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[Audio] QA/QC -203 Statistical Quality Control Part 2 Unit 12: 1 44 Pg:.

[Audio] U-1-2 Statistical Quality Control Part 2 Objectives  Understanding and Applying Quality Control Methods ( Control Charts, Histogram , Pareto Analysis ) in Construction.

[Audio] U-1-2 Statistical Quality Control Part 2 Control Charts  Control charts in construction are statistical tools used in quality control to monitor and control the processes involved in various construction activities.  They help identify variations in the process and determine whether they are due to common causes (inherent to the process) or special causes (due to specific issues). Control charts are essential for ensuring that construction processes, such as concrete pouring, material testing, or pavement laying, meet the required standards and specifications..

[Audio] U-1-2 Statistical Quality Control Part 2 Application in Construction  Concrete Strength Monitoring: By taking samples of concrete and testing their compressive strength, control charts can be used to track whether the concrete meets design specifications. If a trend or shift is detected in the control chart, it signals the need for corrective action before more concrete is poured.  Asphalt Pavement Quality: Control charts can track key properties like density and compaction during road construction. Any deviations in these parameters can be quickly identified to ensure the pavement meets durability requirements..

[Audio] U-1-2 Statistical Quality Control Part 2 Application in Construction  Material Testing: Regular testing of construction materials such as steel, aggregates, or cement can be plotted on control charts to monitor consistency over time.  Dimensional Control: Measurements taken during excavation, foundation setting, or the installation of structural components can be tracked on control charts to ensure the work is done within tolerance limits..

[Audio] U-1-2 Statistical Quality Control Part 2 Steps to Implement Control Charts  Collect Data: Regularly sample data from construction processes (for example, strength tests, dimensional checks).  Plot Data: Plot the data points on the control chart over time.  Set Control Limits: Determine upper and lower control limits based on historical performance or design specifications.  Analyze Variability: Monitor the process to detect any signs of variation that exceed control limits or display unusual patterns.  Take Action: If the control chart shows signs of special cause variation (for example, points outside control limits), investigate the cause and implement corrective measures..

[Audio] U-1-2 Statistical Quality Control Part 2 Benefits of Using Control Charts in Construction  Improved Process Control: Helps in maintaining process stability and preventing defective work.  Reduced Rework: Early detection of issues helps avoid costly rework later in the project.  Data-Driven Decisions: Provides a clear, visual tool for making informed decisions regarding quality control.  Compliance with Standards: Ensures that construction processes comply with industry and project-specific standards..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts  X-Bar and R Charts (Mean and Range Charts):  Purpose: Used to monitor the average (X-Bar) and variability (Range) of a process.  Application: In construction, these charts can monitor the compressive strength of concrete samples over time or the thickness of asphalt layers across different batches.  Process: Samples are taken at regular intervals, and the average and range of each sample set are plotted. Control limits (Upper Control Limit U-C-L--, and Lower Control Limit L-C-L--) are calculated, and any data points outside these limits indicate that the process may need adjustment..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts  Example: Concrete Strength Control Samples of concrete are taken daily, and compressive strength is tested. The X-Bar chart monitors whether the average strength remains within the control limits. If the average deviates, the mix ratio may need adjustment..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (1) X-Bar and R Charts in Construction Scenario: Concrete samples are taken from every batch delivered to a construction site and the compressive strength is measured at 7 days. The target compressive strength is 35 MPa. Collected Data: Sample 1: [36, 35, 34] MPa Sample 2: [33, 35, 36] MPa Sample 3: [34, 35, 35] MPa Sample 4: [32, 33, 34] MPa Sample 5: [36, 37, 35] MPa.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (1) X-Bar and R Charts in Construction Calculating X-bar and Range: Sample 1: X-bar = (36 plus 35 plus 34)/3 = 35 MPa, Range = 36 34 = 2 Sample 2: X-bar = (33 plus 35 plus 36)/3 = 34.67 MPa, Range = 36 33 = 3 Sample 3: X-bar = (34 plus 35 plus 35)/3 = 34.67 MPa, Range = 35 34 = 1 Sample 4: X-bar = (32 plus 33 plus 34)/3 = 33 MPa, Range = 34 32 = 2 Sample 5: X-bar = (36 plus 37 plus 35)/3 = 36 MPa, Range = 37 35 = 2.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (1) X-Bar and R Charts in Construction Control Chart: The X-bar chart would plot the average strength of each sample (for example, 35, 34.67, 34.67, 33, 36) over time, while the R chart tracks the variability within each sample (for example, 2, 3, 1, 2, 2). Control limits for the X-bar and R charts are typically set at ±3 standard deviations from the process mean. Let's assume the upper and lower control limits (UCL and L-C-L--) are: U-C-L (X-bar) = 37 MPa, L-C-L (X-bar) = 33 MPa U-C-L (R) = 4 MPa, L-C-L (R) = 0 MPa.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (1) X-Bar and R Charts in Construction Analysis: If Sample 4 has an X-bar of 33 MPa, which is at the L-C-L--, it would trigger an investigation into why the concrete is underperforming. If the R values stay below 4 MPa, the variability is acceptable, but a sudden spike in range would indicate issues like inconsistent mixing..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts  P-Charts (Proportion Charts):  Purpose: Used to monitor the proportion of defective units in a process.  Application: P-Charts are suitable for tracking defect rates in construction materials like steel bars, concrete batches, or welded joints.  Process: The proportion of defective units in each batch is plotted on the chart. If the defect rate exceeds the control limits, further investigation into the cause is necessary..

[Audio] U-1-2 Quality Control Principles and Process Types of Control Charts  Example: Defective Welds Monitoring Inspecting a sample of 100 welds on a steel frame, and recording how many fail visual or X-ray inspection. The P-chart tracks this failure rate over time. If the proportion of defective welds crosses the control limit, a review of the welding process may be needed..

[Audio] U-1-2 Quality Control Principles and Process Types of Control Charts.

[Audio] U-1-2 Quality Control Principles and Process Example (2) P-Charts in Construction Scenario: During tile installation, a sample of 100 tiles is inspected daily to check for defects (for example, cracks, misalignment). The acceptable defect rate is 5%. Collected Data (Defective Tiles per 100): Day 1: 3 defects Day 2: 6 defects Day 3: 2 defects Day 4: 8 defects Day 5: 4 defects.

[Audio] U-1-2 Quality Control Principles and Process Example (2) P-Charts in Construction P-chart Calculation: Proportion of defective tiles per day: Day 1: 3/100 = 0.03 Day 2: 6/100 = 0.06 Day 3: 2/100 = 0.02 Day 4: 8/100 = 0.08 Day 5: 4/100 = 0.04 Average Proportion (P-bar) = (0.03 plus 0.06 plus 0.02 plus 0.08 plus 0.04) / 5 = 0.046.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (2) P-Charts in Construction Control Limits (UCL and LCL): UCL = P-bar plus 3 * √(P-bar(1 P-bar)/n) = 0.046 plus 3 * √(0.046(1 0.046)/100) ≈ 0.046 plus 3(0.021) = 0.109 LCL = P-bar 3 * √(P-bar(1 P-bar)/n) = 0.046 0.063 = 0 (since the L-C-L cannot be negative for proportions). Analysis: On Day 4, the proportion of defects (0.08) is below the U-C-L of 0.109, meaning it's still within control, but it is a warning that the defect rate is higher than the average. A sustained increase would require further action..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts  C-Charts (Count of Defects per Unit): Purpose: Used for monitoring the count of defects per unit or area. Application: Useful for processes like surface finishing, where multiple defects (for example, cracks, pores, or unevenness) may appear within a defined area. Process: The number of defects per unit (for example, per square meter of plastered wall) is counted and plotted over time..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts  Example: Defects in Wall Plastering Workers count the number of visible cracks on a newly plastered wall. A C-chart tracks these cracks per unit area. If the number of cracks increases significantly, corrective actions (for example, mix adjustments, worker training) are required..

[Audio] U-1-2 Statistical Quality Control Part 2 Types of Control Charts.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (3) C-Charts in Construction Scenario: During road construction, the contractor monitors defects like cracks, potholes, and uneven spots in 100-meter sections. The goal is to keep defects to a minimum. Collected Data (Defects per 100 meters): Section 1: 2 defects Section 2: 5 defects Section 3: 3 defects Section 4: 7 defects Section 5: 4 defects.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (3) C-Charts in Construction C-chart Calculation: The total number of defects = 2 plus 5 plus 3 plus 7 plus 4 = 21 defects. Average Number of Defects (C-bar) = 21/5 = 4.2 defects per section. Control Limits (UCL and LCL): UCL = C-bar plus 3√C-bar = 4.2 plus 3√4.2 ≈ 4.2 plus 3(2.05) = 10.35 defects LCL = C-bar 3√C-bar = 4.2 3(2.05) = -2.85 (LCL is set to 0 since the number of defects cannot be negative)..

[Audio] U-1-2 Statistical Quality Control Part 2 Example (3) C-Charts in Construction Analysis: The number of defects per section is within control limits. However, Section 4 (7 defects) is nearing the U-C-L--, indicating a potential problem with the paving process in that section. If the trend continues, further investigation would be required, possibly checking the quality of the materials or paving technique..

[Audio] U-1-2 Statistical Quality Control Part 2 Histogram Analysis A histogram is a graphical representation of the distribution of data points in a process. It shows the frequency of data points within specified ranges, which helps identify patterns and variation in construction processes. Application in Construction: Concrete Strength Variation: Histogram analysis can help determine the distribution of compressive strength results for concrete batches. If the histogram shows a normal distribution centered around the target strength, the process is under control. However, if the distribution is skewed or has multiple peaks, it indicates inconsistencies in mixing or curing processes..

[Audio] U-1-2 Statistical Quality Control Part 2 Histogram Analysis Steps for Creating a Histogram in Construction: 1.Data Collection: Collect data on key quality parameters (for example, strength, thickness, or material density). 2.Determine Range and Bins: Set the range of data and divide it into equal intervals (bins). 3.Plot the Data: Count how many data points fall within each bin and plot these counts on the histogram. Example: A histogram for compressive strength results of concrete samples may show that most batches fall within acceptable limits, but a few outliers could indicate an issue with specific batches..

[Audio] U-1-2 Statistical Quality Control Part 2 Histogram Analysis.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (4) Histogram in construction Scenario: In this scenario, a contractor is overseeing the construction of a commercial building. During the pouring of the concrete, samples are taken to measure compressive strength. The concrete's target compressive strength is 35 MPa at 28 days. To assess the quality of the concrete, a histogram is used to display the distribution of compressive strength results from 50 different samples. Collected Data (Compressive Strength of 50 Samples at 28 Days): 29 MPa, 30 MPa, 35 MPa, 32 MPa, 34 MPa, 36 MPa, 33 MPa, 31 MPa, 34 MPa, 35 Mpa ,30 MPa, 31 MPa, 37 MPa, 35 MPa, 34 MPa, 36 MPa, 33 MPa, 32 MPa, 34 MPa, 35 Mpa,36 MPa, 32 MPa, 34 MPa, 33 MPa, 34 MPa, 37 MPa, 35 MPa, 31 MPa, 36 MPa, 34 Mpa, 30 MPa, 32 MPa, 33 MPa, 34 MPa, 35 MPa, 36 MPa, 31 MPa, 35 MPa, 37 MPa, 34 Mpa, 32 MPa, 34 MPa, 35 MPa, 33 MPa, 36 MPa, 35 MPa, 34 MPa, 37 MPa, 34 MPa, 31 MPa.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (4) Histogram in construction Step-by-Step Histogram Analysis: Organize the Data into Bins (Intervals): For a clearer representation, we organize the compressive strength values into bins of 2 MPa intervals (for example, 29–30 MPa, 31–32 MPa, et cetera). The range of the data is the difference between the maximum and minimum values Minimum value = 29 Mpa , Maximum value = 37 Mpa , Range = Max value Min value = 37−29=837 29 = 837−29=8 Mpa.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (4) Histogram in construction Calculate the Number of Bins This rule suggests the number of bins should be approximately the square root of the number of data points. Number of data points = 50 Number of bins= 50 ≈7.07 Calculate Bin Width Bin width= Range / Number of bins = 8/7 ≈1.14 Mpa We can round this to 1 or 2 MPa intervals for simplicity. In our previous example, I rounded to 2 MPa intervals for clarity..

[Audio] U-1-2 Statistical Quality Control Part 2 Create Frequency Table: Strength Range (MPa) Frequency (Number of Samples) 29–30 4 31-32 10 33-34 17 35-36 15 37-38 4 Construct Histogram: The histogram will show the frequency of samples falling within each strength range. The x-axis will represent the strength intervals (for example, 29–30, 31–32 MPa), and the y-axis will show the frequency (number of samples)..

[Audio] U-1-2 Statistical Quality Control Part 2 Example (4) Histogram in construction Interpretation: Most Common Range: The majority of the samples fall within the 33–34 MPa range (16 samples). Target Strength: The target strength of 35 MPa is well-represented, with many samples falling in the 35– 36 MPa range (15 samples). Low-Strength Values: There are a few samples that fall below the acceptable strength threshold (less than 30 MPa). This could be a cause for concern and may indicate issues with those specific batches of concrete, such as improper mixing or curing..

[Audio] U-1-2 Statistical Quality Control Part 2 Example (4) Histogram in construction Action: The histogram allows the contractor to quickly visualize the spread of the data. Based on the results, the contractor may decide to investigate the batches that resulted in low compressive strength (below 30 MPa) to ensure no future batches fall below the required strength. The overall distribution shows that most samples are within acceptable limits, but consistent monitoring is needed to maintain quality..

[Audio] U-1-2 Statistical Quality Control Part 2 Pareto Analysis Pareto analysis is based on the 80/20 principle, which states that 80% of defects come from 20% of the causes. This technique helps prioritize quality improvement efforts by identifying the most significant causes of defects in construction processes. Application in Construction: Defect Identification: For example, in a building construction project, 80% of cracks in concrete walls may be due to improper curing, with the remaining 20% coming from substandard materials or environmental factors..

[Audio] U-1-2 Statistical Quality Control Part 2 Pareto Analysis Steps for Pareto Analysis: 1.Identify Defects: List all the defects observed in a construction process. 2.Determine Frequency: Record how often each defect occurs. 3.Rank the Defects: Rank defects in descending order of frequency. 4.Plot a Pareto Chart: Plot the defects on a bar chart with the most frequent on the left, showing their cumulative impact. Example: A Pareto chart might show that 75% of total defects in a road construction project are due to material inconsistencies, followed by 15% due to improper compaction, and the remaining 10% due to poor weather conditions..

[Audio] U-1-2 Statistical Quality Control Part 2 Pareto Analysis.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (5) Pareto Analysis in construction Scenario: A construction project team is encountering problems with defective concrete batches that do not meet the required strength specifications. The project manager decides to conduct a quality control investigation to identify the root causes of these defects and determine which issues contribute most to the problem. After testing 100 batches of concrete, the following defects are identified along with the number of batches affected by each defect: Data on Concrete Defects: Improper Water-Cement Ratio: 35 defective batches , Inadequate Mixing Time: 20 defective batches Poor Quality of Aggregates: 15 defective batches , Contaminated Materials: 10 defective batches Delayed Concrete Placement: 8 defective batches , Incorrect Curing Process: 7 defective batches Other Miscellaneous Issues: 5 defective batches.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (5) Pareto Analysis in construction Step-by-Step Pareto Chart Construction: 1. Organize the Data List the defects in descending order of frequency (in other words, number of defective batches). Defect Number of Defective Batches Improper Water-Cement Ratio 35 Inadequate Mixing Time 20 Poor Quality of Aggregates 15 Contaminated Materials 10 Delayed Concrete Placement 8 Incorrect Curing Process 7 Other Miscellaneous Issues 5.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (5) Pareto Analysis in construction 2. Calculate Cumulative Frequency and Percentage Calculate the cumulative frequency and cumulative percentage of the total defective batches for each cause. Defect Cumulative Batches Cumulative % Number of Defective Batches Improper Water-Cement Ratio 35 35 35/100=35% Inadequate Mixing Time 20 55 55% Poor Quality of Aggregates 15 70 70% Contaminated Materials 10 80 80% Delayed Concrete Placement 8 88 88% Incorrect Curing Process 7 95 95% Other Miscellaneous Issues 5 100 100%.

[Audio] U-1-2 Statistical Quality Control Part 2 Example (5) Pareto Analysis in construction Interpret the Pareto Chart: The Pareto chart will show that the Improper Water-Cement Ratio and Inadequate Mixing Time are the most significant contributors to the defective concrete batches. Together, these two causes account for 55% of all defects. By focusing on addressing these two main issues, the project team could potentially resolve more than half of the problems related to concrete quality..

[Audio] U-1-2 Statistical Quality Control Part 2 Example (5) Pareto Analysis in construction Action Based on Pareto Chart: Improper Water-Cement Ratio: The team should focus on improving quality control during the mixing process to ensure the correct water-cement ratio is maintained. Inadequate Mixing Time: The project manager may need to review the procedures for mixing concrete to ensure that the prescribed mixing time is followed for all batches..

[Audio] U-1-2 Statistical Quality Control Part 2 Summary  Control charts in construction are statistical tools used in quality control to monitor and control the processes involved in various construction activities.  A histogram is a graphical representation of the distribution of data points in a process. It shows the frequency of data points within specified ranges, which helps identify patterns and variation in construction processes.  Pareto analysis is based on the 80/20 principle, which states that 80% of defects come from 20% of the causes. This technique helps prioritize quality improvement efforts by identifying the most significant causes of defects in construction processes..