113400 133070 1400 4144 65198 53200 5600 28252 1400 42000 3850 26502 39256 1344 280 1764 1540 644 168 112 28014 29288 32200 7014 147000 47950 35350 3220 2800 132314 15428 1204 952 48580 26866 1652 3724 39732 364 8540 36848 1022 1050 1078 1022 1022 2828 1512 182 75012 168 1456 6356 9240 14112 4914 462 Revenue 47320 124054 495992 362474 151284 131922 133882 186116 41216 151228 27048 176302 126994 379806 69300 43092 148610 86632 34790 91560 119448 98756 324324 377916 10682 34846 117208 140980 14952 86170 6062 180180 33306 757428 1618932 587664 138768 632744 591752 281596 83258 68572 179200 171332 202860 47348 658560 275716 143444 27720 31556 697298 931854 501774 447062 255052 100744 8428 29050 39732 70532 1952230 922670 192276 462378 360430 423766 139258 569842 157024 48342 466340 38892 234346 757190 574084 69286 526120 445858 17 17 17 17 17 17 17 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 1 17 17 17 17 17 17 17 17 17 17 17 17 17 57 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 6 6 6 6 6 6 6 56 57 57 57 57 57 57 57 57 57 57 57 26 57 26 26 26 26 26 27 27 28 28 28 57 26 39 39 6 6 6 6 6 6 6 56 39 39 39 16 39 50 39 39 1 39 6 6 1 16 16 16 16 16 39 54 6 6 6 6 6 6 6 6 3 3 3 3 3 16 3 6 2 2 2 2 2 2 2 57 25 25 25 25 25 25 25 25 25 25 25 57 25 57 57 57 57 57 9 9 50 50 50 25 57 40 40 2 2 2 2 2 2 2 1 40 40 40 11 40 26 40 40 57 40 2 2 26 11 11 11 11 11 40 57 56 56 56 56 56 2 2 2 7 7 7 7 7 11 7 2 11 11 11 11 11 11 11 54 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 57 57 27 27 27 52 52 26 21 7 7 7 7 7 7 7 17 21 21 21 10 21 27 21 21 4 42 7 7 4 10 10 10 10 10 16 55 16 16 16 16 16 11 11 11 12 12 12 12 12 10 12 42 10 10 10 10 10 10 10 29 29 29 29 29 29 29 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 57 22 12 12 12 12 12 12 12 29 22 22 22 26 22 55 22 22 54 41 12 12 54 26 26 26 57 57 9 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 11 11 11 11 11 10 10 10 26 8 8 8 8 26 8 33 55 55 55 55 55 54 53 8 8 8 8 8 8 8 26 55 55 55 4 55 54 54 54 54 54 54 54 Routings 55 55 55 55 55 55 55 57 29 42 42 42 42 42 42 42 54 55 28 41 41 41 41 41 41 41 57 4 57 57 57 57 57 57 57 48 55 55 55 55 55 55 55 55 54 55 55 55 55 55 55 55 3 8 8 55 29 29 29 53 53 11 7 42 42 12 41 41 57 57 57 28 28 28 55 55 10 27 27 27 48 48 48 39 40 57 54 10 10 10 10 10 29 29 29 4 4 4 4 4 4 54 41 6 6 6 6 6 28 28 28 55 54 54 54 54 55 29 54 7 7 7 7 7 54 54 54 12 12 12 12 12 57 57 57 8 8 8 8 8 55 55 55 54 54 54 54 54 29 29 29 29 4 4 4 4 55 55 55 55 28 57 4 4 55 55 57 57 57 57 57 54 54 54 54 54 53 53 53 53 53 8 8 8 8 8 55 55 55 55 55 Figure 1 P-Q Analysis High-Volume Parts Medium-Volume Parts Low-Volume Parts Table 2 Prioritization of Products using only P-Q Analysis No. 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 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 Part 80-671391 80-4012179 80-35-B357 80-4010346 80-4012174 80-671635-00 80-4030339 80-4030341 80-051-1 80-B113-1001 80-121018-00 80-4041707 80-4009263 80-S113-1001 80-4030011870964 80-4010350 80-9033023-303 80-121148 80-4012169 80-4009270 80-121188-002 80-4009121 80-121009-00 80-4035149 80-3249869 80-4011714 80-191820 80-4067179 80-4010348 80-4010351 80-4011725 80-27750-01 80-27377 80-4010349 80-4030007296094 80-27708-302UP 80-121189 80-4010352 80-4030007296091 80-C27416-2 80-4009262 80-4035144 80-921790 80-4003111 80-C46806-1 80-4012213 80-4059989 80-551500 80-121387 80-3260-041 80-ULC0200 80-NL150T060LT 80-C55581 80-522500 80-NL150T072LT 80-C558-1 80-3260-0980 80-4030007296090 80-C27416-1 80-4012212 80-4039260 80-150T084LT 80-37355-1072 80-9627714-301UP 80-9627713-301UP 80-9627712-301UP 80-9627715-301UP 80-9627716-301UP 80-37355-1084 80-D8097 80-A37353 80-NL150T084LT 80-W101-2006 80-S113-1004 80-G121-1002 80-3260-503 80-4030007296089 80-NL150T096LT 80-NL150T120LT Quantity 147000 133070 132314 117614 113400 75012 65198 53200 48580 48132 47950 42000 39886 39732 39256 38500 36848 35350 33362 32900 32200 30800 29288 28252 28014 28000 26866 26502 21000 19600 16800 15428 14112 12600 9240 8540 7014 7000 6356 5614 5600 5600 4914 4900 4354 4144 3850 3724 3220 2828 2800 1764 1750 1652 1540 1526 1512 1456 1456 1400 1400 1344 1204 1078 1050 1022 1022 1022 952 756 728 644 462 364 280 182 168 168 112 Agg. Qty. 147000 280070 412384 529998 643398 718410 783608 836808 885388 933520 981470 1023470 1063356 1103088 1142344 1180844 1217692 1253042 1286404 1319304 1351504 1382304 1411592 1439844 1467858 1495858 1522724 1549226 1570226 1589826 1606626 1622054 1636166 1648766 1658006 1666546 1673560 1680560 1686916 1692530 1698130 1703730 1708644 1713544 1717898 1722042 1725892 1729616 1732836 1735664 1738464 1740228 1741978 1743630 1745170 1746696 1748208 1749664 1751120 1752520 1753920 1755264 1756468 1757546 1758596 1759618 1760640 1761662 1762614 1763370 1764098 1764742 1765204 1765568 1765848 1766030 1766198 1766366 1766478 Agg. Qty. % 8.3 15.9 23.3 30 36.4 40.7 44.4 47.4 50.1 52.8 55.6 57.9 60.2 62.4 64.7 66.8 68.9 70.9 72.8 74.7 76.5 78.3 79.9 81.5 83.1 84.7 86.2 87.7 88.9 90 91 91.8 92.6 93.3 93.9 94.3 94.7 95.1 95.5 95.8 96.1 96.4 96.7 97 97.2 97.5 97.7 97.9 98.1 98.3 98.4 98.5 98.6 98.7 98.8 98.9 99 99 99.1 99.2 99.3 99.4 99.4 99.5 99.6 99.6 99.7 99.7 99.8 99.8 99.9 99.9 99.9 99.9 100 100 100 100 100 Figure 2 P- $ Analysis P-$ Analysis 2500000 25000000 High-Revenue Parts 2000000 20000000 1500000 15000000 Aggregate Revenue Revenue Revenue Agg Revenue 1000000 Medium-Revenue Parts 10000000 Low-Revenue Parts 500000 5000000 0 0 Parts Table 3 Prioritization of Products using only P-$ Analysis No. Revenue Agg. Rev. 1 80-27708-302UP 1952230 1952230 8.69 2 80-4030011870964 Part 1618932 3571162 Agg. Rev. % 15.89 3 80-27750-01 931854 4503016 20.04 4 80-9033023-303 922670 5425686 24.14 5 80-4067179 757428 6183114 27.51 6 80-4030007296091 757190 6940304 30.88 7 80-35-B357 697298 7637602 33.98 8 80-671391 658560 8296162 36.91 9 80-NL150T060LT 632744 8928906 39.73 10 80-NL150T072LT 591752 9520658 42.36 11 80-150T084LT 587664 10108322 44.98 12 80-4030007296094 574084 10682406 47.53 13 80-3260-041 569842 11252248 50.07 14 80-921790 526120 11778368 52.41 15 80-37355-1072 501774 12280142 54.64 16 80-C27416-2 495992 12776134 56.85 17 80-671635-00 466340 13242474 58.92 18 80-9627713-301UP 462378 13704852 60.98 19 80-37355-1084 447062 14151914 62.97 20 80-W101-2006 445858 14597772 64.95 21 80-9627715-301UP 423766 15021538 66.84 22 80-4010346 379806 15401344 68.53 23 80-4012179 377916 15779260 70.21 24 80-C46806-1 362474 16141734 71.82 25 80-9627714-301UP 360430 16502164 73.43 26 80-4012174 324324 16826488 74.87 27 80-NL150T084LT 281596 17108084 76.12 28 80-121018-00 275716 17383800 77.35 29 80-051-1 255052 17638852 78.48 30 80-4030007296090 234346 17873198 79.53 31 80-121188-002 202860 18076058 80.43 32 80-9627712-301UP 192276 18268334 81.28 33 80-B113-1001 186116 18454450 82.11 34 80-4041707 180180 18634630 82.91 35 80-3249869 179200 18813830 83.71 36 80-4009263 176302 18990132 84.50 37 80-121009-00 171332 19161464 85.26 38 80-3260-0980 157024 19318488 85.96 39 80-C55581 151284 19469772 86.63 40 80-4009121 151228 19621000 87.30 41 80-4010350 148610 19769610 87.96 42 80-121148 143444 19913054 88.60 43 80-4030341 140980 20054034 89.23 44 80-9627716-301UP 139258 20193292 89.85 45 80-G121-1002 138768 20332060 90.47 46 80-D8097 133882 20465942 91.06 47 80-C558-1 131922 20597864 91.65 48 80-4009270 126994 20724858 92.21 49 80-C27416-1 124054 20848912 92.77 50 80-4011725 119448 20968360 93.30 51 80-4030339 117208 21085568 93.82 52 80-191820 100744 21186312 94.27 53 80-4012169 98756 21285068 94.71 54 80-4011714 91560 21376628 95.11 55 80-4010351 86632 21463260 95.50 56 80-4035149 86170 21549430 95.88 57 80-NL150T096LT 83258 21632688 96.25 58 80-S113-1004 70532 21703220 96.57 59 80-4010348 69300 21772520 96.88 60 80-27377 69286 21841806 97.18 61 80-NL150T120LT 68572 21910378 97.49 62 80-3260-503 48342 21958720 97.70 63 80-121189 47348 22006068 97.91 64 80-A37353 47320 22053388 98.13 65 80-4010349 43092 22096480 98.32 66 80-4003111 41216 22137696 98.50 67 80-S113-1001 39732 22177428 98.68 68 80-4030007296089 38892 22216320 98.85 69 80-4012213 34846 22251166 99.01 70 80-4010352 34790 22285956 99.16 71 80-4059989 33306 22319262 99.31 72 80-ULC0200 31556 22350818 99.45 73 80-551500 29050 22379868 99.58 74 80-121387 27720 22407588 99.70 75 80-4009262 27048 22434636 99.82 76 80-4035144 14952 22449588 99.89 77 80-4012212 10682 22460270 78 80-522500 8428 22468698 99.97 79 80-4039260 6062 22474760 100.00 99.94 Figure 3 P-Q-$ Analysis Figure 4 How P-Q-$ Analysis Combines P-Q Analysis and P-$ Analysis 160000 140000 120000 Runners & Repeaters in P-Q Analysis? Included in Sample 80000 Excluded from Sample Completely ignored by P-Q Analysis? 60000 40000 20000 Strangers in P-Q Analysis? Revenue 25 00 00 0 20 00 00 0 15 00 00 0 10 00 00 0 50 00 00 0 0 Quantity 100000
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