Student Manual. Lesson 4- Statistical Concepts. Version /

Transcription

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3 Listed above are the major Learning Outcomes you will have achieved when this lesson is completed. 4-3

4 It is important to understand that there is Variability in constructing transportation projects. Our goal is to minimize Variability. The level of Quality of any material or product is associated with the level of Variability. 4-4

5 Quality Control and Verification sampling and testing are used to measure the quality of the constructed t product. The specific material properties which h are evaluated by QC and Verification sampling and testing are referred to as Quality Characteristics. Quality Characteristics which are specified are normally selected because they: -Relate to initial and long term Performance -Are quantifiable or measurable -Can be measured with good repeatability 4-5

6 Quality Characteristics for QC are selected because they are good indicators to monitor and control production against specification targets and limits. Quality Characteristics selected for QC contribute either directly or indirectly to the long term performance of the product. Shown above are some QC Quality Characteristics for Asphalt and Portland Cement concrete. 4-6

7 Quality Characteristics for Verification are selected because they directly relate to the long-term performance of the product. Shown above are some Verification Quality Characteristics for Asphalt and Portland Cement concrete. Are some quality characteristics more important than others? Typical Quality Characteristics Utilized for Acceptance Hot-Mix Asphalt (HMA) Asphalt Content (25% Pay factor) Air Voids (25% Pay factor) Portland Cement Concrete (PCC) Air Content Compressive Strength In-Place Density (35% Pay factor) % Passing #8 Sieve (5% Pay factor) % Passing #200 Sieve (10% Pay factor) Ride Quality 4-7

8 Variability exists in all construction materials. It is one of the key factors that is integral to Quality Assurance and must be understood. d Variability can be controlled but not eliminated. Construction materials, even under the best controlled production, can be expected to have some amount of variability. It is important to keep in mind, that each material has some inherent variability. 4-8

9 Variability- there are four primary sources of Variability in construction materials, those being: - Material Variability - Sampling Variability - Testing variability - Production and Placement 4-9

10 Materials variability is for the most part due to Mother Nature, in that the variation exists in the materials naturally. It is quite unrealistic to expect perfect homogeneity in any raw or processed source of construction materials. However, this variability is generally small when like materials are compared. 4-10

11 Sampling Variability is caused by variation that is in the sampling methods used. Even if the standard sampling procedures are followed, some amount of sampling variability will occur, because we are human. No two people will perform sampling identically. 4-11

12 Testing Variability is caused by variation that is in the testing methods and equipment. Even if the technician i carefully follows the standard d procedures, and the equipment is properly calibrated, there is some variability. Naturally, for both sampling and testing, should liberties be taken with altering the procedures or methods, regardless of how small, more variability has been introduced. Additionally, equipment that is not properly calibrated or properly functioning just adds to the list of variables. 4-12

13 Construction Variability is a result of the variations that occur in construction and production processes. Additional variables can be introduced through inconsistent production and construction methods. 4-13

14 Typical Quality Measures used in Quality Assurance Specifications are selected because they quantify the average quality, the variability, or both. Quality Measures that we will review are: The Mean The Range The Variance The Deviation The Standard Deviation The Percent Within Limits (PWL) For example, the Mean of all strength test results might be specified as the Quality Measure for a LOT of Portland Cement concrete. Or, the Percent Within Limits (PWL) of all in-place density test results might be used as the Quality Measure for earthwork densities. PWL is the Quality Measure that is most often recommended for use in Quality Assurance Specifications. 4-14

15 Specification Limits Are statistical limits that are applied to test results of multiple samples when evaluating the quality of a LOT using some Quality measure such as PWL. They are usually comprised of an Upper Specification Limit (USL), a Lower Specification Limit (LSL), or both. It is important to recognize that since these are statistical limits, individual sample test results may fall outside of the limits and still be included in the Acceptance determination. Engineering Limits Are sometimes used in conjunction with Specification Limits and sometimes not. As an example, strength test results for Portland Cement Concrete are typically evaluated using the Mean of three consecutive test results, but still requires that no individual test result falls below a specified Engineering Limit. There usually is an Upper Engineering g limit (UEL) andalower Engineering g Limit (LEL). Results falling outside these limits are generally considered below an acceptable level. Acceptance Limits Are limits that are placed on the Quality Measure (e.g. the minimum allowable PWL), not on the test values of samples for an individual Quality characteristic. While test values are evaluated with Specification and Engineering Limits, the actual computed quality level for a specific Quality Measure is evaluated against the Acceptance Limit. 4-15

16 The Mean coincides with the center or midpoint of a Normal Distribution Curve. Ideally, the Mean should be the Target Value for Quality Characteristics with an acceptance range. The mean target value needs to be above the minimum limit for pass/fail specifications. The Mean is denoted by an X with a bar over it (x), and is called x-bar. The Mean of a Statistical Sample is computed by adding all of the individual material sample test values (x i ) in the Statistical Sample and dividing the sum ( ) ofthose test values by the number of samples (n). Therefore: x = = x i X 1 + X 2 + X 3 +. n Where: x = Mean x i = Individual id test t value = Sum of all n = number of samples 4-16

17 In this example, 14 tests were performed on a project. The individual test values were recorded d and the Mean was computed as shown above. 4-17

18 The simplest measure of dispersion (i.e. Variability) which can be determined for asetof measurements or test values is the Range. The Range for a Statistical Sample (i.e. multiple samples) is computed as shown above; by subtracting the lowest sample value from the highest. Although it is a single, easy to determine measurement, its primary drawback is that it does not utilize all of the information (sample values) available in the statistical sample. Since the Range only accounts for the two extreme values, it provides no measure of the dispersion of the other values. It is often used in Control Chart applications. 4-18

19 Using the same 14 tests, the table above shows how the Range was determined. d 4-19

20 One simple measure used to express how much an individual id sample value varies from the Mean of a set of measurements or test values is referred to as a Deviation. This is simply calculated by subtracting the mean from the single sample value: Deviation = (x i x) Where: x = Mean x i = Individual test value = Sum of all n = number of samples 4-20

21 The variance is another mathematical measure of the spread or dispersion of sample values. Where the Range provides an indicator of the spread of test values from the highest to lowest, the Variance looks at the overall Deviation of values from the Mean. The Variance is denoted by the term s 2. The variance (s 2 ) of a distribution of sample test values is computed by squaring each Deviation from the Mean (x i - x) 2, adding these squares, and dividing their sum ( ) by the number of samples (n) minus one. Thus, the Variance provides an idea of how the results are scattered about the Mean. It can be used for comparing Contractor QC and Verification sample test results. Where: x = Mean x i = Individual test value = Sum of all n = number of samples s 2 = Variance 4-21

22 Using the same 14 tests, the table above shows how the Variance (s 2 )was determined. d 4-22

23 The Standard Deviation is another measure of spread or variation, and is derived from the Variance. It provides a measure of the average Deviation i of the individual id sample values from the Mean. The Standard Deviation of a Population is denoted by the symbol and the Standard Deviation of a Statistical Sample is denoted with by s. The Standard deviation(s) is computed by taking the square root of the Variance (s 2 ) of a distribution of sample test values. If the number (n) of samples that comprise the Statistical Sample is greater than 200, the Population Standard Deviation ( ) should be used. Please note that that the n denominator is different in the two calculations. Where: x = Mean x i = Individual test value = Sum of all n = number of samples s 2 = Variance s = Standard Deviation of Statistical Sample = Standard Deviation for Populations 4-23

24 Using the same 14 tests, the table above shows how the Standard Deviation (s) was determined. d 4-24

25 Quality Assurance type Specifications have pay adjustment procedures that are linked to the computed quality levell for each Quality Characteristics. i To compute the quality level, the Quality Level Analysis (QLA)- Standard Deviation method, is used. This mathematical procedure estimates the percentage of a LOT that is within the Specification Limits or PWL. Typically, the PWL for each Quality Characteristics is calculated using the Mean and Standard Deviation of the Acceptance sample test results for a given LOT of material. A specific Pay Factor is assigned for each PWL and this is subsequently applied to the LOT quantity and corresponding contract unit price to compute a pay adjustment. 4-25

26 A is more variable. Even though A s average would be on target, each data point varies greatly from the target. Why aren t the average values a good enough measure? 4-26

27 If these two data sets are for the same material, we would say that something is out of control. The two graphs have the same mean (average), but have different variability. We are interested in the cause of the variability. If it is inherent variability, then we cannot control it; it is a property of the material. WE NEED TO KNOW: WHAT IS ACCEPTABLE VARIABILITY FOR THIS PARTICULAR MATERIAL? 4-27

28 Target Values are based upon the Mean for a particular material. The upper and lower limits are established based upon a desired engineering value related to material performance. The mean needs to be above the lower Limit. Establishing Limits for QA Specs expect to achieve the desired result if measured data falls within the established limits of our target value 95% of the time. Establishing Limits for QA Specs expect to achieve the desired result if measured data falls within the established limits of our target value 95% of the time. 95% of Data 4-28

29 One of the key terms used in quantifying or measuring quality is Population. 4-29

30 In Quality Assurance Specification, the term LOT is used to represent a Population of material (e.g. HMA, PCC, Soils, etc.) which h is incorporated into the product. SSRBC sets forth the size of a LOT, by construction type and material. The LOT size is intended to represent material which is indeed from the same source and which has been produced and placed essentially under the same controlled conditions. For Example- Section 120- Excavation & Embankment- a LOT is a single lift of finished material not to exceed 500 feet in length, or a single run of pipe connecting two structures, whichever is less. On some very small projects, the Plans may define the LOT as the entire quantity of material produced and placed on that project. This is often referred to as Job- Mix Formula (JMF). Some drawbacks to the JMF approach are: -Material may be placed over an extended period (1-2 years) -The entire material may truly have not been produced and placed under the same conditions (changes in equipment, changes in weather, material source, etc.) LOT 500 feet 4-30

31 LOTs may be divided into smaller quantity amounts of uniform size, which are called sublots. 4,000 tons 1,000 tons 1,000 tons 1,000 tons 1,000 tons LOT 5 sublot 1 sublot 2 sublot 3 sublot

32 Shown above are the SSRBC LOT sizes for Asphalt, Concrete and Earthwork. 4-32

33 To measure a particular Quality Characteristic of a LOT or sublot, we could obtain a sample from every part of the LOT. For example- we want to test the compressive strength of 500 CY of PCC. We could test every yard, but then we wouldn t have much concrete left. This is called complete enumeration. Obviously, this is not practical or cost-effective, therefore we obtain a Statistical Sample. Statistical Samples are those samples obtained from a LOT which can provide information that may be used to quantity the quality of the entire LOT. 4-33

34 There are a variety of sample types that can be obtained when sampling LOTs. Biased Sampling- A sampling procedure whereby samples obtained from a LOT do not have an equal probability of being chosen. Representative Sample- a non-random sample which, in the opinion of the sampler, represents an average condition of a material or an item of construction. Uniform Interval Sampling- a non-random procedure in which samples are obtained at fixed intervals of material production or material quantity. Quota Sampling- a non-random procedure in which samples are obtained at the discretion and convenience of the sampler to satisfy the required number of samples for a LOT. Selective Sampling- a non-random procedure in which a sample is obtained only for informational purposes to guide Quality Control or Verification actions. Random Sampling- a sampling procedure where each sample is obtained from the LOT has an equal probability of being selected. For Asphalt, LOTs are divided into smaller quantity amounts of uniform size, which are called sublots. There are no sublots in FDOT earthwork construction and concrete. 4-34

35 Department Verification: The Engineer will conduct a Verification The Engineer will select test locations, including Station, Offset, and Lift, using a Random Number generator based on the Lots under consideration. Each Verification test evaluates all work represented by the Quality Control testing completedinthoselots. (All other specifications have similar language) To eliminate biased samples (both QC and Verification), Random Sampling is to be performed. Random sampling protects against known defects, unknown defects, cycles and patterns. It has a low inherent risk, low risk in unknown situations, and high reliability. Furthermore, it does not required a knowledgeable sampler (one who understands patterns, etc.) 4-35

36 Random sampling is just that, random. Every truck, lift, station has an equal chance of being selected. When you choose the location, truck, LOT, etc. based on what or where you want to sample or test, it is biased. For instance, if Verification always choose the 4 th LOT of 4 consecutive LOTs of earthwork for density testing, it would be considered biased. 4-36

37 LOTs are divided into sublots (for asphalt) to ensure that samples are not concentrated by the random numbers in one particular location. sublots allow for samples to be taken from within equal segments of the LOT. This is referred to as Stratified Random Sampling. This method is used to ensure that samples are obtained from throughout the LOT. 4-37

38 There are a variety of methods for determining Random sampling locations. It is important to determine which method the Engineer will be using, as the specifications require the Engineer to provide the Random Number generator. The QC Manager and their staff should be made aware of the system to be used in advance of construction and all parties agree. Example Random Number Generators: -ASTM D Standard Practice for Random Sampling of Construction Materials -Computer/calculator capable of generating random numbers -Throwing dice -Random Number Table created through software, such as MS Excel or proprietary software available for purchase. 4-38

39 This is the Random Number Chart FDOT. The following Random Number Chart and instructions can be obtained from the SMO website. The following pages have a full size of the chart and detailed instructions on its use. 4-39

40 er Chart FDOT om Numbe Rando 4-40

41 Random Number Sampling Plans A random number generator is to be used to help select random frequencies and locations for materials. Random number charts are published in a variety of publications and available on scientific calculators and computers. Other published random number charts and electronic generators are approved to use in order to generate a random sampling plan. Random Number Chart FDOT is published and available at the State Materials Office Web page. Asphalt plant and roadway quality control and verification sample random number locations are generated by the Composite Pay Factor worksheet. Suggestions for using Random Number Chart FDOT Determine the number of samples you plan on obtaining using the project documents. 1. Pick a number between 1 and 100. This is the row number you selected. 2. Pick another number between 1 and 7. This is the column number. 3. Enter the chart using the row and column numbers you selected. 4. Assign a unique random number from the chart for each sample you plan to obtain. You may go right to left, up or down, or left to right from the row and column you entered in step 3. If you come to a random number that does not generate a valid location for sampling, skip that number and move on to the next number in the sequence. 5. The random numbers can be used as a percentage or individual digits to select sample frequencies or locations. EXAMPLES Concrete Plan for a 230 cy placement with a sample frequency of 1 per lot, 50 cy lot size. Expect5 lots, 1 sample for each 50 cy lot. Pick 63 and 4 as row and column numbers to enter chart. Pick five numbers reading left to right. (0.1224, , , , ) Using the percentage method: Lot 1 : 50 cy x =6.12, select the truck at the 6 cy point Lot 2 : 50 cy x =6.57, select truck at the 57 cy point ( for Lot 1 = 57) Lot 3: 50 cy x =38.34, select truck at 138 cy point. ( for lots 1&2=138) Lot 4: 50 cy x =30.70, select truck at 181 cy point. ( for lots 1,2&3=181) Lot 5: 30 cy x =29.07, select truck at 229 cy point. ( for lots 1 thru 4 = 229) 4-41

42 Earthwork Stabilized Subgrade Contractor completes stabilization and compaction operations for a subgrade section of 1400 lineal feet with a width of 24 feet. Three Lots of stabilized subgrade. You plan for 3 density tests (1 location per Lot) and 9 stabilizing mixing depth (3 locations per Lot). Density locations: Pick 18 and 2 as row and column numbers to enter random number chart. Reading left to right: , , , , and Note 6 random numbers are selected as you need random distance locations from the beginning of the lot station and random width locations from the edge of the stabilized area. Lot 1: Length, 500 x = 320 Width, 24 x = 0.34 Select location 320 from beginning station of Lot 1 and 0.34 from the right side of the stabilized area. Lot 2: Length, 500 x Width, 24 x = 17.8 Select location 485 from beginning station of Lot 2 and 17.8 from the right side of the stabilized area Lot 3: Length, 400 x = 33 Width, 24 x = 13.5 Select location 33 from beginning station of Lot 3 and 13.5 from the right side of the stabilized area Mixing depth check locations can be selected in a similar manner using 3 locations per Lot. Tips : Enter the chart at a unique location each time it is used. Avoid starting at the top, (row 1, and column 1). And reading to the right like a book each for successive chart uses. Keep it simple! Close your eyes and point to a spot on the page to start if you can t decide which numbers between 1 and 100 or 1 and 7 are good starting points. Avoid the temptation to pick new random numbers just because you don t agree with the random selection. You can always use Independent verification ( IV) testing if the random selection is obviously missing an area of particular concern. Record all the test data for every test conducted. 4-42

43 Remember- Random sampling ensures that each specimen in a LOT has the same chance of being selected for the sample. Stratified random sampling additionally involves the selection of two or more defined sublots of a given LOT. Stratified random sampling is used to ensure that the specimens for the sample are obtained from throughout the LOT, and are not concentrated in one portion or sublot of the LOT. It is possible, but not likely, that in a LOT all of the random numbers could have us sampling in the morning: we avoid this through the use of sublots. 4-43

44 Chance Causes of variability are inherent to any method or process and must be expected. These were discussedd earlier in this chapter (i.e. sampling variability, testing variability, etc.). Assignable Causes are those that can be shown directly to cause a variation in the process (during this operation it was pouring rain, it was extremely cold during this phase, the equipment used in the placement process was changed, etc.). 4-44

45 Control Charts are useful tools for monitoring and ensuring the quality of a product or process. These can be used by the QC Manager as an aid in the Quality Control process and some of their uses include: -Early detection of trouble -Establishment Etblih tof process capability -Identify variability of production or process -Permanent record of quality Some of the benefits from their use include: -Decrease in overall product variability -Assist in achievement of higher pay adjustments - Instill a quality awareness 4-45

46 8 RUN CHART Test Number Individual Air Content 8 STATISTICAL CHART Test Number Mean Air Content 4-46

47 Run Charts plot individual material sample values (n=1) and check the measurements or test results against the Specification i Limits. i Targets for Run Charts are typically established by the Contractor for their process for a particular Quality Characteristic within the Specification Limits. The Target should coincide with either a know or assumed Mean process capability. For example, based upon the development of a specific mix design (Hot Mix Asphalt, Concrete, etc.) a Contractor or Producer would typically utilize the target value from the mix design as the target for the run chart. The limits are usually either the Specification limits and/or the Engineering Limits. (Engineering Limits are established based upon a desired engineering value related to material performance, such as 4% Air Voids in HMA) Shown above is a Run Chart illustrating the tracking of the percent passing the 300 µm Sieve. Notice the Percent Passing, the Quality characteristic being measure, is on the vertical axis and the sample number on the horizontal axis. Note this chart has both Upper and Lower Specification and Engineering Limits. 4-47

48 The case study presented here is a Run Chart used by Luck Stone Corporation at their Leesburg Plant. The chart is setup for individual tests for a No. 88 stone. The chart uses a combination of Specification Limits (5 to 30% passing) and plant process limits. For controlling the No. 88 stone, the No. 4 sieve is identified as the key sieve for measuring the effect of the change in the setup. Setups are the documentation required to measure every every change in stone control process. The setups contain data on the crusher settings required, the locations of the various screen sizes, the screen size and wire cloth screen size. In this case study, evidence is presented to show the impact of setup change on gradation by the shift in trends from one setup (#1-9) to another (#10-20).The setup change was necessitated by the material being coarser than desired, brought on by crusher liner wear. This was noticed by a plant technician who noticed a run of tests (#1-9) being on the Coarse side of the Target Mean. To compensate for this liner wear, the wire clothscreensizewas changed from ¼ cloth to 3/16 cloth, making the product finer. The change was effective as shown by Test #10 being slightly above the Target Mean. 4-48

49 Statistical Control Charts always use Subgroups of data rather than individual sample results. The minimum i Subgroup size is n=2 and typically is in the range of n=3 to 5. (A Subgroup is a predetermined number of samples whose Mean or Range are plotted on a Statistical Control Chart). There are three primary types of Statistical Charts that are typically used for transportation construction material Quality Control. X Chart (X Bar)- plots the Grand Mean of Subgroup Means based on the number of subgroups. R Chart- plots the Mean Range for the Subgroup Ranges based upon the number of subgroups. Moving Average Chart- plots a moving average for a predefined number of samples or subgroups. The X Bar and R Charts are the most widely used for the process control of construction materials and both must be used to estimate whether a process is in control. The X Bar chart is used to determine when the center (process Mean) changes and the R Chart is used to determine when the spread (process Variability) changes. 4-49

50 The key element of these charts is the proper designation of the Control Chart Limits, which may not be the same as those used for Acceptance. They are defined as: Action Limits; statistically derived boundaries applied to a Control Chart in controlling material production or placement. As shown above, these are expressed as Upper Control Limit (UCL) and the Lower Control Limit (LCL). When values of the material characteristics fall within these limits, the process is under control. When values fall outside the limits, there is an indication that some Assignable Cause is present causing the process to be out of control, such as the vibrator for the compactor broke. This chart relies on the fact that we may assume that the distribution of measurements surrounding the Mean value occurs within a ±3 Standard Deviations of the Mean. Therefore, think of it as a bell-shaped curve turned on its side, as shown above. 4-50

51 Examples: HMA LOT - 4,000 tons sublot - 1,000 tons Earthwork LOT - single lift of finished embankment not to exceed 500 linear feet PCC Class II Bridge Deck LOT is 50 CY or one day s production whichever is less 4-51

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54 Now, lets look at some examples on how random sampling is used for each of the materials previously discussed. 4-54

55 Suppose a contractor s technician is to sample a bituminous mixture to obtain material for determination of AC content. The LOT size is 4,000 Tons and the sample consists of 3 split samples per 1,000 Ton sublot. If we assume that the LOT begins at the 12,000 th Ton, then we can use a random number table to select the Tons from which the samples will be taken and; therefore, we can determine from which truck to take our sample. 4-55

56 These random numbers are generated by an Excel spreadsheet. The spreadsheet dh tthen takes these numbers and performs the computations ti thatt determines which ton is sampled for each sublot. 4-56

57 Remember, the beginning tonnage of the LOT (sublot 1) was 12,000 tons and each sublot size was 1,000 tons. Therefore, the end of sublot 1 (beginning of sublot 2) would be tons, the end of sublot 2 (beginning of sublot 3) would be tons, the end of sublot 3 (beginning of sublot 4) would be tons, and the end of sublot 4 (end of the LOT) would be tons. 4-57

58 sublot tons x = tons Sample the th ton in the sublot Therefore, sample the ton overall sublot tons x = tons Sample the th toninthe sublot Therefore, sample the ton overall sublot tons x = tons Sample the th toninthe sublot Therefore, sample the ton overall sublot tons x = tons Sample the th toninthe sublot Therefore, sample the ton overall 4-58

59 Truck #?? contains the 740 th ton for sublot 1 Truck #?? contains the 600 th ton for sublot 2 Truck #?? contains the 10 th ton for sublot 3 Truck #?? contains the 270 th ton for sublot

60 Contractor takes random samples from each sublot that is each split into QC, VT, & RT samples. Then, the Department randomly selects one of the sublots for Verification (VT) testing. 4-60

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67 These random numbers are generated by an Excel spreadsheet, random number table, or any other approved random number generator. 4-67

68 Remember, the beginning cubic yards of LOT 13 was 600 cy and each LOT size was 50 cy. Therefore, the end of LOT 13 (beginning of LOT 14) would be cy, the end of LOT 14 (beginning of LOT 15) would be cy, the end of LOT 15 (beginning of LOT 16) would be cy, and the end of LOT 16 would be cy. 4-68

69 LOT cy x = cy Sample the cy in the LOT Therefore, sample the CY overall LOT cy x = cy Sample the cy in the LOT Therefore, sample the CY overall LOT cy x = cy Sample the cy in the LOT Therefore, sample the CY overall LOT cy x = cy Sample the cy in the LOT Therefore, sample the CY overall 4-69

70 Truck #?? contains the 621 st CY for LOT 13 Truck #?? contains the 657 th CY for LOT 14 Truck #?? contains the 730 th CY for LOT 15 Truck #?? contains the 791 st CY for LOT 16 If Verification is going to test the same load then, QC technician casts one additional cylinder from the same sample, the QC hold cylinder 4-70

71 Verification randomly selects one of the 4 LOTs where QC obtained a sample and will independently perform plastic properties test and cast a set of cylinders from a separate sample from the same load of concrete as the Contractor s QC sample. Verification casts one additional hold cylinder from each sample. 4-71

72 Suppose a contractor s technician is to collect material to take to the lab for maximum density determination ti (Proctor). The maximum the LOT size can be is 500 ft, which is what we have here. The frequency of sampling is one per two consecutive LOTs (QC) and one per 8 consecutive LOTs (VT). If we assume that the LOTs in question begins at station and 13 RT of C/L Construction. Then the QC technician can use a random number table to select the stations and offsets from which the samples will be taken. 4-72

73 These random numbers are generated by an Excel spreadsheet, random number table, or any other approved random number generator. For this exercise in class, write in the Station and first Offset Random Numbers only. 4-73

74 Remember, the beginning station of the LOT 1 was and each LOT size was 500 feet. Therefore: LOT Beginning Station Ending Station

75 LOTs 1 & 2 Y 1000 feet x = feet (124+78) + = (Station) X 20 feet x = feet = C/L Const. LOTs 3 & 4 Y 1000 feet x = feet (134+78) + = (Station) X 20 feet x = feet = C/L Const. LOTs 5& 6 Y 1000 feet x = feet (144+78) + = (Station) X 20 feet x = feet = C/L Const. LOTs 7 & 8 Y 1000 feet x = feet (154+78) + = (Station) X 20 feet x = feet = C/L Const. Y 20 ft. X 1,000 ft. (2 LOTs) 4-75

76 QC obtains enough material to split into QC, VT, &RTsamples (3-way split). Then, the Verification technician randomly selects one of the 4 split samples for Verification (VT) testing. 4-76

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79 NOTES 4-79