Perform a univariate analysis and answer the following questions:

a.What is the average number of strips per shift?

b.Strips of which thickness cluster are the most common, and strips of which thickness cluster are the least common?

Solid as Steel: Production Planning at thyssonkrupp On Monday, March 31, 2014, production manager Markus Schulze received a call from Reinhard Tger, senior vice president of thyssenkrupp Steel Europe's production operations in Bochum, Germany. Tger was preparing to meet with the company's chief operating officer and was eager to learn the reasons why the current figures of one of Bochum's main production lines were far behind schedule. Schulze explained that the line had had three major breakdowns in early March and therefore would miss the planned utilization rate for that month. Consequently, the scheduled production volume could not be carried out. Schulze knew that a lack of production capacity utilization would lead to unfullled orders at the end of the planning period. In a rough steel market with fierce competition, however, delivery performance was an important differentiation factor for thyssenkrupp. Tger wanted a chance to review the historic data, so he and Schulze agreed to meet later that week to continue their discussion. After looking over the production gures from the past ten years, Tiiger was shocked. When he met with Schulze later that week, he expressed his frustration. \"Look at the historic data!\" Tager said. \"All but one of the annual deviations from planned production are negative. We never achieved the production volumes we promised in the planning meetings. We need to change that!\" \"I agree,\" Schulze replied. \"Our capacity planning is based on forecast figures that are not met in reality, which means we can't fulfill all customers' orders in time. And the product cost calculations are affected, too.\" \"You're right,\" Tiger said. \"We need appropriate planning figures to meet the agreed delivery time in the contracts with our customers. What do you think would be necessary for that?" \"Hm, I guess we need a broad analysis of data to identify the root causes.\" Schulze answered. \"It'll take some time to build queries for the databases and aggregate data. And\" \"Stop!\" Tager interrupted him. \"We need data for the next planning period. The planning meeting for May is in two weeks .\" thyssenkru pp Steel Europe A major European steel company. thyssenkrupp Steel Europe was formed in a 1999 merger between historic German steel makers Thyssen and Krupp, both of which had been founded in the nineteenth century, thyssenkrupp Steel Europe annually produced up to 12 million metric tons of steel with its 27,600 employees. In scal year 20142015, the company accounted for 8.7 billion of sales, roughly a quarter of the group sales of its parent company, thyssenkrupp AG, which traded on the DAX 30 (an index of the top thirty blue-chip German companies). Its main drivers of success were customer orientation and reliability in terms of product quality and delivery time. Bochum Productlon Llnee The production lines at thyssenkrupp Steel's Bochum site were supplied with interim products delivered from the steel mills in Duisburg, 40 kilometers west of Bochum. Usually, slabs1 were brought to Bochum by train and then processed in the hot rolling mill (see Figure l). The outcome of this production step was coiled hot strip] (see Flglro 2) with mill scale} on its surface. Whether the steel would undergo further processing in the cold rolling mill or would be sold directly as \"pickled hot strip," the mill scale needed to be removed from the surface. The production line in which Tiger and Schulze were interested, a so-called push pickling line (PPL), was designed to remove mill scale from the upstream hot rolling process. To remove the scale, the hot strip was uncoiled in the line and the head of the strip was pushed through the line. The processing part of the line held pickling containers lled with hot hydrochloric acid, which removed the scale from the surface. Following this pickling, the strip was pushed through a rinsing section to remove any residual acid from the surface. After oiling for corrosion protection, the strip was coiled again. The product of this step, pickled hot strip, could be sold to B2B customers, mainly in the automotive industry. Other types of pickling lines were operated as continuous lines, in which the head of a new strip was welded to the tail of the one that preceded it. The differentiating factor of a PPL was its batching process, which involved pushing in each strip individually. Production downtimes due to push-in problems did not occur at continuous lines, but with PPLs this remained a concern. Nevertheless, thyssenkrupp chose to build a PPL in 2000 because ' Slabs are solid blocks ofsteel formed in a continuous calling process and then cut into lengths ofabout 20 meters. 2 A coiled hot strip is an intermediate product in steel production. Slabs are rolled at temperatures above I,OOOC. As they thin out they become longer: the result is a at strip that needs to be coiled. 'Mill scale isan iron oxide layeron the hot strip's surface that iscreatedjustai'ter hot rolling. when the steel is exposed to air (which contains oxygen). Mill scale protects the steel to a certain extent, but it is unwanted in l'unher processes such as stamping or cold rolling. Ill-n 1. 5mm: thyssenkrupp m. http://www.thyssenkruppcom/en/presse milder. htmlhphoton-tltl. Spam-J thyssenkrupp so. http://www.thysscnltruppcom/cn/pmm fbildcr nxmlaphchd-uv 1. increasing demand for high-strength steel made it profitable to invest in such a production line. At that time, high-strength steel grades could not be welded to one anotherwith existing machines, and the dimensions (at a thickness of more than 7.0 millimeters) could not be processed in continuous lines. every plant manager received an overview of past periods. Comparable production lines of different sites were benchmarked internally. The material produced on the PPL was not simply a commodity called steel. Rather, it was a portfolio of different steel grades-that is, different Throughout this case, the term "ton" refers to a metric ton. $ Tons produced are usually reported by shift (eight metallurgical compositions with specific mechanical properties. (For purposes of hours), by month, and eventually by fiscal year. this case, the top five steel grades in terms of annual production volume have The metric run time ratio is calculated as run time over operating time (e.g., 8 hours of operating time, or 480 been randomly assigned numbers from 1 to 5.) Within these top five grades were minutes, with 48 minutes of downtime yields a RTR of 90%). Shortages can refer to material shortages, lack of orders, labor disputes, or energy/fuel shortages (external) two high-strength steel grades. These high-strength grades were rapidly cooled after the hot rolling process-from around 1,000 C down to below 100 C. Deviation from Planned Throughput Removing the mill scale generated during this rapid cooling process required a different process speed in the pickling line. Only one of the five grades could be Steel production lines had typical characteristics and an average performance processed without limitations in speed and without expected downtimes. calculated based on an average production portfolio, mostly determined empirically using historic figures. For planning purposes, a fixed number was Performance Indicators usually used to place order volumes on the production lines and in this way "fill capacities." On a monthly basis, real orders then were placed to a certain At thyssenkrupp, managers responsible for production lines needed to report amount, which was capped by the line capacity. Each month's production regularly on the performance of the lines and the fulfillment of individual figures had three possible outcomes. objectives. The output, or throughput, of the production lines had always been an important metric. Even today, coping with overcapacities and customers The first possibility was that the planned throughput would be reached and at the increasing demands concerning product quality, the line throughput was part of end of the month there would be extra capacity. In this case, the extra capacity the set of key performance indicators. These indicators were taken into account would be filled with orders from the next month if the intermediate product for internal benchmarking against comparable production lines at other sites. already were available for processing. Otherwise, the line would stand still The line- specific variable production cost was calculated as cost over without fulfilling orders. This mode was very expensive because idle capacity throughput and was expressed in euros per metric ton. Capacity planning was would be wasted, and fixed costs occurred anyway. based on these figures, eventually resulting in delivery time performance. In the steel industry, production reports contained performance indicators at different The second possibility was that the planned throughput would not be reached. levels of aggregation. A very important metric was throughput (tons* produced) This would mean that at the end of the month, orders would be left that could per time unit'; the performance indicator run time ratio (RTR) was the portion not be fulfilled. This mode was also very expensive because the planned of time used for production (run time) compared to the operating time of a capacity could not be used, and real production costs were higher than pre- production line. calculated. Product calculation would result in prices that were too low, so contribution margins would be much lower than expected-or even negative. Operating time = Calendar time -(legal holidays, shortages," all scheduled maintenance In the third scenario, the exact planned throughput would be met (+/- 100 tons per month, or +/- 1,200 tons per year, was set as accurate). This was the ideal Run Time = Operating time - (breakdowns, exceeding downtime for case, but this had occurred only once in the first ten years of line history (see the maintenance, set-up time) annual figures in Table 1). Both figures were reported not only on a daily basis (i.e., a 24-hour production period) but also monthly and per fiscal year. Deviations from planned figures were typically noted in automated reports containing database queries. Thus,Table 1: Annual Deviation from Planned Production in the First Ten Years of Line Operation Annual Deviation from Planned Width: 800 to 1,650 mm Year of Operation Production (tons) - 23,254 Thickness: 1.5 to 12.5 mm - 22,691 + 1,115 Maximum throughput: 80,000 tons per month -22,774 VOUAWN - 2,807 - 20,363 (financial crisis) 66,810 Then Schulze reviewed available past production data, beginning with the night 21,081 shift on October 1, 2013, up until the early shift on April 4, 2014. Unfortunately, - 4,972 he had to omit a few shifts during this six-month period because of missing or 9.486 obviously erroneous data. Schulze's data set accompanies this case in a spreadsheet. Each month, production management had to explain the deviation from planned The explanation of the variables in the data set is as follows: figures. Many reasonable explanations had been given in the past. Major breakdowns were a common explanation because downtimes directly influenced Shift: The day and time at the beginning of a shift. the RTR. The RTR theory-the lower the run time ratio, the higher the negative Shift type: deviation from the plan-was often mentioned as the dominating force behind The production line operated 24/7 with three eight-hour shifts; the early shift ("E") started at 6 a.m., the late (or Midday) shift ("M") started at 2 the PPL not achieving the planned throughput. p.m., and the night shift ("N") started at 10 p.m. The production engineers' gut feeling was that a straightforward reason would Shift number: thyssenkrupp Steel used a continuous rolling shift system with five explain patterns that showed peaks "against the RTR theory," namely the different shift groups (shift group 1, shift group 2, etc.). The binary variables indicate whether the shift group i worked a particular shift. material structure: The resulting throughput can be explained on the basis of whether the material structure is favorable or unfavorable. A specific metric of Weekday: The line operated Monday through Sunday, but engineers usually worked the structure was the ratio meters per ton (MPT), a dimension indicator. The Monday to Friday on a dayshift basis (usually starting at 7 a.m.). MPT theory reflected the fact that material with a low thickness and/or a low Throughput: The throughput (in tons) during a shift. width carried a lower weight per meter. In other words, it took longer to put one ton of material through the production line if the process speed remained Delta throughput: The deviation (in tons) of actual throughput from planned throughput. constant. According to the MPT theory, negative deviations in months with average or above-average RTR could be explained by this metric. Data Schulze realized he had to compile data carefully in order to have any hope of finding possible explanations for the deviations from planned throughput. He decided to define aggregate clusters for material dimensions such as the width and the thickness of the strips. The technical data of the Bochum PPL relevant to the data collection were:MPT: A dimension indicator (meters per ton). Thickness clusters: Each cluster represented a certain scope of material thickness in millimeters within the technical feasible range of the production line. Strips fell into one of three clusters. The variables "thickness 1." "thickness 2," and "thickness 3" denote the number of strips from the first, second, and third thickness clusters, respectively, that were processed during a shift. Width clusters: Each cluster represented a certain scope of material width in millimeters within the technically feasible range of the production line. Strips fell into one of three width clusters. The variables "width 1," "width 2," and "width 3" denote the number of strips from the first, second, and third width clusters, respectively, that were processed during a shift. Steel grades: Strips of many different steel grades were processed on the line. The steel grades 1 to 5 are the grades with the largest portion by volume. The variables "grade 1," "grade 2," "grade 3," "grade 4," and "grade 5" denote the proportion (in %) of steel of that grade that was processed during a given shift. The remaining strips were of other steel grades; their proportion is given by "grade rest." RTR: The run time ratio (in %), which is calculated as run time divided by operating time. Schulze quickly realized he had data on more variables than he could employ for his analysis. Obviously, the total number of strips in the three width clusters had to be the same as the total number of strips in the three thickness clusters. Similarly, the proportions of the six different steel grades always added up to 100%. Schulze also decided to omit the dimension indicator (MPT) for his own analysis, as he now had much more detailed and reliable information about the size of the strips. After the analysis of the aggregated and clustered data, Schulze looked at his prediction model for delta throughput. From his experience, he knew he had found the key drivers for deviations from the planned production volume. "Look at this equation," he said to the production engineer in charge of the PPL. "The model coefficients determine the outcome, which is the deviation from planning. If we had the forecast figures for May, I could predict the deviation based on this model. Please get the numbers of coils from the different clusters and the proportions of the different steel grades. For the RTR, I'm guessing 86% is an appropriate figure."