PS Exam Preparation

Comprehensive preparation for the NCEES Principles and Practice of Surveying (PS) exam. 5 modules covering all 5 exam domains with 50 in-depth topics.

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Lesson 5

QA/QC Methods

Learning Objectives

After completing this topic, you should be able to:

Distinguish between quality assurance (QA) and quality control (QC)
Design field verification procedures for surveying operations
Apply office check procedures to calculations and deliverables
Explain the role of redundant measurements in quality management
Apply statistical tests to evaluate measurement quality
Develop and implement quality management plans for survey projects

Overview

Quality management in surveying has two complementary components: quality assurance (QA) prevents errors from entering the work, while quality control (QC) detects errors that have already occurred. Together, they form a systematic approach to ensuring that survey products meet the required accuracy, completeness, and reliability standards.

The cost of finding and correcting errors increases dramatically the later they are discovered. An error caught during a field check costs minutes; the same error caught after a map is filed may cost thousands of dollars and irreparable damage to professional reputation. The PS exam tests your ability to design and apply QA/QC procedures appropriate to the type and accuracy of the work being performed.

Figure PS.4.3 — Quality Assurance vs Quality Control

Quality Assurance vs. Quality Control

Definitions

Concept	Definition	Timing	Focus
Quality Assurance (QA)	Systematic activities to ensure that quality requirements will be fulfilled	Before and during work	Prevention of defects
Quality Control (QC)	Activities to verify that deliverables meet specified requirements	After work is completed	Detection of defects

QA Activities in Surveying

Quality assurance is proactive. It establishes the conditions for quality work:

QA Activity	Purpose
Standard operating procedures (SOPs)	Ensure consistent methods across all crews and projects
Equipment calibration schedules	Maintain instrument accuracy
Training programs	Ensure personnel competency
Project planning	Define accuracy requirements and methods before work begins
Checklists	Prevent omission of required steps
Peer review assignments	Ensure independent review of all work
Document templates	Standardize deliverable format and content

QC Activities in Surveying

Quality control is reactive. It verifies that the work meets requirements:

QC Activity	Purpose
Field checks	Verify measurement accuracy in the field
Closure checks	Verify mathematical consistency
Independent computations	Verify calculations by a different person
Plat review	Verify completeness and accuracy of deliverables
Client review	Obtain feedback before finalizing
Statistical analysis	Verify that measurements meet accuracy standards

Field Quality Control

Redundant Measurements

The most fundamental QC principle in surveying is redundancy. A single measurement provides no way to assess its quality. Redundant measurements allow both error detection and accuracy estimation.

Measurement Type	Minimum Redundancy	Method
Angle	Direct and reverse (face left/face right)	Average eliminates instrument errors
Distance	Forward and back measurement	Difference reveals blunders
Level	Backsight and foresight from balanced setup	Loop closure detects errors
GNSS	Multiple sessions or repeat occupations	Coordinate comparison
Traverse	Close back to known point	Closure computation

Field Check Procedures

Traverse Checks:

Close the traverse back to the starting point or to another known point
Compute angular closure (should not exceed the allowable value based on accuracy requirements)
Compute linear closure and express as a ratio
Compare closure to project accuracy requirements

Leveling Checks:

Close level loops back to the starting benchmark
Check section closures against allowable values
Compare to published benchmark values when available

Level Order	Allowable Closure
First Order, Class I	3.0 mm x sqrt(K)
First Order, Class II	4.0 mm x sqrt(K)
Second Order, Class I	6.0 mm x sqrt(K)
Second Order, Class II	8.0 mm x sqrt(K)
Third Order	12.0 mm x sqrt(K)

Where K = one-way leveling distance in kilometers. These are allowable loop misclosure tolerances per FGCS standards (not to be confused with the standard error per kilometer values used for station classification).

Common wrong path — using per-km standard error as if it were loop tolerance. Two different numbers look similar and are routinely confused: (1) standard error per km values used to classify a station (e.g., 0.7 mm/√K for First Order Class II), and (2) allowable loop misclosure tolerances used to accept or reject field work (e.g., 4.0 mm × √K for First Order Class II). The first is a statistical quality metric; the second is a field acceptance limit — and they differ roughly by a factor of four. Students sometimes apply the classification value as if it were the field tolerance and reject good work, or apply the loop tolerance as if it defined the class and accept work that doesn't meet standard. The correct rule: when the exam says "allowable misclosure for a closed loop," use the 3/4/6/8/12 mm×√K values above. When it asks about "standard error per km" or "station classification," use the 0.5/0.7/1.0/1.3/2.0 mm×√K values (roughly). Read the question for which one is being tested.

Quick retrieval check — try before reading on.

▶A crew runs a closed level loop of total length 8.4 km for a Second Order Class I project. The measured misclosure is 15.5 mm. Does the work meet standard?

Allowable misclosure = $6.0 \text{ mm} \times \sqrt{K} = 6.0 \times \sqrt{8.4} = 6.0 \times 2.898 = 17.39$ mm. The measured 15.5 mm is within the 17.39 mm tolerance, so yes, the work meets Second Order Class I. Distribute the 15.5 mm misclosure across the loop (typically by proportioning to the distances between benchmarks) and proceed with adjustment. Note: the same loop would not meet Second Order Class II if you accidentally applied 8.0 mm × √K (16.7 mm or better) — oh wait, that's also met. Let's try First Order Class II: $4.0 \sqrt{8.4} = 11.60$ mm — 15.5 mm fails. So the same data passes some orders and fails others; always check against the specific order the project requires.

GNSS Checks:

Compare coordinate solutions from different sessions
Check baseline residuals from network adjustment
Verify results against known control points
Monitor solution quality indicators (PDOP, number of satellites, fix quality)

Total Station Checks:

Compare direct and reverse angle readings
Verify prism constant settings
Check to known distances and directions
Verify backsight orientation at each setup

Blunder Detection

Blunders (gross errors) are the most dangerous type of error because they can be large enough to invalidate results but may not be obvious in the data:

Common Blunder	Detection Method
Wrong prism height	Independent height verification, compare to ground elevation
Wrong point number	Field sketches, point descriptions, systematic numbering
Transposition error	Independent reading, digital recording
Wrong target	Verify target identification before measuring
Misidentified monument	Compare to record dimensions, independent verification

Real-Time Field Verification

Modern data collectors and GNSS receivers provide real-time quality indicators:

Indicator	What It Tells You
GNSS fix quality	Fixed integer ambiguity (best) vs. float vs. autonomous
PDOP	Geometry of satellite constellation (lower is better, typically below 3.0)
RMS	Root mean square of residuals from least squares solution
Number of satellites	More satellites generally improve solution quality
Baseline length	Longer baselines may reduce RTK accuracy
Age of corrections	Older corrections reduce RTK accuracy

Office Quality Control

Calculation Checks

All calculations should be verified by a person other than the one who performed them:

Calculation Type	Check Method
Traverse adjustment	Independent computation using same raw data
Coordinate geometry (COGO)	Reverse computation to verify results
Area calculations	Independent computation, DMD/DPD check
Curve calculations	Check using multiple formulas or independent computation
Elevation interpolation	Spot check against original data
Legal description	Plot the description and verify closure

Map and Plat Review

Before delivery, every map or plat should be reviewed against a checklist:

Boundary Survey Plat Review Checklist:

Item	Verification
Title block complete	Project name, surveyor name, license number, date
North arrow and scale	Correct orientation and representative fraction
Basis of bearings	Stated and consistent with evidence
Bearing and distance on all lines	Present and mathematically consistent
Monument descriptions	All found and set monuments described
Adjoining information	Adjacent owners or parcels identified
Easements	Recorded easements shown or noted
Area	Computed and shown, consistent with dimensions
Legend	All symbols defined
Certification	Proper language, signed, sealed
Mathematical closure	Bearings and distances close within tolerance
Record vs. measured comparison	Discrepancies noted and explained

Document Review

Written deliverables (reports, legal descriptions, certifications) should be reviewed for:

Technical accuracy of all statements
Consistency with the survey plat
Proper legal and professional language
Completeness of required elements
Freedom from ambiguity
Correct client and property identification

Statistical Quality Methods

Standard Deviation and Standard Error

The standard deviation describes the dispersion of individual measurements:

Standard deviation (s) = sqrt( sum of (xi - mean)^2 / (n - 1) )

The standard error of the mean describes the uncertainty of the average:

Standard error = s / sqrt(n)

Increasing the number of measurements (n) improves the precision of the mean, but with diminishing returns.

Confidence Intervals

Confidence intervals express the range within which the true value is expected to lie:

Confidence Level	Multiplier (k)
68.3% (1 sigma)	1.00
90%	1.645
95% (2 sigma)	1.960
99%	2.576
99.7% (3 sigma)	3.00

For a measurement with mean x-bar and standard error SE, the 95% confidence interval is: x-bar +/- 1.96 x SE.

Outlier Detection

Statistical tests can identify measurements that are likely blunders:

The 3-Sigma Rule: Any measurement deviating from the mean by more than 3 standard deviations is likely a blunder and should be investigated.

The Pope Test (Tau Test): A more rigorous test for outliers in least squares adjustments. The test statistic is compared to a critical value based on the number of redundant observations and the desired confidence level.

Chi-Square Test for Variance

The chi-square test evaluates whether the actual precision of measurements matches the expected (a priori) precision:

If the test indicates the actual precision is significantly worse than expected, the observations may contain undetected blunders or the error model may be incorrect
If the actual precision is significantly better than expected, the a priori error estimates may be too conservative

Positional Accuracy Standards

Several standards define positional accuracy requirements:

Standard	Method	Common Application
NSSDA	RMSE at 95% confidence	Mapping and GIS
ASPRS	Based on RMSE	Photogrammetric mapping
FGDC	Based on NSSDA	Federal mapping programs
ALTA/NSPS	Relative positional precision	Land title surveys

The ALTA/NSPS standards define Relative Positional Precision (RPP) as the uncertainty in the location of any boundary point relative to any other boundary point, at the 95% confidence level. The standard is a single formula: 2 cm + 50 ppm of the distance between any two boundary points. This applies to all boundary points regardless of the measurement method used (total station, GNSS, or otherwise).

Quality Management Plans

Elements of a Quality Management Plan

For larger projects or firms seeking consistent quality, a formal quality management plan includes:

Element	Content
Quality policy	Management commitment to quality
Roles and responsibilities	Who performs and reviews each type of work
Procedures	SOPs for field, office, and delivery operations
Training requirements	Qualifications for each role
Equipment management	Calibration schedules, maintenance logs
Document control	Version management, filing standards
Corrective actions	Process for addressing quality failures
Records	What records to keep and for how long

ISO 9001 and Surveying

Some surveying firms pursue ISO 9001 certification for their quality management systems. Key ISO 9001 principles applicable to surveying:

Customer focus -- Understanding and meeting client requirements
Process approach -- Managing activities as interconnected processes
Continual improvement -- Systematically improving processes and outcomes
Evidence-based decision making -- Using data to drive quality decisions

While ISO certification is not required for surveying firms, the underlying principles improve any firm's quality management.

Common Quality Failures

Root Cause Analysis

When quality failures occur, root cause analysis prevents recurrence:

Failure	Apparent Cause	Root Cause	Corrective Action
Wrong boundary line on plat	CAD error	No independent plat review	Require peer review of all plats
Monument set in wrong location	Field crew misread coordinates	No field verification procedure	Require check measurement to second known point
Legal description does not close	Typo in bearing	No independent plot of description	Require all descriptions to be plotted by a different person
Client receives wrong file version	Multiple file versions in project folder	No version control system	Implement file naming convention and version control

Cost of Quality

The cost of quality includes:

Prevention costs -- Training, procedures, planning (invest here)
Appraisal costs -- Inspections, reviews, testing (necessary but reactive)
Internal failure costs -- Rework, scrap, re-survey (expensive but contained)
External failure costs -- Liability claims, client losses, reputation damage (most expensive)

Investing in prevention is always cheaper than correcting failures after delivery.

Exam Tips

Know the difference between QA (prevention) and QC (detection) -- the exam frequently tests this distinction
Understand that redundant measurements are the foundation of quality in surveying
Know the allowable closure standards for leveling by order and class
Statistical concepts (standard deviation, confidence intervals, outlier detection) are testable
Understand the concept of Relative Positional Precision as defined in the ALTA/NSPS standards
Quality management questions may present a scenario and ask you to identify the appropriate check procedure
Remember that finding errors before delivery is always preferable to finding them after