Engineering

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Engineering

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Chapter 5

Problems 5-6, 5-8, 5-12, 5-13

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Statistics 157 FREQUENCY DIAGRAMS AND HISTOGRAMS 5. Make a frequency distribution of the following data. Is this distribution bimodal? Multimodal? Skewed to the left? Skewed to the right? Normal? 225, 226, 227, 226, 227, 228, 228, 229, 222, 223, 224, 226, 227, 228, 225, 221, 227, 229, 230 6. Working in a call center is not an easy job. As cus- tomers contact the center, the employees must access a variety of computer screens in order to answer cus- tomer questions. The Call Center Six Sigma team is very interested in how long calls typically last. Use the following information for “length of time of call” to create and interpret a histogram. 8. Manufacturers ofrefrigeration systems for restaurant food storage are very concerned that their units are able to maintain precise temperature control. At AB's testing lab, a refrigeration unit has been equipped with newly designed seals. The temperature inside the unit has been monitored and measured every 30 minutes. Use the data from this test to construct and interpret a frequency diagram (see chart below). Temperature C 4 8 6 7 7 10 8 11 9 13 8 5 9 6 9 10 7 8 7 6 7 8 11 9 8 12 8 10 1 minute 2 minutes 3 minutes 4 minutes 5 minutes 6 minutes 4 15 34 22 25 36 7 minutes 8 minutes 9 minutes 10 minutes 11 minutes 12 minutes 40 45 30 10 8 3 9. PL Industries machines shafts for rocker arm assem- blies. One particularly complex shaft is shown in Figure P5.1. The existing machining cell is currently unable to meet the specified tolerances consistently. PL Industries has decided to replace the existing machines with CNC turning centers. The data at the right are from a run offheld at the CNC vendor’s facility. The indicated portion of the shaft was chosen for inspec- tion. The diameter specifications for the round shaft are 7.650 + 0.02 mm. To prevent scrap ticular operation, there is no lower specification. The data are scaled from 7.650, meaning that a value of 0.021 is actually 7.671 mm. Create a frequency dia- gram with the data. for this par- 0.011 0.013 0.018 0.007 0.002 0.020 0.014 0.006 0.002 7. NB Plastics uses injection molds to produce plastic parts that range in size from a marble to a book. Parts are pulled off the press by one operator and passed on to another member of the team to be finished or cleaned up. This often involves trimming loose mate- rial, drilling holes, and painting. After a batch of parts has completed its cycle through the finishing process, a sample of five parts is chosen at random and certain dimensions are measured to ensure that each part is within certain tolerances. This information (in mm) is recorded for each of the five pieces and evaluated in the chart below. Create a frequency diagram. Are the two operators trimming off the same amount of mate- rial? How do you know? 0.006 0.004 0.003 0.010 0.015 0.011 0.020 0.020 0.012 0.015 0.004 0.009 0.020 0.012 0.011 0.012 0.004 0.017 0.010 0.011 0.018 0.015 0.010 10. Create a histogram with the shaft data in Problem 9. Describe the distribution's shape, spread, and location. 11. Create and interpret a histogram using the data in Problem 8. Part Name: Mount Critical Dimension: 0.654 + 0.005 Tolerance: +0.005 Method of Checking: Caliper Date Time Press Samp 4 Samp 1 0.6550 Samp 2 0.6545 Samp 3 0.654 Samp 5 45 9/20/92 0100 #1 9/20/92 0300 #1 0.6540 0.6540 0.6545 0.6545 0.6545 9/20/92 0500 #1 0.6540 0.6540 0.6540 0.6540 0.6535 9/20/92 0700 #1 Oper Jack Jack Jack Jack Mary Mary Mary Mary 0.6540 0.6540 0.6540 0.6540 0.6540 9/21/92 1100 #1 0.6595 0.6580 0.6580 0.6595 0.6595 9/21/92 1300 #1 0.6580 0.6580 0.6585 0.6590 0.6575 9/21/92 1500 #1 0.6580 0.6580 0.6590 0.6580 0.6575 0.6585 0.6585 9/22/92 0900 #1 0.6570 0.6580 0.6580 Statistics 159 III 119.9 120.0 un // 12. Gold, measured in grams, is used to create circuit boards at MPL Industries. The following measure- ments of gold usage per batch of circuit boards have been recorded in a tally sheet. Create a histogram with the following information. Describe the shape, loca- tion, and spread of the histogram. The target value is 120.1 41 120.2 MIT 145 grams. 125 138 LH1 / 126 139 127 140 U11 128 II/ 141 41 / 129 142 UH I 130 143 LH I 131 144 U11 15. Use the concepts of symmetry and skewness to describe the histogram in Problem 8. 16. Why is it important to use both statistical measures and descriptive concepts when describing a histogram? 17. Create a histogram with the information from Prob- lem 7. Is this histogram bimodal? 18. Hysteresis is defined as the ability of a torque con- verter clutch to absorb the torsional vibrations and the energy dissipated by the drive train through the isolator or damper assembly of the clutch assembly. Experimental lab and vehicle testing has been done to determine the correct amount of hysteresis the clutch should have to perform properly. It was determined that 15 to 25 ft-lbs of hysteresis would provide proper operation of the torque converter clutch. Prototype assemblies have been built and tested to ensure that the design can be manufactured to meet specification limits before production begins. Use the following information to create a histogram. How are the pro- totypes performing? 132 배 145 W II/ 133 146 U11 U11 134 147 135 148 un I MIT un // un / MIT 136 149 137 III/ 150 ИИ 13. At a local bank, the time a customer spends waiting to transact business varies between 1 and 10 minutes. Create and interpret a histogram with the following data: Number of Units Hysteresis 14 1 Wait Time Frequency 5 15 0 1 min 16 8 2 min 10 17 16 3 min 16 18 33 25 19 56 18 20 64 4 min 5 min 6 min 7 min 8 min 9 21 79 6 22 90 4 23 77 9 min 2 24 78 10 min 1 25 58 26 54 14. A manufacturer of CDs has a design specification for the width of the CD of 120 + 0.3 mm. Create a his- togram using the following data. Describe the distribu- tion's shape, spread, and location. 27 50 28 32 29 26 Measurement 30 11 119.4 Tally III IIII un 31 7 119.5 32 1 119.6 33 3 119.7 WI/ 34 1 119.8 111 11
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Engineering, Chapter 5
FREQUENCY DIAGRAMS AND HISTOGRAMS
5-6. Working in a call center is not an easy job. As customers contact the center, the employees
must access a variety of computer screens in order to answer customer questions. The Call Center
Six Sigma team is very interested in how long calls typically lasts. Use the following information for
“length of time of call” to create and interpret a histogram.

SOLUTION:
Calculating for the range:
Range = Highest weight – Lowest weight
= 12 – 1
= 11
Let width of the class interval = 4
Therefore, the number of class intervals = 11 /4 = 2.75 ≈ 3 intervals
FREQUENCY TABLE
L...


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