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Block 23 Sampling - Theory 13
- 1. Senior/Graduate HMA Course Quality Control / Quality Assurance Sampling for Quality Control Construction QC QA Sampling 1
- 2. Requirements For a Sampling and Testing Program 1. Frequency of Tests? 2. Location of Samples? 3. Size of Samples? 7-2 Construction QC QA Sampling 2
- 3. Reasons for Sampling Materials 1 . Certification or Source Approval 2 . Process/Quality Control 3 . Acceptance 4 . Independent Verification Samples Construction QC QA Sampling 3
- 4. Types of Sampling 1 . Judgment Sampling 2 . Quota Sampling 3 . Systematic Sampling 4 . STRATIFIED SAMPLING 5 . RANDOM SAMPLING Construction QC QA Sampling 4
- 5. Lot or Population Construction QC QA Sampling 5
- 6. Sample from a Lot Specimen 1 Specimen 3 Specimen 2 Construction QC QA Sampling 6 7-4
- 7. Sampling Location Random Locations x Biased Locations Construction QC QA Sampling 7
- 8. Random Sampling Random Versus Stratified Random Construction QC QA Sampling 8
- 9. Random Sampling • Any portion of the population has equal chance of being selected • Bias is introduced when judgment is used - Use the tables! • Use random number tables Construction QC QA Sampling 9
- 10. RANDOM SAMPLING With simple random Sampling, All samples could end Up in one section of a Roadway lot ROADWAY LOT Construction QC QA Sampling 10
- 11. Stratified Random Sampling Sublot Sublot Sublot Sublot 1 2 3 4 Sta Sta Sta Sta Sta 100 110 120 130 140 Construction QC QA Sampling 11
- 12. Sampling Roadway Location Example LOT Size: 4000 LF Pavement Width: 12 FT 4 Sample Cores per LOT LOT begins at Sta 100+00 Construction QC QA Sampling 12
- 13. LOT Sublot Sublot Sublot Sublot 1 2 3 4 Sta Sta Sta Sta Sta 100 110 120 130 140 Construction QC QA Sampling 13
- 14. Sublot 1- Sample Location Longitudinal (X) Transverse (Y) Construction QC QA Sampling 14
- 15. RANDOM NUMBER Sublot 2 Sublot 4 TABLE Sublot 1 Sublot 3 74 60 01 27 43 X 29 21 78 01 43 Y 28 37 00 49 97 73 08 87 32 97 72 14 09 70 41 Construction QC QA Sampling 15
- 16. Sublot 1 Coordinate X = .74 x 1000 = 740 FT Coordinate Y = .29 x 12 = 3.5 FT. 740 Feet 12 FT 3.5 Feet 1000 Feet Construction QC QA Sampling 16
- 17. Sublot 2 Coordinate X = 0.60 x 1000 = 600 FT Coordinate Y = 0.21 x 12 = 2.5 FT Construction QC QA Sampling 17
- 18. Stratified Random Sampling Sublot Sublot Sublot Sublot 1 2 3 4 Sta Sta Sta Sta Sta 100 110 120 130 140 Construction QC QA Sampling 18
- 19. Stratified Random Sampling Sample Location 107+40 116+00 120+10 132+70 Sublot Sublot Sublot 2 9.4’ 1 4 Sublot 3.5’ 2.5’ 3 0.1’ Construction QC QA Sampling 19
- 20. Sampling at the HMA Plant Example Problem • Lot size is 5000 tons • The sub-lot size is 1000 tons • Sublot samples – – Select a block of numbers from the random number table • Calculate the sampling sequence Construction QC QA Sampling 20
- 21. Select Sublots • From a random number generator you got the following: 0.37 0.90 0.66 0.67 0.68 Construction QC QA Sampling 21
- 22. Select Sublots • The next step is to determine which ton you are going to test within the 5000 MG (ton) lot. • The first sample would be at 0.37 * 1000 or 370 MG (tons) • The second sample would be at 0.90 *1000 + 1000 or 1900 MG (tons) • The third sample would be at 0.66 * 1000 + 2000 or 2660 MG (tons) Construction QC QA Sampling 22
- 23. Questions? Construction QC QA Sampling 23
Notas del editor
- The instructor is to refer to Appendix A-1 of the AASHTO Test Procedure “To develop a Quality Control/Quality Assurance Plan for Hot Mix Asphalt”. This document is available from AASHTO or your local SHA.
- There are four basic reasons for sampling materials. They include: 1. Certification of source Approval - Samples of the material that is proposed for use by a supplier and/or contractor are taken and tested for approval. This ensures that the minimum material requirements are satisfied. 2. Process or quality control - Samples are taken on a lot-by-lot basis during production or use of the material to ensure that the process is "in control." This includes samples to periodically check the materials that are being obtained from previously approved sources (aggregates and asphalt). It also includes samples taken at the plant and paving site. 3. Acceptance - Samples that are taken to determine compliance with the specifications. 4. Independent/verification Samples - Samples that are taken for evaluating testing procedures. These types of samples are also referred to as independent assurance samples.
- There are five different classifications of sampling types which define where the samples are taken. They include: 1. Judgment Sampling - The location of samples for this type of sampling is based upon the judgment of the technician or inspector. The sample is supposed to be selected to represent the overall quality or condition of the mixture being sampled. However, individual bias is almost always present and there is always a chance of both a conscious and an unconscious bias. 2. Quota Sampling - Sampling during strategic time frames or every time a procedure, equipment or source is changed in the construction process. This requires highly trained and experienced technicians or inspectors. 3. Systematic Sampling - The sampling of materials at uniform time, distance or production intervals. 4. Stratified Sampling - The sampling of materials that includes two or more independent parts (or specimens) of a given quantity of material. When a material is categorized by lots, the lots are divided into multiple parts based on a reasonable breaking point. 5. Random Sampling - This sampling involves the selection of samples so that each increment or specimen comprising the sample has the same chance of being chosen from the lot.
- The cluster of grapes (sometimes a large cube-shaped object is used in the example) can be thought of as a "lot," consisting of the individual grapes (or the smaller cube-shaped blocks) that represent potential "specimens." Assume that the grape cluster (or cube) represents a lot of hot mix and that we wish to know the asphalt content of the hot mix in the lot. Keep in mind that it is always the properties of the lot that we wish to identify. To determine the best estimate of asphalt content, every bit of material in the lot should be tested (complete enumeration).
- Obtaining valid samples is not automatic. The following are two possible procedures for obtaining samples: 1. Random Sampling - A procedure in which any given measurement in the population is as likely to be included as any other. 2. Biased Sampling - A procedure in which certain individual measurements have a greater chance of being included than others. From a statistical standpoint, random sampling is an absolute necessity. Biased sampling occurs when the inspector uses "judgment" regarding where or when to take the sample. The use of random sampling is necessary when obtaining samples to use for determining specification compliance. This should not be confused with inspection used to identify materials or construction obviously not in compliance.
- Random sampling ensures that each portion of a lot has an equal chance of being selected for the sample. Stratified random sampling additionally involves the selection of two or more defined parts of a given lot. Stratified 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 section of the lot.
- “ Random” does not mean “haphazard”; it means that the sample is selected without bias or choice. In practice it may be difficult to train technicians who have been accustomed to inspection to randomly select samples without regard to quality. Their tendency is to make sure that defective materials are represented in the sample, thus unconsciously biasing the sample. Random sampling must be followed when using a statistically-based procedure, like Quality Assurance. Samples can be taken based on either on the basis of the length of the roadway or on the basis of material mass.
- The large rectangle represents the lot, perhaps one day’s paving from which cores are to be obtained. Using a random number table, it is possible, (but not necessarily likely) that all of the cores could be selected within the first half of the lot. For our example the specifications require four samples per lot.
- To avoid this possibility, the lot can be stratified into a number of sublots equal to the sample size to be selected from the lot. One core is then randomly selected from each sublot. This ensures that each portion of the lot has the same chance of being selected while, at the same time, ensuring that the sample is spread out over the entire lot.
- Suppose one is to sample a bituminous mixture from the roadway to obtain cores for density determination. The specifications state that the lot size shall be 4,000 linear feet of pavement, and that the sample consists of 4 cores per lot. If we assume that the pavement width is 12 feet and the lot begins at station 100+00, then we can use a random number table to select the sampling locations.
- The lot begins at station 100+00 and ends at station 140+00 (I.e.., 4000 feet in length). Five equal sublots are required, so the sublot length is 4,000/4 = 1,000 feet. The sublot locations are represented on the figure.
- Now that the sublot boundaries have been identified. the location of the core within each sublot must be determined. To accomplish this, the location must be randomized in the longitudinal as well as the transverse direction.
- The random number table can be used to determine both the transverse and the longitudinal locations for the cores. Two sets (columns, rows, etc.) of random numbers are selected, one for the transverse position, the other for the longitudinal position. A set of 4 random numbers for the longitudinal (X) position and 4 random numbers for the transverse (Y) position of the sample may be chosen by using the second block of numbers from the table.
- These X and Y random numbers are multiplied by the sublot length and paving width, respectively as shown in the example below: Sublot #1 (start at station 100+00) Coordinate X = 0.74 x 1,000 = 740 ft. Coordinate Y = 0.29 x 12 = 3.5 ft. Sublot #2 (start at station 110+00) Coordinate X = 0.60 x 1000 = 600 ft. Coordinate Y = 0.21 x 12 = 2.5 ft.
- To avoid this possibility, the lot can be stratified into a number of sublots equal to the sample size to be selected from the lot. One core is then randomly selected from each sublot. This ensures that each portion of the lot has the same chance of being selected while, at the same time, ensuring that the sample is spread out over the entire lot.
- This is an example of stratified random sampling. These examples were based on a sampling for density control and thus were based on distances down the road but it should be noted to the student that this same process can be used for sampling on an hourly basis or a tonnage basis.
- The instructor is to refer to Appendix A-1 of the AASHTO Test Procedure “To develop a Quality Control/Quality Assurance Plan for Hot Mix Asphalt”.
- If you use a random number generator or a random number table you could generate these five random numbers between zero and one.
- Using the random numbers shown on the previous slide the process would be as shown here.