Chapter 5 - Precision. Accuracy and Tolerance

SPA204/Appendix 6.0 /Notes

PRECISION, ACCURACY AND TOLERANCE

Exact Value and Nearest Value Exact Value • • •

Obtain when we start counting. Known as discrete quantity (Kuantiti diskret) Example: 1. Number of student in a classroom. 2. Number of pencils in a box. 3. Number of chairs in stadium. 4. Number of fans in an artist concert.

Nearest Value • • •

Obtain when we start measuring. Known as (Kuantiti selanjar) Example: 1. Height of a student. 2. Length of highway in Malaysia. 3. Areas of a classroom. 4. Volume of water in a bottle. 5. Depth of a hole.

Precision and Tolerance Precision: • The ability of measuring equipment taking reading consistently every time measurement was made. • Precision of measuring equipment depends on the smallest unit available on that equipment. • < Unit available > precise the measuring equipment. • To determine the preciseness of measuring equipment repeated readings should be taken. • Precision also determined by looking at relative deviation. • < Relative deviation > precise the measuring equipment. Relative deviation = Mean deviation x 100% Mean reading

Tolerance: • The probability of the largest error in a measurement. • Half of the different between largest measurements with smallest measurements. Tolerance

= ½ (Largest measurement – smallest measurement) = ½ (Upper limit – lower limit) = ½ (Smallest measurement unit)

Kolej Komuniti Kepala Batas, Kementerian Pengajian Tinggi Malaysia Prepared by: Rosiadi Bin Tajudin

SPA204/Appendix 6.0 /Notes

PRECISION, ACCURACY AND TOLERANCE

Tolerance specification = (Measurement + Tolerance) Upper Limit, Lower Limit and Tolerance Range Upper limit: • Largest value of a measurement (Measurement quantity + Tolerance) Lower limit: • Smallest value of a measurement (Measurement quantity – Tolerance)

Tolerance range = (Upper limit – Lower limit)

Accuracy • • •

The ability of measuring equipment taking exact reading as in real value. The accuracy of measuring equipment is determined by the smallest unit available on that equipment. It also determined by errors value (Ralat) in which < errors > exact the value given by measuring equipment.

Errors = (Real measurement – Obtainable measurement)

Conclusion Precision and accuracy of measuring equipment can be simplified as on figure below. Dart board Centre

Dart > Precise, < accuracy

< Precise, > accuracy

> Precise, > accuracy

Kolej Komuniti Kepala Batas, Kementerian Pengajian Tinggi Malaysia Prepared by: Rosiadi Bin Tajudin

SPA204/Appendix 6.0 /Notes

PRECISION, ACCURACY AND TOLERANCE

Class Activity (Examples and exercise) Examples 1. Identify the quantity below as exact value or nearest value.

a. b. c. d. e.

Amount of curtains. Length of 50 chairs arrange in a rows. Number of books in a book shelves. Height of a building in a town. Areas of a mosque.

2. The table below show the mass of nails in gram obtained after four times reading. Num. of reading 1 2 3 4

Nails mass (gm) 4.0 3.7 4.2 3.9

Get the relative deviation for the above readings to determine the precision of measuring equipment used. 3. Given, diameter of a ball is between 3.54cm and 3.60cm, what is its tolerance. 4. Given, length of a wood is 10 cm. what is its, a. Tolerance b. Largest value c. Smallest value and d. Tolerance range 5. Determine the preciseness for 2 rulers by differentiate its relative deviation for the readings taken as shown on table below. Num. of reading 1 2 3 4 5

Ruler A 29.8 30.1 30.0 29.9 30.2

Ruler B 30.0 30.5 29.8 28.9 31.1

6. Calculate largest errors allowed for each value below and get its tolerance specification. a. 3.5 m ≤ Width ≤ 3.6 m b. 1.5 km ≤ Distance ≤ 1.6 km c. 14.25 cm2 ≤ Areas ≤ 14.56 cm2

Kolej Komuniti Kepala Batas, Kementerian Pengajian Tinggi Malaysia Prepared by: Rosiadi Bin Tajudin

SPA204/Appendix 6.0 /Notes

PRECISION, ACCURACY AND TOLERANCE

7. Calculate the tolerance, upper limit, lower limit and tolerance range for each measurement:

a. Length = 15 cm b. Mass = 10.5 gm c. Temprature = 32.0 oC 8. Given, 4 ≤ m ≤ 8 and 6 ≤ n ≤ 13, what is its, a. Maximum value for m + n b. Minimum value for m + n c. Maximum value for n – m d. Minimum value for n – m 9. Given, s = 4cm and t = 8 cm, what is, a. Maximum value for s + t b. Minimum value for s + t c. Maximum value for t – s d. Minimum value for t – s

Kolej Komuniti Kepala Batas, Kementerian Pengajian Tinggi Malaysia Prepared by: Rosiadi Bin Tajudin

SPA204/Appendix 6.0 /Notes

PRECISION, ACCURACY AND TOLERANCE

Exercise 1. Identify the quantity below as exact value or nearest value.

a. b. c. d.

Number of pages in a book. Volume of a water tank. Highway length. Weight of a box.

2. The table below show diameter of a ball obtained after 5 readings taken. What is the relative deviation for that reading. Num. of reading 1 2 3 4 5

Diameter (cm) 2.14 2.13 2.17 2.15 2.17

3. Given diameter of a cylinder is 5.05 cm. what is its,

a. b. c. d.

Tolerance Largest value Smallest value and Tolerance range

4. The weight of an apple is between 120.34 g and 120.50 g, what is its tolerance. 5. Given, 3 ≤ x ≤ 5 and 15 ≤ y ≤ 45, what is its, a. Maximum value for x + y b. Minimum value for x + y c. Maximum value for y – x d. Minimum value for y – x 6. Given, a = 20 cm and b = 5 cm, what is, a. Maximum value for a + b b. Minimum value for a + b c. Maximum value for a – b d. Minimum value for a – b

Kolej Komuniti Kepala Batas, Kementerian Pengajian Tinggi Malaysia Prepared by: Rosiadi Bin Tajudin