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Definition Sle Size, n Upper Range, D4 Lower Range, D3 2 0 3 0 4 0 5 0 Mean Factor, A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.266 0 6 7 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 8 9 0.076 0.136 0.184 0.223 0.284 10 12 Refer to Table S6.1 – Factors for Computing Control Chart Limits (3 sigma) for this problem. Thirty-five sles of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 57.75 lb.; Average range R = 1.64 lb. a) For the given sle size, the control limits for 3-sigma x chart are: Upper Control Limit (UCLZ) = = lb. (round your response to three decimal places). Lower Control Limit (LCL;) = 1b. (round your response to three decimal places). = b) The control limits for the 3-sigma R-chart are: Upper Control Limit (UCLR) = 1b. (round your response to three decimal places). = Lower Control Limit (LCLR) = Ib. (round your response to three decimal places). Houston North Hospital is trying to improve its image by providing a positive experience for its patients and their relatives. Part of the “image” program involves providing tasty, inviting patient meals that are also healthful. A questionnaire accompanies each meal served, asking the patient, among other things, whether he or she is satisfied or unsatisfied with the meal. A 150-patient sle of the survey results over the past 7 days yielded the following data: Day 1 No. of Unsatisfied Patients 24 20 6 2 3 N 8 + O O Sle Size 150 150 150 150 150 150 150 4 17 5 6 8 26 15 7 The control limits to include 99.73% of the random variation in meal satisfaction are: UCLA = (enter your response as a number between 0 and 1, rounded to three decimal places). = LCLp = (enter your response as a number between 0 and 1, rounded to three decimal places). Based on the developed control limits, the number of unsatisfied patients has been Telephone inquiries of 100 IRS “customers” are monitored daily at random by Xiangling Hu. Incidents of incorrect information or other nonconformities (such as impoliteness to customers) are recorded. The data for last week follow: No. of Nonconformities Day 1 2 2 6 16 3 4 20 5 9 a) Using 3 standard deviations, the c-chart for the nonconformities is: UCLC = nonconformities (round your response to two decimal places). LCLC = nonconformities (round your response to two decimal places and if your answer is negative, enter this value as 0). b) According to the c-chart, there variation in the incidents of incorrect information given out by the IRS telephone operators. Refer to Table 56.1 – Factors for Computing Control Chart Limits (3 sigma) for this problem. West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at West’s Austin plant, believes there is no problem because his batteries have had an average life of 40 hours, about 10% longer than competitors’ models. To raise the lifetime above this level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the process was running properly, West took sles of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table: Sle Data Sle Data 1 Hour Sle Taken 14 2 3 4 5 XI х R 1 2 w 5 Hour Sle Taken 1 2 3 4 R 49 30 19 40 37 35 2 36 15 33 42 41% H88 15 8 40 28 40 36 35 60 28 52 24 16 17 20 22 OOO OWN 41 36 41 45 39 49 26 42 35 60 46 46 29 39 61 33 40 54 40 40 44 37 40 25 36 41 37 54 47 30 5 6 18 43 47 51 31 55 48 50 41 40.0 39.0 36.0 41.2 36.8 47.8 34.8 41.2 37.4 40.2 41.0 42.2 41.6 40 28 14 23 26 26 44 37 34 35 48 46 38 39 41 39 30 19 20 21 7 8 42 47 23 50 47 39 32 47 40 41 41 40 31 40 33 41 31 38 45 39 40 28 41 44 40 36 31 37 40 40 X 39.8 43.4 38.2 37.4 43.0 42.6 38.4 38.4 39.0 38.4 40.6 43.2 22 9 19 17 9 9 22 14 34 30 10 56 43 34 44 45 61 4 23 24 38 37 36 32 36 40 53 37 48 11 44 37 41 42 35 38 41 53 30 27 19 32 26 51 34 1 13 12 25 41 13 This exercise contains only parts a and b. = a) For the given data, the x = hours (round your response to three decimal places). For the given data, mean range = hours (round your response to two decimal places). With z=3, the control limits for the mean chart are: UCLE hours (round your response to three decimal places). LCLE = hours (round your response to three decimal places). The control limits for the range chart are: UCLR = hours (round your response to two decimal places). LCLR = hours (round your response to two decimal places). With these limits established, West now takes 5 more hours of data, which are shown in the following table. Calculate the mean and range for each hour that the sle data is taken. (Enter your responses for the mean to one decimal place and enter your responses for the range as whole numbers.) Sle Data Hour Sle Taken 1 3 4 5 х R IN 26 38 43 28 46 51 27 34 43 39 36 56 28 52 39 40 35 44 29 48 60 34 42 52 30 36 27 37 44 41 b) Do the sles for hours 26 through 30 indicate that the process is in control? Based on the x-chart, the process has been Based on the R-chart, the process has been What is the reasoning behind setting the upper and lower control limits 30; from the mean? х O A. The limits of the Z table are set at +303 + B. We know that 99.73% of assignable variation is contained within 307, and thus any data point outside of the limits is likely due to natural variation OC. 95.45% of the time, the sle averages will fall within + 30 if the process has only natural variation D. We know that 99.73% of natural variation is contained within 30j, and thus any data point outside of the limits is likely due to assignable variation + Boxes of Honey-Nut Oatmeal are produced to contain 16.0 ounces, with a standard deviation of 0.15 ounce. For a sle size of 49, the 3-sigma x chart control limits are: Upper Control Limit (UCLE) = ounces (round your response to two decimal places). Lower Control Limit (LCL;) = 0 ounces (round your response to two decimal places). Some degree of variability is present in almost all processes. True O False The causes of variation in statistical process control are: A. Type I and Type II. B. natural causes and assignable causes. C. producer’s causes and consumer’s causes. D. cycles, trends, seasonality, and random variations. O E. mean and range. Statistical process control charts: A. indicate to the process operator the average outgoing quality of each lot. B. display upper and lower limits for process variables or attributes and signal when a process is no longer in control. C. display the measurements on every item being produced. D. indicate to the operator the true quality of material leaving the process. O E. are a graphic way of classifying problems by their level of importance, often referred to as the 80-20 rule. Using an SPC Chart to Examine American Airlines’ Pilots “Sick Out” Source: “American Airlines Flight Delays Pile Up,” Wall Street Journal, http://online.wsj.com/article/SB10000872396390444083304578014550524246128.html, posted 9/23/2012. This article in the Wall Street Journal notes how “American Airlines continued to rack up high numbers of flight delays and cancellations, blaming a dispute with its pilots union. The union, meanwhile, denied that pilots disrupted flights unnecessarily.” 8.00% 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% Sept 18 2011 Sept 18 2012 Percent of Pilots Sick Can the same set of data be used to make opposite points in an argument, asks The Journal? It’s not that statistics lie, it is more in how all of the available data points are presented, as we can see in this story regarding the alleged “sick out” of American Airlines pilots in 2011-2012. Here is a 13 month “snapshot” of percent of pilots out sick at American: 9/18/11, 4.9%; 10/18/11, 9.5% ; 11/18/11, 5.0% ; 12/18/11, 6.5%, ; 1/18/12, 5.4% ; 2/18/12, 6.6% ; 3/18/12, 6.6% ; 4/18/12, 6.0% ; 5/18/12, 7.0% ; 6/18/12, 7.4%; 7/18/12, 6.1%; 8/18/12, 6.6%; and 9/18/12, 7.5%. (The number of pilots dropped a few percent during this period in American’s financial struggles, from a high of 7,840 to a current 7,563.) “By my calculations,” writes a reporter, “the number of pilots on sick leave was 45.7% higher on Sept. 18, 2012, than on Sept. 18, 2011, up 177 pilots. That seems like an increase in sick leave usage.” (See the bar chart above used to make this point.) American’s spokesman adds that sick leave “has been up more than 20 percent year over year and has been elevated for months.” ” American Airlines % Pilots Out Sick 12.00% 10.00% 8.00% . 6.00% 4.00% 2.00% 0.00% 9/1/11 10/1/11 11/1/11 12/1/11 1/1/12 2/1/12 3/1/12 4/1/12 5/1/12 6/1/12 7/1/12 8/1/12 9/1/12 13 Month SPC Chart ” Counters the union: “Contrary to claims by management, we have confirmed that pilot sick rates have not deviated from historical norms.” (Note the SPC p-chart showing percent of sick days.) Critical Thinking Questions: 1. The data available indicate that O A. the pilots did not disrupt the flights. B. the pilots’ union caused high flight delays at American. C. the same set of data can be used to support opposing points. D. you can never trust statistical data. 2. The SPC-chart shown O A. indicates the percent sick days is in control. B. does not provide a clear answer. C. is an x-bar chart. D. is an R-chart. 3. What happens to the reporter’s claim if the most recent 2 months of data are removed? O A. There is no change. B. The change from 9/18/11 – 7/18/12 no longer supports the claim. O C. We have no way of knowing. OD. The change over the period 9/18/11 – 7/18/12 is even greater. 4. SPC charts are useful O A. for proving union claims in general. B. to monitor pilot flying hours. C. in all airline applications. D. to see if a process such as this is in control. The effective capacity and efficiency for the next quarter at MMU Mfg. in Waco, Texas, for each of three departments are shown: Department Design Fabrication Finishing Effective Capacity 96,000 160,000 64,000 Recent Efficiency 0.90 1.02 1.05 What is the expected production for each department next quarter? Design department = units (enter your response as a whole number). = Fabrication department = units (enter your response as a whole number). Finishing department = units (enter your response as a whole number). Southeastern Oklahoma State University’s business program has the facilities and faculty to handle an enrollment of 2,000 new students per semester. However, in an effort to limit class sizes to a “reasonable” level (under 200, generally), Southeastern’s dean, Holly Lutze, placed a ceiling on enrollment of 1,500 new students. Although there was le demand for business courses last semester, conflicting schedules allowed only 1,450 new students to take business courses. The utilization rate for Southeastern = % (enter your response as a percentage rounded to one decimal place). = The efficiency rate for Southeastern = % (enter your response as a percentage rounded to one decimal place). The three-station work cell at Pullman Mfg., Inc. is illustrated in the figure below. It has two machines at station 1 in parallel (i.e., the product needs to go through only one of the two machines before proceeding to station 2). 20 min/unit Station 1 Machine A o Station 2 Station 3 4 min/unit 6 min/unit Station 1 Machine B 20 min/unit a) The throughput time is minutes (enter your response as a whole number). b) The bottleneck time of this work cell is minutes per unit (enter your response as a whole number). is the bottleneck station. d) If the firm operates 10 hours per day, 6 days per week, the weekly capacity of this work cell is units (enter your response as a whole number). The three-station work cell illustrated in the figure below has a product that must go through one of the two machines at station 1 (they are parallel) before proceeding to station 2. Capacity: 30 units/hr Station 1 Machine A 12 Station 2 Station 3 Station 1 Machine B Capacity: 5 units/hr Capacity: 12 units/hr Capacity: 30 units/hr a) The bottleneck time of the system is minutes per unit (enter your response as a whole number). b) is the bottleneck station. c) The throughput time is minutes (enter your response as a whole number). d) If the firm operates 11 hours per day, 5 days per week, the weekly capacity of this work cell is units (enter your response as a whole number).
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