SWTJC STEM – ENGR 1201 Content Goal 13 Quality Factors 1.Accuracy refers to how close the reported value comes to the true value. 2.Precision refers to the clustering of a group of measurements. Good modeling requires good data. To achieve this, the physical properties of a model must be measured and reported with quality. How do scientists and engineers express measurement quality?

SWTJC STEM – ENGR 1201 Content Goal 13 Accuracy The accuracy of a measurement refers "to how close the reported value comes to the true value". Two common methods for expressing accuracy are I.Mathematical error, also called percent error. II.Range of uncertainty, also called tolerance.

Mathematical error is reported in three different ways: Given: reported value - the measured value expected value - the theoretically correct or desired value Then: a.absolute error = reported value - expected value b.relative error = absolute error / expected value c.percent error = relative error · 100% SWTJC STEM – ENGR 1201 Content Goal 13 Mathematical Error

Given: reported value = 122 mm expected value = 120 mm Then: a. absolute error = reported value - expected value absolute error = 122 mm – 120 mm = 2 mm  Ans b. relative error = absolute error / expected value relative error = 2 mm / 120 mm =  Ans Note: relative error has no units. c. percent error = relative error · 100% percent error = · 100% = 1.7 %  Ans SWTJC STEM – ENGR 1201 Content Goal 13 Mathematical Error

The following are general classifications for errors: 1.For consumer purposes, 5-10% error is acceptable 2.For engineering purposes, 1% error is acceptable 3.For scientific purposes, 0.1% error is acceptable SWTJC STEM – ENGR 1201 Content Goal 13 Classification of Error

Range of uncertainty is reported as a nominal value plus or minus an amount called the tolerance. Reported value: 120 mm ±1 mm = 119 mm to 121 mm SWTJC STEM – ENGR 1201 Content Goal 13 Range of Uncertainty nominal value tolerance range of uncertainty

Range of uncertainty is also reported as a nominal value plus or min Range of uncertainty is reported as a nominal value plus or minus an amount called the tolerance us an percent tolerance. Reported value 120 mm ±2% = mm to mm Note: 2% of 120 = 2.4, = 117.6, = SWTJC STEM – ENGR 1201 Content Goal 13 Range of Uncertainty nominal value tolerance range of uncertainty

Actually, there is a third, less formal way of reporting accuracy. The digit representing the smallest value reported implies that the measurement is “accurate to that digit”. If it were not, then why report it? A reported value m implies the measurement was accurate to the nearest 0.01m (a cm). A reported value m also implies the measurement was accurate to the nearest 0.01m (a cm). SWTJC STEM – ENGR 1201 Content Goal 13 Informal Accuracy Reporting

The precision of a measurement refers to " the clustering of a group of measurements and can be determined by calculating standard deviation, standard error, or confidence interval". Precision is usually expressed by the number of significant digits reported for the magnitude of the measurement. 3 significant digits is good; 5 significant digits is excellent. A weighing scale that reports 128 grams is less precise than one that reports grams. SWTJC STEM – ENGR 1201 Content Goal 13 Precision

Precision in measurement comes at a price! 3 significant digits, commercial quality – Costs $100 4 significant digits, industrial quality – Costs $500 5 significant digits, scientific quality - Costs $2500 SWTJC STEM – ENGR 1201 Content Goal 13 Precision Costs $’s

Measurement precision must be interpreted in light of measurement accuracy. Let’s use a target practice example: SWTJC STEM – ENGR 1201 Content Goal 13 Precision – Target 1 The best situation, the shots are tightly clustered (high precision) on the center circle (high accuracy).

Measurement precision must be interpreted in light of measurement accuracy. Let’s use a target practice example: SWTJC STEM – ENGR 1201 Content Goal 13 Precision – Target 2 The next situation, shots are near the center (high accuracy), but not tightly clustered (low precision).

Measurement precision must be interpreted in light of measurement accuracy. Let’s use a target practice example: SWTJC STEM – ENGR 1201 Content Goal 13 Precision – Target 3 In the next situation, a tight cluster (high precision) is far off center (low accuracy ).

Measurement precision must be interpreted in light of measurement accuracy. Let’s use a target practice example: SWTJC STEM – ENGR 1201 Content Goal 13 Precision – Target 4 Finally, widely scattered shots (low precision) appear away from the center (low accuracy).

Which is the best and which is worst? SWTJC STEM – ENGR 1201 Content Goal 13 Precision - Comparison Best Most Insidious Why? Worst

Errors in measurement can be classified in two types: 1. Systematic Errors “result from an inherently wrong measurement” 2. Random Errors “result from externally introduced factors” SWTJC STEM – ENGR 1201 Content Goal 13 Error Types

Systematic errors “result from an inherently wrong measurement” The measuring instrument and/or procedure is flawed in some specific way. One characteristic of systematic errors is that they are generally either positive or negative and of roughly constant value. SWTJC STEM – ENGR 1201 Content Goal 13 Systematic Errors Tires Example I Jake has decided to use oversize tires on his truck, but his dad reminds him this could affect the speedometer and odometer readings. Explain.

SWTJC STEM – ENGR 1201 Content Goal 13 Systematic Errors Tires Speedometer and odometer operation is based on number of tire rotations. The new tire will make fewer revolutions. Why? Old TireNew Tire Show that a 10% increase in tire diameter will cause a 10% low reading in speed and distance. (Exam question)

SWTJC STEM – ENGR 1201 Content Goal 13 Systematic Errors Barometric Pressure Example II San Juana has been assigned a school project to record atmospheric pressure at noon for a two week period and plot the data with Excel. She learns of an Internet site operated by her school that provides hourly data including atmospheric pressure. So for two weeks she links to the site and records the data in a spreadsheet. She creates the chart and prepares to turn in the project when she learns that the school’s electronic barometer was improperly calibrated and was reading 0.05 inches of Hg too high. Why is this a systematic error?

SWTJC STEM – ENGR 1201 Content Goal 13 Systematic Errors Barometric Pressure

SWTJC STEM – ENGR 1201 Content Goal 13 Random Errors Random errors are “not inherent to the measuring process”. Frequently they are introduced by external factors that cause a scattering of the measured data. When the scattering is distributed equally about the true value, the error can be mitigated somewhat by making multiple measurements and averaging the data. Vibration in mechanical devices produces random errors. In electronic devices, noise produces random errors.

SWTJC STEM – ENGR 1201 Content Goal 13 Random Errors Wave Action Example I Jane is working as an intern for the national park service during the summer and has been assigned the task of monitoring the water level at Lake Amistad near Del Rio, Texas. A measurement rod at the end of a pier is marked with depth graduations to make the job easier. At 11:00 AM the first day she prepares to take the daily measurement, but immediately encounters a problem. Wind induced wave action on the lake causes the water level to rise and fall on the measurement rod making it difficult to read. Why is the error random? How can she mitigate it.

SWTJC STEM – ENGR 1201 Content Goal 13 Random Errors Wave Action Measuring Rod Mean Wave Height (M) Low Water Point (L) High Water Mark (H) Typical Wave Jane Reports: M = (H + L) /2

SWTJC STEM – ENGR 1201 Content Goal 13 Random Errors Engine Test Example II Richard is helping test engine performance at Southwest Research Labs in San Antonio. Fuel pressure is being monitored electronically and recorded using a computer. The data is copied to Excel and plotted. A typical recorded segment is shown in the chart below. Because of engine vibration effects on the pressure sensor as well as electronically induced noise, the fuel pressure data is somewhat erratic (blue line). The effects are clearly random in nature so he proposes to add an averaging circuit to "smooth" the output. After doing so, the fuel pressure data plot is much smoother (red line). By averaging out the error, the resulting data is more representative of the actual fuel pressure.

SWTJC STEM – ENGR 1201 Content Goal 13 Random Errors Engine Test

SWTJC STEM – ENGR 1201 Content Goal 13 Quality Factors 1.Accuracy "refers to how close the reported value comes to the true value“ 2.Precision "refers to the clustering of a group of measurements“ Scientists and engineers express measurement quality using,

Errors in measurement can be classified in two types: 1. Systematic Errors results from a measurement that is inherently wrong. 2. Random Errors results from the effect of external factors. SWTJC STEM – ENGR 1201 Content Goal 13 Error Types