i ii mci \_anui auui id

(2009 edition)

Jeff C Gust

Robert M. Graham

Michael A. Lombardi

[T

Ititut ftitute of

ind Technology

m.t of Commerce

Special

Publication

960-12

NIST Special Publication 960-12

Stopwatch and Timer

Calibrations

(2009 edition)

Jeff C. Gust

Richard J. Bagan, Inc. Robert M. Graham

Sandia National Laboratories

Michael A. Lombardi

National Institute of Standards and Technology

January 2009

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

National Institute of Standards and Technology

Patrick D. Gallagher, Deputy Director
Certain equipment, instruments or materials are identified in this paper in order to adequately specify the experimental details. Such identification does not imply recom- mendation by the National Institute of Standards and Technology nor does it imply the materials are necessarily the best available for the purpose.

Official contribution of the National Institute of Standards and Technology; not subject

to copyright in the United States.

National Institute of Standards and Technology

Special Publication 960-12 Natl. Inst. Stand. Technol.

Spec. Publ. 960-12

80 pages (January 2009)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2009

For sale by the Superintendent of Documents

U.S. Government Printing Office

Internet: bookstore.gpo.gov Phone:(202) 512-1800 Fax:(202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
Foreword >

FOREWORD

Stopwatch and timer calibrations are perhaps the most common calibrations performed

in the field of time and frequency metrology. Hundreds of United States laboratories

calibrate many thousands of timing devices annually to meet legal and organizational

metrology requirements. However, prior to the publication of the first edition of this guide in May 2004, no definitive text had existed on the subject. This NISTRecommended

Practice Guide was created to a fill a gap in the metrology literature. It assists the

working metrologist or calibration technician by describing the types of stopwatches

and timers that require calibration, the specifications and tolerances of these devices, the

methods used to calibrate them, and the estimated measurement uncertainties for each

calibration method. It also discusses the process of establishing measurement traceability

back to national and international standards.

iii

Acknowledgements

ACKNOWLEDGEMENTS

The authors thank the following individuals for their extremely useful suggestions

regarding this new revision of the guide: Georgia Harris and Val Miller of the NIST

Weights and Measures Division, Warren Lewis and Dick Pettit of Sandia National

Laboratories, and Dilip Shah, the chair of the American Society for Quality (ASQ)

Measurement Quality Division.

v

Table of Contents

Contents

Section 1 introduction to Stopwatch and Timer Calibrations 1

1 .A. The Units of Time Interval and Frequency 1

1 .B. A Brief Overview of Calibrations 4

1. C. Traceability and Coordinated Universal Time (UTC) 5

Section 2: Description of Timing Devices that Require Calibration 9

2. A. Stopwatches 9

2.B. Timers 14

2. C. Commercial Timing Devices 15

Section 3: Specifications and Tolerances 17

3.A. Interpreting Manufacturer's Specifications 17

3.B. Tolerances Required for Legal Metrology 22

Section 4: Introduction to Calibration Methods 25

Section 5: The Direct Comparison Method 27

5. A. References for the Direct Comparison Method 27

5.B. Calibration Procedure for Direct Comparison Method 31

5. C. Uncertainties of Direct Comparison Method 33

Section 6: The Totalize Method 41

6.A. Calibration Procedure for the Totalize Method 41

6.B. Uncertainties of Totalize Method 43

6. C. Photo Totalize Method 47

Section 7: The Time Base Method 51

7. A. References for the Time Base Method 51

7.B. Calibration Procedure for the Time Base Method 51

7.C. Uncertainties of Time Base Method 56

Section 8: How to Determine if the Calibration Method Meets the Required

Uncertainty 57
Stopwatch and Timer Calibrations

Section 9: Other Topics Related to Measurement Uncertainty 59

9.A. Uncertainty Analysis of Using a Calibrated Stopwatch to Calibrate another Device 59

9.B. The Effects of Stability and Aging on Calibrations

of 32 768 Hz Crystals 60

9.C. Factors That Can Affect Stopwatch Performance 62

Appendix A: Calibration Certificates 65

Appendix B: References 67
List of Figures

List of Figures

Figure 1. The calibration and traceability hierarchy 6

Figure 2. Type I digital stopwatch 11

Figure 3. Type II mechanical stopwatch 1

1

Figure 4. Interior of digital (Type I) stopwatch 12

Figure 5. Inner workings of a mechanical (Type II) stopwatch or timer... 13

Figure 6. A collection of timers 14

Figure 7. Sample manufacturer's specifications for a digital stopwatch

(Example 1) 18

Figure 8. Sample specifications for a digital stopwatch (Example 2) 20

Figure 9. Typical performance of quartz wristwatches using 32 768

Hz time base oscillators 21

Figure 10. Portable shortwave radio receiver for reception of audio

time signals 30

Figure 11. Reaction time measurements (four operators, 10 runs each)

for the direct comparison method 36

Figure 12. Averaging measurement results for four different operators.... 3

6

Figure 13. Block diagram of the totalize method 41

Figure 14. Using the start-stop button of the stopwatch to start the counter 42

Figure 15. Measured reaction times (four operators, 10 runs each) for

totalize method 44

Figure 16. Mean reaction times (four operators, 10 runs each) for the

totalize method 45

Figure 17. Photo totalize start reading. .47

ix
:ch and Timer Calibrations

List of Figures, cont'd

Figure 18. Photo totalize stop reading 48

Figure 19. Ambiguous photo totalize reading 49

Figure 20. Time base measurement system for stopwatches and timers. ..52

Figure 2 1 . A time base measurement system for stopwatches and timers

with an integrated graphics display 54

Figure 22. Graph of the frequency stability of two stopwatches 61

Figure 23. Factors that can change the quartz time base frequency 62

Figure 24. Stopwatch accuracy versus temperature 63

Figure Al. Sample calibration certificate, (page 1) 65

Figure Al. Sample calibration certificate, (page 2) 66
List ofTables

List of Tables

Table 1 - Metric prefixes (may be applied to all SI units) 2

Table 2 - Unit values, dimensionless values, and percentages 4

Table 3 - Type I and Type II stopwatch characteristics 9

Table 4 - Legal metrology requirements for field standard stopwatches and

commercial time devices 22

Table 5 - Comparison of calibration methods 25

Table 6 - Traceable audio time signals 27

Table 7 - The contribution of a 300 ms variation in reaction time to the

measurement uncertainty 32

Table 8 - Uncertainty analysis for direct comparison method (digital DUT)

using a land line 38

Table 9 - Uncertainty analysis for direct comparison method (digital DUT)

using a cell phone 39

Table 10 - Uncertainty analysis for direct comparison method (analog DUT)

using a land line 39

Table 1 1 - Uncertainty analysis for totalize method 46

Table 12 - The effect of the length of the measurement time on stability

(based on 25 readings) 53

Table 1 3 - Uncertainty analysis of using a calibrated stopwatch to calibrate

another device 60

XI

Intr lion

Section 1 Introduction to Stopwatch and Timer Calibrations

This document is a recommended practice guide for stopwatch and timer

calibrations. It discusses the types of stopwatches and timers that require

calibration, their specifications and tolerances, and the methods used to calibrate

them. It also discusses measurement uncertainties and the process of establishing

measurement traceability back to national and international standards.

This guide is intended to serve as a reference for the metrologist or calibration

technician. It provides a complete technical discussion of stopwatch and timer

calibrations by presenting practical, real world examples ofhow these calibrations

are performed.

There are nine sections in this guide. Section 1 provides an overview, and serves

as a good introduction if you are new to the field of metrology or to time and

frequency measurements. Section 2 describes the types of timing devices that

require calibration. Section 3 discusses specifications and tolerances. Sections 4

through 7 discuss calibration methods and their associated uncertainties. Section

8 provides additional information to help determine if the selected calibration

method can meet the required level of uncertainty, and Section 9 discusses other

topics related to measurement uncertainty. A sample calibration report and

references are provided in the appendices.

1.A. The Units of Time Interval and Frequency

Stopwatches and timers are instruments used to measure time interval, which is defined as the elapsed time between two events. One common example of a time

interval is a person's age, which is simply the elapsed time since the person's

birth. Unlike a conventional clock that displays time-of-day as hours, minutes,

and seconds from an absolute epoch or starting point (such as the beginning of the

day or year), a stopwatch or timer simply measures and displays the time interval

from an arbitrary starting point that begins at the instant when the stopwatch is started. The standard unit oftime interval is the second (s) [1]. Seconds can be accumulated

to form longer time intervals, such as minutes, hours, and days; or they can be

sliced into fractions of a second such as milliseconds (10~3 s, abbreviated as ms) or microseconds (10~6 s, abbreviated as us). Table 1 lists these and other

i
Stopwatch and Timer Calibrations

prefixes that can be used with seconds, as well as the multiples/submultiples and

symbols used to represent them. The second is one of the seven base units in the

International System of Units (SI). Other units (most notably the meter and the

volt) have definitions that depend upon the definition of the second.

Table 1 - Metric prefixes

(may be applied to all SI units)

lVhiltinlps and Siibmiiltinlps Prpfix jy niuvji

1 000 000 000 000= 10 12 tera T

1 000 000 000= 109 giga G

1 000 000= 106 mega M

1 000= 103 kilo k

1 = 10°

0.001 = io-3 milli m

0.000 001 = io-6 micro u

0.000 000 001 = io-9 nano n

0.000 000 000 001 = IO 12 pico P

0.000 000 000 000 001 = IO 15 femto f

The SI defines the second based on a property of the cesium atom, and for this reason cesium oscillators are regarded as primary standards for both time interval

and frequency. A second is defined as the time interval required for 9 192 63 1 770

transitions between two energy states ofthe cesium atom to take place. The atomic

definition ofthe second, together with current technology, allows it to be measured

with much smaller uncertainties than any other SI unit. In fact, the National

Institute of Standards and Technology (NIST) can currently measure a second

with an uncertainty of less than 1 part in 10 15

, or more than 1 billion (109) times

smaller than the uncertainties required for the calibrations described in this guide!

The resolution of a stopwatch or timer represents the smallest time interval

that the device can display. Resolution is related to the number of digits on the

device's display for a digital stopwatch, or the smallest increment or graduation on the face of an analog stopwatch. For example, if a stopwatch display shows

two digits to the right of the decimal point, it has a resolution of 0.01 s (10 ms, or 1/100 of a second). This means, for example, that it can display a value of 42.12
Introck : : m

s or 42.13 s. but that it lacks the resolution to display 42.123 s. Resolution of 10

ms is common for digital stopwatches, but some devices have 1 ms resolution

(0.001 s). or even smaller. For analog stopwatches, a common resolution is 1 5 of a second, or 0.2 s. Although stopwatches and timers measure time interval, they do so by using

el frequency source. Frequency is the rate of a repetitive event, defined as the

number of events or cycles per second. The standard unit of frequency (f) is the

hertz (Hz), which is not a base unit of the SI. but one of the 21 derived SI units.

One hertz equals one event per second, one kilohertz (kHz) equals 103 events

per second, one megahertz (MHz) equals 106 events per second, and so on. The

period (I) is the reciprocal of the frequency. T= If. For example, a 1 MHz sine

wave would produce 106 cycles per second, or one cycle every microsecond.

A time base oscillator (sometimes called a clock or reference oscillator) produces

the frequency signals used by the stopwatch or timer to measure time intervals. In today's devices, the time base oscillator is nearly always a quartz crystal oscillator.

However, older devices used either a mechanical oscillator, the alternating

current (AC) line frequency (60 Hz in the United States), or an oscillator based on a tuned electronic circuit as their frequency source. The time base oscillator serves as the reference for all of the time and frequency functions performed by

the device. The most common frequency used by quartz time base oscillators is 32 768 (= 2

15) Hz. In this case, when the stopwatch or timer has counted 32 768

oscillations from its time base oscillator, it then records that 1 s has elapsed. If you want to think of this time base as a clock, it "ticks" 32 768 times per second,

or once every 30.518 us. Throughout this guide, time interval is always presented in units of seconds (or

fractions of a second), and frequency is presented in units of hertz (or multiples

of a hertz). However, measurement uncertainties are presented as dimensionless

values that represent a fractional percentage error. Since these dimensionless

values are usually very small percentages, they are often expressed in scientific

notation. For example, if a stopwatch has a measurement uncertainly" of 1 s over a time interval of 10 000 s. the uncertainty is expressed as either a percentage (0.01

%) or as a dimensionless value ( 1 x 10"). Table 2 provides more examples.

3
Stopwatch and Timer Calibrations

Table 2 - Unit values, dimensionless values, and percentages.

Time

uncertainty

Length

of test Dimensionlessuncertainty

(literal)

Dimensionless

uncertainty

(scientific

notation)

Percentage

uncertainty

(%)

1 s 1 minute 1 part per 60 1.67 x 10- 1.67

1 s 1 hour 1 part per 3600 2.78 x 10-4 0.027 8

1 s 1 day 1 part per 86 400 1.16 x lO"5 0.001 16

1 s 100 s 1 part per hundred 1 x lO"2

1

1 s 1000 s 1 part per thousand 1 x lO 3 0.1

1 s 10 000 s 1 part per 1 thousand 1 x 10-4 0.01

1 s 100 000 s 1 part per 100 thousand 1 x lO 5 0.001

1 ms 100 s 1 part per 100 thousand 1 x io-5 0.001

1 ms 1000 s 1 part per million (1 ppm) 1 x IO'6 0.000 1

1 ms 10 000 s 1 part per 10 million 1 x 10" 0.000 01

1 ms 100 000 s 1 part per 100 million 1 x IO'

8 0.000 001

1.B. A Brief Overview of Calibrations

Like all calibrations, stopwatch and timer calibrations are simply comparisons

between the device under test (DUT) and a measurement reference, or standard.

When a stopwatch or timer is calibrated, either a time interval standard or a frequency standard is used as the measurement reference. If a time interval

standard is used, it is compared to the DUT's display. If a frequency standard is used, it is compared to the DUT's time base oscillator. Both types of calibrations are described in detail later in this guide.

Most of the calibrations described in this guide are laboratory calibrations,

as opposed to field calibrations. To understand what this means, consider an example where a stopwatch is calibrated in the laboratory against a standard,

and a calibration certificate and/or sticker are issued to the customer. That

same stopwatch or timer can then be thought of as a field standard, a working

standard, or a transfer standard, and used as the measurement reference during

a field calibration. In other words, it can be brought outside the laboratory and

used to calibrate another timing device, such as a parking meter. The same basic

4
Intr. m

principles that apply to laboratory calibrations apply to field calibrations,

although laboratory calibrations generally take longer and are made much

more carefully because the required measurement uncertainties are smaller.

Devices that are field calibrated are generally not used as a measurement

reference for performing other calibrations. Instead, they are working

instruments used for scientific, business, or legal purposes. Therefore, their

calibration can be thought of as a periodic test or inspection that ensures

that these devices are working properly and meeting their specifications.

Common sense dictates that the measurement reference for any calibration

(either the laboratory reference or the field standard) must always

outperform the devices it needs to test. A parking meter, for example,

might have an acceptable uncertainty of 1 % when timing a 5 minute

interval (±3 s). A field standard stopwatch used to test a parking meter

should be certified to an uncertainty small enough so that it contributes no

significant uncertainty to the parking meter calibration. In other words, we

need to be able to trust our reference so that we can trust our measurement

of the DUT.

When a laboratory calibration is completed, the metrologist has determined

the offset 1 of the DUT with respect to the reference. This offset can be

stated as a percentage or in units of time interval or frequency (or both) on the calibration certificate, and should be quantified with a statement

of measurement uncertainty. Field calibrations are generally "pass/fail"

calibrations. This means that the device is tested to see whether it meets

its intended or legal metrology requirements, and it either passes or fails. If it fails, it is removed from service until it can be adjusted, repaired, or

replaced.

1.C. Traceability and Coordinated Universal Time (UTC)

As previously discussed, when a device is calibrated by comparing it to a measurement reference, the reference must be more accurate (have lower

compared to a more accurate standard. That more accurate standard

1 The term 'offset' is commonly used in the discipline of frequency

and time measurement and will be used throughout this text. In terms of

the ISO Guide to the Expression of Uncertainty in Measurement [2], the

offset would be considered the measurement result. 5
Stopwatch and Timer Calibrations

needs to be periodically compared to an even more accurate standard, and so on,

until eventually a comparison is made against a national or international standard

that represents the best physical realization ofthe SI unit that is being measured (in

this case, the SI second). This measurement traceability hierarchy is sometimes

illustrated with a pyramid as shown in Figure 1 . The series of comparisons back

to the SI unit is called the traceability chain. Metrological traceability is defined,

by international agreement, as: Theproperty ofa measurement result whereby the result can be related to a reference through a documented

unbroken chain of calibrations, each contributing to the measurement uncertainty. [3] The definition of metrological traceability implies that unless the measured value

is accompanied by a stated measurement uncertainty, the traceability chain is broken. It is the responsibility of the calibration laboratory to determine and

report the uncertainty of its measurements to its customers so that metrological

traceability is maintained [4].

Typical Calibration Hierarchy

Figure 1. The calibration and traceability hierarchy.

The International Bureau of Weights and Measures (BIPM) located near Paris,

France, is responsible for ensuring the worldwide uniformity of measurements
Introduction

and their traceability to the SI. The BIPM collects and averages time interval and

frequency data from more than 60 laboratories around the world and creates a time scale called Coordinated Universal Time (UTC) that realizes the SI second

as closely as possible. Thus, UTC serves as the international standard for both

time interval and frequency. However, the BIPM does not produce a physical

representation of the second; it simply calculates a weighted average that is published weeks after the actual measurements were made. This document, known

as the BIPM Circular T, shows the time offset of each contributing laboratory

with associated uncertainties, and can be downloaded from the BIPM web site (www.bipm.org). The laboratories that provide data to the BIPM maintain the

oscillators and clocks that produce the actual signals that are used as measurement

references. Most of these laboratories are national metrology institutes (NMIs)

that serve as the caretakers of the national measurement references for their

respective countries. Thus, to establish traceability to the SI for time interval and

frequency calibrations, the traceability chain for a measurement must link back

to signals that originate from an NMI or a national timekeeping laboratory. The

NMI that is chosen as a reference must contribute to the derivation of UTC by

sending its measurement data (with associated uncertainties) to the BIPM.

NIST is the ultimate reference point for most measurements made in the United

States, and as such, submits time and frequency data to the BIPM. NIST provides

it own real-time representation ofUTC, designated UTC(NIST), that is distributed

to the public using a variety of radio, telephone, and Internet signals. These

signals are described in more detail in Section 5, and can serve as references for

measurements that are traceable back to the SI. The traceability chain is easy to visualize ifyou think ofit as a series ofcalibrations.

Every link in the chain is a calibration; comparing a device to a higher standard,

until eventually a comparison is made to the SI unit. Every calibration has some

measurement uncertainty. At the top of the chain, the measurement uncertainties

are so tiny they are insignificant to those of us who calibrate stopwatches and

timers. For example, the difference between the best possible estimate of

the SI second and UTC(NIST) is measured in parts in 10 16

. This represents a time offset of less than 0.1 ns (10~ 10 s) over the course of a day. As we move

down the traceability chain to the actual calibration of a stopwatch or timer, the

| uncertainties become larger and larger. For example, if the calibration laboratory uses an audio signal from NIST radio station WWV (Section 5) to calibrate its standard, the uncertainty of the received tones might be 1 ms. This uncertainty

7
Stopwatch and Timer Calibrations

is still small enough for the WWV tones to be used as a stopwatch calibration

reference, because the uncertainty introduced by an operator starting and stopping

the watch (human reaction time) is much larger, typically tens or even hundreds

of milliseconds. In summary, as long as each link of the chain and its uncertainty

are known, traceability to the SI can be established.

Stopwatch and timer calibrations are among the least demanding of all time

and frequency measurements. Relatively speaking, the instruments requiring

calibration are low cost, and the acceptable measurement uncertainties can be

quite large. Even so, for legal, technical, and practical reasons it is very important

to establish traceability to the SI for these calibrations. If a valid traceability

chain to the SI is established, it ensures that the working device was properly

calibrated, and, if correctly used, will produce valid results.

8
Description ofTin

Section 2

Description of Timing Devices that Require Calibration

This section describes the various types ofstopwatches (Section 2. A. Stopwatches)

and timers (Section 2.B. Timers) that are calibrated in the laboratory. These

types of stopwatches and timers are often used as transfer standards to perform

field calibrations of the commercial timing devices described in Section 2.C.

2.A. Stopwatches

Stopwatches can be classified into two categories, Type I and Type II [5]. Type

I stopwatches have a digital design employing quartz oscillators and electronic

circuitry to measure time intervals (Figure 2). Type II stopwatches have an

analog design and use mechanical mechanisms to measure time intervals (Figure

3). The key elements of Type I and Type II stopwatches are summarized in

Table 3.

Table 3 - Type I and Type II stopwatch characteristics.

Description Type I Stopwatch

(digital)

Type II Stopwatch

(analog)

Operating principle

Time measured by division

of time base oscillator

Time measured by

mechanical movement

Time base • Quartz oscillator

• Mechanical

mainspring

• Synchronous

motor, electrically

driven

Case

• Corrosion resistant metal

• Impact resistant plastic

Crystal

• Protects display

• Allows for proper

viewing

• May be tinted • May employ

magnification

• Protects dial/hands

• Allows for proper

viewing

• Must be clear and

untinted

Minimum time interval • 48 hours without

replacement of

battery

• 3 hours without

rewinding

9
Stopwatch and Timer Calibrations

Table 3 - Continued

Description

Type II Stopwatch

(analog)

Type II Stopwatch

(analog)

Start and stop

• Single control to start/stop

• Audible signal of

start/stop

Reset

• Must reset stopwatc i to zero

Split time (if equipped)

• Must indicate

whether display

mode is regular or

split time.

Force to operate controls

• Must not exceed 1 .8 N (0.40 lbf)

Dial and hands

• Face must be white

• Graduations must

be black or red

• Hands must be

black or red

Required markings

• Unique, nondetachable serial number

• Manufacturer's name or trademark

• Model number (Type I only)

Digital display

• Provide delimiting

character for hours, minutes,

seconds (usually

colon)

Minimum increment • <0.2s

Minimum elapsed time

at rollover

• 1 hour • 30 minutes

Physical orientation

• Stopwatch meets to physical orientation erance regardless of

10
Description ofTiming Devices

Figure 2. Type I digital stopwatch. Figure 3. Type II mechanical

stopwatch.

2.A.I. Basic Theory of Operation

Every stopwatch is composed of four elements: a power source, a time base, a counter, and an indicator or display. The design and construction of each

component depends upon the type of stopwatch.

2.A.l.a. Digital (Type I) Stopwatches

The power source of a Type I stopwatch is usually a silver-oxide or alkaline

battery that powers the oscillator and the counting and display circuitry. The

time base is a quartz crystal oscillator that usually has a nominal frequency of

32 768 Hz, the same frequency used by nearly all quartz wristwatches. The

32 768 Hz frequency was originally chosen because it can be converted to a 1 pulse per second signal using a simple 15 stage divide-by-two circuit. It also

has the benefit of consuming less battery power than higher frequency crystals.

Figure 4 shows the inside of a typical digital device, with the printed circuit

board, quartz crystal oscillator, and battery visible. The counter circuit consists

of digital dividers that count the time base oscillations for the period that is initiated by the start/stop buttons [6, 7]. The display typically has seven or eight

digits.

11
Stopwatch and Timer Calibrations

Figure 4. Interior ofdigital (Type I) stopwatch.

2.A.l.b. Mechanical (Type II) Stopwatches

In a traditional mechanical stopwatch, the power source is a helical coil spring,

which stores energy from the winding of the spring. The time base is usually

a balance wheel that functions as a torsion pendulum. The rate at which the

spring unwinds is governed by the balance wheel, which is designed to provide a consistent period of oscillation relatively independent of factors such as friction,

operating temperature, and orientation. In most mechanical stopwatches, the

balance wheel is designed to oscillate at 2.5 periods per second, which produces

5 "ticks" or beats per second. The balance wheel is connected to an escapement

that meters the unwinding of the coil spring and provides impulses that keep the

balance wheel moving. It is this metered unwinding of the coil spring that drives

the counter indicator. In this type of device, the counter is composed of a gear

train that divides the speed of rotation of the escapement wheel to the appropriate

revolution speed for the second, minute, and hour hands. The time interval from

the counter is displayed either on a face across which the second and minutes

hands sweep, or on a series of numbered drums or discs that indicate the elapsed

time (Figure 5) [6].

12
Description ofTiming Devices

Figure 5. Inner workings ofa mechanical (Type II) stopwatch or timer.

13
Stopwatch and Timer Calibrations

Another form of the Type II stopwatch uses a timer driven by a synchronous

motor that also drives the hands or numbered wheels. For this device, the power

source is the 60 Hz AC line voltage. The power source drives an electric motor

within the timing device. The time base is derived from the controlled regulation

of the 60 Hz frequency of AC electric power as supplied by the power utility

company. The frequency limits for distributed AC power in the United States are 59.98 Hz to 60.02 Hz, or 60 Hz ± 0.033 % of the nominal value. However, the

actual frequency is controlled much more accurately than this, in order to advance

or retard the grid frequency and synchronize the power distribution system [8]. The counter and display circuitry are similar to those used in the mechanical

stopwatches previously discussed.

2.B. Timers

Timers, unlike stopwatches, count down from a preset time period instead of

counting up from zero. They can be small, battery-operated devices that are used

to signal when a certain time period has elapsed, or they can be larger devices

that plug into a wall outlet and control other items (Figure 6). A parking meter

is an example of a countdown timer. Inserting a coin starts the internal timer

counting down from an initial preset point. When the preset time has elapsed,

the EXPIRED flag is raised.

Figure 6. A collection oftimers.

14
Description of Tir=

. ; : is

One type of timer used extensively in industry is the process control timer. As

their name implies, process control timers measure or control the duration of a

specific process. For example, when a product is made, it may need to be heat

treated for a specific length of time. In an automated manufacturing system, the

process control timer determines the length of time that the item is heated. In some applications, such as integrated circuit manufacturing, the timing process can be critical for proper operation.

Process control timers are also used in many different types of laboratory

environments. Calibration laboratories use timers to calibrate devices such as radiation detectors, by regulating the amount of time that the device is exposed to the radiation source. The uncertainty in the time of exposure directly influences

the overall measurement uncertainty assigned to the detector calibration.

Timers are also used in the medical field. For example, medical laboratories use

process control timers when specimen cultures are grown. Hospitals use timers to regulate the amount of medication given to patients intravenously.

2.C. Commercial Timing Devices

Many types of timing devices are used every day in commercial applications.

Parking meters, automatic car wash facilities, taxicab meters, and commercial

parking lots are examples of entities that either charge a certain amount for a specified period, or provide a certain period of service for a specified amount of

money.

The calibration requirements and allowable tolerances for these devices are usually determined on a state-by-state basis by state law, or locally by city or municipality ordinances. The allowable uncertainties are often 1 % or larger.

Generic guidance is provided in Section 3.

15

Specifications an ices

Section 3

Specifications and Tolerances

Whether we are developing a calibration procedure, or performing an uncertainty

analysis for a given calibration process, we need to be able to understand and

interpret the specifications and tolerances for both the DUT and the test equipment

associated with the calibration. This section reviews both manufacturer's

specifications and legal metrology requirements for stopwatches and timing

devices.

3.A. Interpreting Manufacturer's Specifications

When reviewing manufacturer's specification sheets, it quickly becomes obvious

that not all instrument manufacturers specify their products in the same way. This

section defines and describes the most common types of specifications quoted for

stopwatches and timing devices.

3.A.I. Absolute Accuracy Specifications

The absolute accuracy

2 of an instrument is the maximum allowable offset from

nominal. Absolute accuracy is defined in either the same units, or a fractional

unit quantity of the measurement function for an instrument. For example, the

absolute accuracy of a ruler might be specified as ±1 mm for a scale from to 15 cm.

In the case of timing devices, it isn't useful to provide an absolute accuracy

specification by itself. This is because a device's time offset from nominal will

increase as a function of the time interval. If the timing device were able to measure an infinite time interval, the offset (or difference in time from nominal)

of the device would also become infinitely large. Because of this, when timing

devices are specified with an absolute accuracy number, it is also accompanied by

a time interval for which this specification is valid. As an example, the absolute

accuracy specification for the stopwatch shown in Figure 7 is 5 s per day.

2 In this section, the term "accuracy" is used in order to allow the reader to correlate the concepts

of this chapter directly with published manufacturer specifications. In terms of the ISO Guide

to the Expression of Uncertainty in Measurement [2], the quantities associated with accuracy are understood to be uncertainties. 17
Stopwatch and Timer Calibrations

Handsome stopwatch with large

display provides timing to

1 /1 00th of a second over a range

of 9 hours 59 minutes and 59.99

seconds.

Accurate to ± 5 s/day

Built-in memory recalls up to ten

laps.

Clock function (1 2 or 24 hrs)

features a programmable alarm

with an hourly chime plus builtin calendar displays day, month

and date.

Countdown timer function

features input ranges from one

minute to 9 hours, 59 minutes.

Dimensions/Weight: 2.5 x 3.2 x.8: (63x81 x 20 mm): 2.8 oz.

Water resistant housing is com

plete with lithium battery

Figure 7. Sample manufacturer s specifications for a digital stopwatch

(Example 1).

If the stopwatch in Figure 7 were used to measure a time interval longer than one

day, we could determine a new absolute accuracy figure by simply multiplying

the original specification by the longer time interval. For example 5 s per day

becomes 10 s per two days, 35 s per week, and so on. While it is usually acceptable to multiply the absolute accuracy specification by

longer time intervals than the period listed in the specifications, caution must

18
Specifications and Tolerances

be used when dividing the absolute accuracy specification for shorter time

intervals than the period listed in the specifications. This is because for shorter

measurements periods, a new source of uncertainty, the resolution uncertainty of

the instrument, becomes an important consideration. For example, the absolute

accuracy of the example stopwatch (Figure 7) during a time interval of 30 s is determined as

s x 30 s = —x—^-day = 0.0017s

day day 2880

We can see from the specifications in Figure 7 that the stopwatch has a resolution

of 1/100 of a second, or 0.01 s. In this case, computing the absolute accuracy

specification for a 30 s interval results in a number (0.00 1 7 s) that is about six times

smaller than the smallest value the stopwatch can display. Most manufacturers of

timing devices do not consider the resolution ofthe product in their specifications,

but we will include resolution uncertainty in our examples.

3.A.2 Relative Accuracy Specifications

While absolute accuracy specifications are helpful, sometimes it is more

desirable to specify accuracy relative to the measured time interval. This makes

its significance easier to understand. For this purpose, we define a quantity called

relative accuracy:„ . . A Absolute Accuracy

Relative Accuracy

Measured Time Interval

Using the previous example from Figure 7, the stopwatch has an absolute accuracy

specification of 5 s per day, so the relative accuracy is:

Relative Accuracy = = ———= 0.000 058 = 0.0058 % = 5.8 x 10"5

. lday 86 400 s

Note that because the absolute accuracy specification and the measured time

interval are both expressed in seconds, the unit cancels out; leaving a dimensionless

number that can be expressed either as a percentage or in scientific notation.

Relative accuracy specifications can also be converted back to absolute time units

if necessary. For example, Figure 8 shows the manufacturer's specifications for

19
Stopwatch and Timer Calibrations

a stopwatch that is accurate to 0.0003 % (although not stated, it is assumed that

this percentage has been stated as a percent of reading or relative accuracy).

To compute the time accuracy for a 24 h measurement, we simply multiply the

relative accuracy by the measurement period:

0.0003 % x 24 h = 0.000 072 h = 0.2592 s This computation shows that this stopwatch is capable of measuring a 24-hour

interval with an accuracy of about 0.26 s. However, it is again important to note that when measuring small time intervals, the resolution uncertainty of the

stopwatch must be considered. For example, if the stopwatch in Figure 8 is used

to measure a time interval of 5 s, the computed accuracy is much smaller than the

resolution of the stopwatch:

0.0003 %x5s = 0.000 015 s

Timer: 9 hours, 59 minutes, 59 seconds,

99 hundredths.

Stopwatch: Single-action timing: timein/time-out; continuous timing; cumulative split, interval split and eight memories. Triple display shows cumulative

splits, interval splits and running time

simultaneously.

Features: Captures and stores up to eight separate times. After timed event is complete, stopwatch displays information in its memory. Counter box show

number of split times taken. Solid-state

design with an accuracy of 0.0003 %.

Durable, water-resistant construction

makes stopwatch suitable for field use

(operates in temperature from 1 ° to 59° C

[33° to 1 38° F]). With triple line LDC: top

two lines are each 1/8 in. high (3.2 mm);

third line is Vfc in. high (6 mm).

Figure 8. Sample specifications for a digital stopwatch (Example 2).

20
Specifications and Tolerances <

3.A.3. Typical Performance

During the NIST centennial celebration of 200 1

, an exhibit at the NIST laboratories

in Boulder, Colorado, allowed visitors to measure the time base accuracy of their

quartz wristwatches. Over 300 wristwatches were tested. Nearly all quartz

wristwatches contain a 32 768 Hz time base oscillator, the same technology

employed by a Type I digital stopwatch. The results of these measurements,

showing the loss or gain in seconds per day for the watches, are summarized in

Figure 9, and give some idea of the typical performance of a quartz stopwatch

or timer. Roughly 70 % of the watches were able to keep time to within 1 s per

day or better, a relative accuracy of approximately 0.001 % (1 x 10~5 ). About 12

% had a relative accuracy larger than 5 s per day, or larger than 0.005 %. It is interesting to note that nearly all of the watches in this study gained time, rather

than lost time; and were presumably designed that way to help prevent people

from being late. This characteristic will not necessarily apply to stopwatches and

timers.

Quartz Wristwatch Performance

40

35

3D

25-

20-"' O

15

0* 10

d> 5

EL

«5

^

L

-1 *0,5 03 1 2

Seconds Per Day

5 More

Figure 9. Typical performance ofquartz wristwatches using 32 768 Hz time

base oscillators.

21
Stopwatch and Timer Calibrations

3.B. Tolerances Required for Legal Metrology

General specifications for field standard stopwatches and commercial timing

devices are provided in Section 5 . 5 5 ofNISTHandbook 44 [9] , and are summarized

in Table 4. NIST Handbook 44 is recognized by nearly all 50 states as the legal

basis for regulating commercial weighing and measuring devices. However,

some state governments and some regulatory agencies have other specifications

that need to be satisfied for a given calibration. Therefore, be sure to check and

understand the required tolerances and regulations for the types of calibration

that a calibration laboratory is asked to perform [10].

Table 4 - Legal metrology requirements for field standard stopwatches and

commercial time devices.

Commercial

timing

device

Interval Measured

Overregistration Underregistration

Requirement Uncertainty Requirement Uncertainty

Parking meter

30 minutes

or less None NA

1 s per minute, but

not less than 2 minutes

11.7% to 16.7%

Over 30

minutes

up to and

including 1 hour

None NA

5 minutes

plus 4 s per minute over 30 minutes

Over 1 hour

None NA

7 minutes

plus 2 minutes per hour over 1 hour

Time clocks and time

recorders

3 s per hour, not to exceed 1 minute per day

0.07 %

to 0.08 %

3 s per hour, not to exceed

1 minute per day

0.07 % to 0.08 %

Taximeters 3 s per minute 5 %

9 s per minute on the initial interval, and

6 s per minute on subsequent

intervals

10% to 15%

Other timing

devices

5 s for any

interval of 1 minute or more NA 6 s per minute 10%

22
Specifications an< . trances < The terms overregistration and underregistration are used when specifying the

accuracy ofcommercial timing devices. The terms are used to describe conditions

where the measurement device does not display the actual quantity. In timing

devices, underregistration is the greatest concern, because an underregistration

error occurs when the timing device indicates that the selected time interval has

elapsed before it actually has. An example of underregistration would be paying

for 10 minutes on a parking meter, and then having the meter indicate that time

had expired when only 9 minutes and 45 s had actually elapsed.

NIST Handbook 44 [9] specifies that instruments that are required to calibrate

timing devices must be accurate to within 15s per 24 h period (approximately

0.017 %). If stopwatches are used as the calibration standard, this becomes

the minimum allowable tolerance for the stopwatch. Another reference, NIST

Handbook 105-5 [5] states that the tolerance for instruments used to calibrate

timing devices must be three times smaller than the smallest tolerance ofthe device

being calibrated. Handbook 105-5 also provides a nearly identical specification

for stopwatches, stating that the tolerance for stopwatches is ±0.02 % of the time

interval tested (approximately 2 s in 3 hours), rounded to the nearest 0.1 s. The uncertainties listed above were meant to be achievable with Type II (mechanical) devices, but Type I devices are normally capable of much lower

uncertainties. As a result, organizations and jurisdictions that rely exclusively on digital stopwatches (Type 1) might require that devices be calibrated to a tolerance of 0.01 %, or even 0.005 %. For example, the State of Pennsylvania

code [11] uses the same specifications as NIST Handbook 44 for mechanical

stopwatches (15 s per 24 hours), but states that a quartz stopwatch shall comply

with the following more rigorous standards:

(i) The common crystalfrequency shall be 32 768 Hz

with a measuredfrequency within plus or minus 3 Hz, or approximately 0. 01 % ofthe standardfrequency.

(ii) The stopwatch shall be accurate to the equivalent

ofplus or minus 9 seconds per 24-hour period.

I

1

23
atch and Timer Calibrations

3.B.I. Time Clocks and Time Recorders

The specification for both overregistration and underregistration is 3 s per hour,

not to exceed 1 minute per day.

3.B.2. Parking Meters

The specifications for parking meters have no tolerance for overregistration.

Parking meters with a time capacity of 30 minutes or less are specified to have a maximum underregistration error of 1 s per minute, but not to exceed 2 minutes

over the 30 minute period. For parking meters with a capacity of greater than 30

minutes, but less than 1 hour, the tolerance for underregistration is 5 minutes, plus

4 s per minute for every minute between 30 minutes and 60 minutes. Parking

meters that indicate over 1 hour have an underregistration tolerance of 7 minutes

plus 2 minutes per hour for time intervals greater than 1 hour.

3.B.3. Other Timing Devices

All other timing devices have an overregistration tolerance of 5 s for any time

interval of 1 minute or more and an underregistration tolerance of 6 s per indicated

minute. If the instrument is a digital indicating device, the tolerance is expanded

by one half of the least significant digit.

24
Met

Section 4

Introduction to Calibration Methods

There are three generally accepted methods for calibrating a stopwatch or timer:

the direct comparison method, the totalize method, and the time base method.

The first two methods consist of time interval measurements that compare the

time interval display of the DUT to a traceable time interval reference. In the case of the direct comparison method, the time interval reference is normally a

signal broadcast by an NMI, usually in the form of audio tones. In the case of the

totalize method, the time interval reference is generated in the laboratory using

a synthesized signal generator, a universal counter, and a traceable frequency

standard. The third method, the time base method, is a frequency measurement. It compares the frequency of the DUT's time base oscillator to a traceable frequency

standard [12]. The properties of the three methods are briefly summarized in

Table 5, and the following three sections are devoted to the three methods. Each

section explains how to perform a calibration using each method, and how to estimate the measurement uncertainties.

Table 5 - Comparison of calibration methods. ^^^^—^ftlethod

Properties —

Direct comparison Totalize

Time base

measurement

Equipment Requirements Best Better Better Speed Good Better Best

Uncertainty Good Good Best

Applicability Good Best Better The methods used to estimate the uncertainty of measurement are described in

the ISO Guide to the Expression of Uncertainty in Measurement (GUM) [2].

This guide does not attempt to summarize the GUM, but does strive to produce

estimates ofuncertainty that are consistent with the GUM. The resulting expanded

uncertainty of measurement is presented with a coverage factor that represents an

approximate 95 % level of confidence.

25

The Direct Comparison Method

Section 5

The Direct Comparison Method

The direct comparison method is the most common method used to calibrate

stopwatches and timers. It requires a minimal amount of equipment, but has

larger measurement uncertainties than the other methods. This section describes

the references used for this type of calibration and the calibration procedure.

5.A. References for the Direct Comparison Method

The direct comparison method requires a traceable time-interval reference. This

reference is usually an audio time signal, but in some cases a traceable time display can be used. The audio time signals are usually obtained with a shortwave radio

or a telephone. Since time interval (and not absolute time) is being measured,

the fixed signal delay from the source to the user is not important as long as

it remains relatively constant during the calibration process. A list of traceable

audio time sources is provided in Table 6.

Table 6 - Traceable audio time signals.

National Radio

Metrology T A . Telephone call Broadcast

t j • . , Location , Institute (NMI) numbers letters frequencies

National Institute _ _ 1t . *-cu a a Fort Collins, _ in of Standards m^ /lftft7111 , 2.5,5,10,

a^ u 1 Colorado, (303)499-7111 * WWV 1C OAAyrTT and Technology TT . A ,

' 15, 20 MHz

(NIST)

United States

National Institute

j^auaj of Standards .'. /oao^k /nn* umrVU 2.5,5,10,

JrT, , , Hawaii, (808) 335-4363 * WWVH * c\lTT and Technology TT . , ' v 7 15 MHz

(NIST)

United States

United ,

. States Naval ^r^T* <202) 762" 1401 * Observatory

Umted

(202) 762- 1 069 * (USNO)

MatCS

27
Stopwatch and Timer Calibrations

United Colorado

States Naval

Observatory

Springs,

Colorado.

(719)567-6742 * (USNO) United States

• National

Research Council

(NRC)

Ottawa,

Ontario,

Canada

(613) 745-1576

(English language)

(613) 745-9426(§,

(French language)

3.33.7.850.

14.67 MHz

(442) 215-39-02 * (442)211-05-06 ! (442) 21 1-05-07 #

(442) 21 1-05-08 ##

Time

Centro Nacional

de Metrologia

(CENAM)

Queretaro.

Mexico

announcements

are in Spanish, a country code must

be dialed to access

these numbers

from the United

States, see www.

cenam.mx for more

information.

XEQK

(Mexico

City)

1.35 MHz

Korea Research

Institute of

Standards and

Science (KRISS)

Taedok,

Science

Town,

Republic of

Korea

HLA 5 MHz

National Time

Service Center

Lintong,

Shaanxi, BPM 2.5, 5, 10. 15 MHz

(NTSC) China

* Coordinated Universal Time (UTC)

@ Eastern Time

! Central Time

# Mountain Time

## Pacific Time

28
The Direct Com 3 3 son

Please note that local "time and temperature" telephone services are not traceable

references and should not be used. For traceable calibrations, use only sources

that originate from a national metrology institute, such as those listed in Table

6. The following sections briefly describe the various radio and telephone time

signals, and provide information about the types of clock displays that can and

cannot be used.

5.A.I. Audio Time Signals Obtained by Radio

The radio signals listed in Table 6 include a voice announcement of UTC and

audio ticks that indicated individual seconds. WWV, the most widely used station,

features a voice announcement of UTC occurring about 7.5 s before the start of

each minute. The beginning of the minute is indicated by a 1500 Hz tone that

lasts for 800 ms. Each second is indicated by a 1 kHz tone that lasts for 5 ms. The best way to use these broadcasts is to start and stop the stopwatch when the

beginning of the minute tone is heard.

Most of the stations listed in Table 6 are in the high-frequency (HF) radio

band (3 MHz to 30 MHz), and therefore require a shortwave radio receiver. A

typical general-purpose shortwave receiver provides continuous coverage of the

spectrum from about 150 kHz, which is below the commercial AM broadcast

band, to 30 MHz. These receivers allow the reception of the HF time stations on all available frequencies. The best shortwave receivers are designed to work

with large outdoor antennas, with quarter-wavelength or half-wavelength dipole

antennas often providing the best results. However, in the United States, adequate

reception of at least one station can usually be obtained with a portable receiver

with a whip antenna, such as the one shown in Figure 10. This type of receiver

typically costs a few hundred dollars or less. HF radio time stations normally broadcast on multiple frequencies because

some of the frequencies are not available at all times. In many cases, only one

frequency can be received, so the receiver might have to be tuned to several

different frequencies before finding a usable signal. In the case of WWV, 10

MHz and 15 MHz are probably the best choices for daytime reception, unless the

laboratory is within 1000 km of the Fort Collins, Colorado station, in which case

2.5 MHz might also suffice. Unless the receiver is near the station, the 5 MHz

signal will probably be the easiest to receive at night [13].
! 1 Timer Calibrations

Figure 10. Portable shortwave radio receiverfor reception ofaudio time

signals.

5.A.2. Audio Time Signals Obtained by Telephone

The telephone time signals for NIST radio stations WWV and WWVH are simulcasts of the radio broadcasts, and the time (UTC) is announced once per

minute. The length of the phone call is typically limited to 3 minutes. The

format of the other broadcasts varies. The USNO phone numbers broadcast UTC

at 5 s or 10 s intervals. The NRC phone number broadcasts Eastern Time at 10

s intervals, and CENAM offers separate phone numbers for UTC and the local

time zones of Mexico.

5.A.3. Time Displays

It might be tempting to use a time display from a radio controlled clock or from a web site synchronized to UTC as a reference for stopwatch or timer calibrations.

As a general rule, however, these displays are not acceptable for establishing

traceability. Nearly all clock displays are synchronized only periodically, and

between synchronizations rely on a free running local oscillator whose frequency

uncertainty is usually unknown. And of course, an unknown uncertainty during

any comparison breaks the traceability chain. For example, a low cost radio

controlled clock that receives a 60 kHz signal from NIST radio station WWVB

is usually synchronized only once per day. In between synchronizations, each

"tick" of the clock originates from a local quartz oscillator whose uncertainty

is unknown, and that probably is of similar or lesser quality than the oscillator

inside the device under test. The NIST web clock at (time.gov) presents similar

problems. It synchronizes to UTC(NIST) every 10 minutes if the web browser is left open. However, between synchronizations it keeps time using the computer's

clock, which is usually of poorer quality than a typical stopwatch, and whose

30
The Direct Comp< i ' n M

uncertainty is generally not known. In contrast, each "tick" of an audio broadcast

from WWV originates from NIST and is synchronized to UTC. Therefore, WWV

audio always keeps the traceability chain intact.

There are a few instances where a time display can be used to establish traceability.

One example would be a display updated each second by pulses from a Global

Positioning System (GPS) satellite receiver. In this case, if the traceable input

signal were not available, the display would stop updating. Therefore, if the

display is updating, then it is clear that each "tick" is originating from a traceable

source. However, nearly all GPS receivers have the capability to "coast" and

keep updating their display even when no satellite signals are being received. In order for a GPS display to be used as a reference, there must be an indicator on

the unit that shows whether the display is currently locked to the GPS signal, or

is in "coast" mode. If the receiver is in "coast" mode, it should not be used as a

calibration reference.

Another example ofa traceable time display would be a digital time signal obtained

from a telephone line, such as signals from the NIST Automated Computer Time

Service (ACTS), which is available by dialing (303) 494-4774 [13]. With an

analog modem and simple terminal software (configured for 9600 baud, 8 data

bits, 1 stop bit, and no parity), you can view time codes on a computer screen, and use these codes as a reference in the same way that you would use the audio

time announcements from WWV. However, the length of a single telephone call

is limited to 48 s. In theory, Internet time codes could be used in the same way,

but the transmission delays through the network can vary by many milliseconds

from second to second. For this reason, the currently available Internet signals

should not be used as measurement references.

5.B. Calibration Procedure for Direct Comparison Method

Near the top of the hour, dial the phone number (or listen to the radio broadcast)

of a traceable source of precise time. Start the stopwatch at the signal denoting

the hour, and write down the exact time. After a suitable time period (depending on the accuracy of the stopwatch), listen to the time signal again, and stop the

stopwatch at the sound of the tone, and write down the exact stopping time.

Subtract the start time from the stop time to get the time interval, and compare

this time interval to the time interval displayed by the stopwatch. The two time

intervals must agree to within the uncertainty specifications of the stopwatch

for a successful calibration. Otherwise, the stopwatch needs to be adjusted or

rejected.

31
Stopwatch and Timer Calibrations

5.B.I. Advantages of the Direct Comparison Method

This method is relatively easy to perform and, if a telephone is used, does not

require any test equipment or standards. It can be used to calibrate all types of

stopwatches and many types of timers, both electronic and mechanical.

5.B.2. Disadvantages of the Direct Comparison Method

The operator's start/stop reaction time is a significant part of the total uncertainty,

especially for short time intervals. Table 7 shows the contribution of a 300 ms

variation in human reaction time to the overall measurement uncertainty, for

measurement periods ranging from 1 s to 1 day.

Table 7 - The contribution of a 300 ms variation in reaction time to the measurement uncertainty.

Hours Minutes Seconds Uncertainty (%)

10 3

1 60 0.5

10 600 0.05 30 1800 0.01666

1 60 3600 0.00833

2 120 7200 0.00416

6 360 21 600 0.00138

12 720 43 200 0.00069

24 1440 86 400 0.00035

As Table 7 illustrates, the longer the time interval measured, the less impact the

operator's start/stop uncertainty has on the total uncertainty of the measurement.

Therefore, it is better to measure for as long as practical to reduce the uncertainty

introduced by the operator, and to meet the overall measurement requirement.

To get a better understanding of the numbers in Table 7, consider a typical

stopwatch calibration where the acceptable measurement uncertainty is 0.02 %

(2 x 10 4

). If the variation in human reaction time is known to be 300 ms for the

direct comparison method, a time interval of at least 1500 s is needed to reduce

32
The Direct Comparison Method 4

the uncertainty contributed by human reaction time to 0.02 %. However, if we

use a 1500 s interval, we could possibly be measuring the variation in human

reaction time, and nothing else. Therefore, we need to extend the time interval so

that human reaction time becomes an insignificant part of the measurement. For

example, NIST Handbook 105-5 [4] states that a stopwatch is considered to be

within tolerance if its time offset is 2 s or less in during a three hour calibration.

Three hours is a long enough time interval to exceed the 0.02 % requirement and

to ensure that the uncertainty contribution ofhuman reaction time is insignificant.

There is no hard and fast rule, the length of the calibration can vary according to each laboratory's procedures, but it must be long enough to meet the uncertainty

requirements for the device being tested. If your uncertainty requirement is 0.01 % or lower, the direct comparison method might not be practical.

5.C. Uncertainties of Direct Comparison Method

The Direct Comparison Method has three potentially significant sources of

uncertainty that must be considered: the uncertainty ofthe reference, the reaction

time of the calibration technician, and the resolution of the DUT.

5.C.I. Uncertainty of the Traceable Time Interval Reference

If the reference signal is one of the telephone services listed in Table 6, two

phone calls are usually made. The first call is made to obtain the signal to

start the stopwatch, and the second call is made to obtain the signal to stop the

stopwatch. If both calls are made to the same service and routed through the same phone circuit, the delay through the circuit should be nearly the same for

both calls. Of course, the delays will not be exactly the same, and the difference

between the two delays represents the uncertainty of the time interval reference. In most cases, this uncertainty will be insignificant for our purposes, a few

milliseconds or less. For example, callers in the continental United States using

ordinary land lines can expect signal delays of less than 30 ms when dialing

NIST at (303) 499-71 1 1, and these delays should be very repeatable from phone

call to phone call. Even in a theoretical case where the initial call had no delay,

and the final call had a 30 ms delay, the magnitude of the uncertainty would be

limited to 30 ms. However, if an ordinary land line is not used, the uncertainties associated with

telephone time signals must be assumed to be larger. For example, wireless

phone networks or voice over Internet protocol (VOIP) networks sometimes

introduce larger delays that are subject to more variation from phone call to phone call than ordinary land lines. If wireless or VOIP networks are used,

33
Stopwatch arid Timer Calibrations

however, it is reasonable to assume that the transmission delay does not exceed

150 ms, since the International Telecommunication Union (ITU) recommends

that delays be kept below this level to avoid the distortion of voice transmissions

[14]. Calls made from outside the continental United States might occasionally

be routed through a communications satellite, introducing delays of about 250

ms. Although the use of satellites is now rare, if the first call went through a

satellite, and the second call didn't (or vice versa), a significant uncertainty would

be introduced. Therefore, common sense tells us that a laboratory in Illinois (for

example) shouldn't start a calibration by calling the NIST service in Colorado,

and then stop the calibration by calling the NIST service in Hawaii. Based on

this discussion, it is recommended that an uncertainty of 150 ms be assigned

if wireless or VOIP networks are used, or 250 ms if calls are routed through a

satellite. During a single phone call, the uncertainty of the time interval reference is essentially equal to the stability of a telephone line (the variations in the delay)

during the call. Phone lines are surprisingly stable. The ITU recommendations

for timing stability within the telephone system call for stabilities of much less

than 0. 1 ms for the North American Tl system [15]. A NIST study involving the

Automated Computer Time Service (ACTS), a service that sends a digital time

code over telephone lines, showed phone line stability at an averaging time of 1 s to be better than 0.1 ms over both a local phone network and a long distance

network between Boulder, Colorado and WWVH in Kauai, Hawaii [16]. While it is not possible to guarantee this stability during all phone calls, it is reasonable to assume that the stability should be much less than 1 ms during typical calls, which

are limited to about 3 minutes in length. Thus, the uncertainties contributed by

phone line instabilities are so small that they can be ignored for our purposes.

If the radio signals listed in Table 6 are used as a reference instead of a telephone

signal, the arrival time ofthe signal will vary slightly from second to second as the

length ofthe radio signal path changes, but not enough to influence the results of a stopwatch or timer calibration. Shortwave signals that travel over a long distance

rely on skywave propagation, which means that they bounce off the ionosphere

and back to Earth. A trip from Earth to the ionosphere is often called a hop, and

a hop might add a few tenths of a millisecond, or in an extreme case, even a full millisecond to the path delay. Normally, propagation conditions will remain the

same during the course of a calibration, and the variation in the radio signal will

be negligible, often less than 0.01 ms. Even if an extra hop is added into the radio

path during the calibration; for example if a one hop path becomes a two hop

34
The Direct Comparison Method

path, the received uncertainty of the radio signal will still not exceed 1 ms [13].

If a traceable time display is used instead of a radio signal or telephone signal,

it can generally be assumed that the uncertainty of the display is less than 1 ms. This is because instruments that continuously synchronize their displays to tracable signals will normally have repeatable and stable delays. However, in

order for this uncertainty estimate to be valid, be sure to use only time displays

that meet the traceability requirements discussed in Section 5. A. 3. 5.C.2. Uncertainty Due to Human Reaction Time

To understand the effect ofhuman reaction time on stopwatch and timer calibration

uncertainties, a small study was conducted at Sandia National Laboratories. Four

individuals were selected and asked to calibrate a standard stopwatch using the

direct comparison method. Two separate experiments were conducted. In the

first experiment, the operators were asked to use a traceable audio time signal,

and in the second experiment, the operators were asked to use a traceable time

display. The time base of the stopwatch was measured before and after each test (using the Time Base Method), and its offset from nominal was found to be small

enough that it would not influence the test. Therefore, differences in readings

between the stopwatch being tested and the standard would be due only to the

operator's reaction time. Each operator was asked to repeat the measurement

process 10 times, and the resulting 10 differences between the standard and the

stopwatch were recorded and plotted (Figure 11).

As shown in Figure 11, the average reaction time was usually less than ±100

ms, with a worst-case reaction time exceeding 700 ms. The mean and standard

deviation for each operator was computed and graphed in Figure 12. This graph

indicates that the average (mean) reaction time of the operator can be either

negative (anticipating the audible tone) or positive (reacting after the audible

tone). Figure 12 also shows that in addition to the average reaction time having

a bias, the data is somewhat dispersed, so both elements of uncertainty will need

to be considered in a complete uncertainty budget. For this experiment, the

worst case mean reaction time was 120 ms and the worst case standard deviation was 230 ms. It should be noted that in the measurements recorded in Figure 12,

Operators 1 and 2 had no previous experience calibrating stopwatches. Based on

these results, it is recommended that each calibration laboratory perform tests to determine the uncertainty of their operator's reaction time.

35
Stopwatch and Timer Calibrations

Human Reaction Time, Direct Comparison, Audio Method

Measured Reaction Time Deviation over 10 Runs

80

BL7Q6050

4030 vT 0-20 C 10 o

5g 00

TO> -0.10 Q -0.20

-0.30

-0 40

-0.50

»0.60

-0 70

-0.80

i « » t

*

Run Number

Figure 11. Reaction time measurements (four operators, 10 runs each) for the

direct comparison method.

Human Reaction Time, Direct Comparison, Audio Method

Mean Bias and Standard Deviation

> < f

i 12 3 4 Operator Number

Figure 12. Averaging measurement results forfour different operators.

36
The Di »arison Method

When a traceable time display was used, the uncertainty due to human reaction

time was found to be approximately the same as the human reaction time for an

audible tone. Keep in mind that these results are presented to illustrate the nature

of uncertainty due to human reaction time, and to provide a very rough estimate

of its magnitude. We strongly encourage each person calibrating stopwatches

and timers to perform repeatability and reproducibility experiments to help better

determine the uncertainty of human reaction time.

5.C.3. Device Under Test (DUT) Resolution Uncertainty

Since the direct comparison method requires observing data from the DUT

display, the resolution ofthe DUT must also be considered. For digital indicating

devices, resolution uncertainty is understood to be half of the least significant

digit, with an assumed rectangular probability distribution. For an analog watch,

the same method of determining resolution uncertainty may be used because the

watch moves in discrete steps from one fraction of a second to the next.

5.C.4. Uncertainty Analysis

This section provides an example ofhow data collected using the direct comparison

method can be used to perform an uncertainty analysis. For this estimate of

uncertainty we will include the mean bias as an estimate of uncertainty, rather

than correcting for it, because the mean bias can be either negative or positive,

and may vary from time to time for the same user [17]. In this calibration

process, the mean bias can be considered a measurement of reproducibility, and

the standard deviation a measure of repeatability.

5.C.4.a. Uncertainty Distributions

Because of the lack of knowledge regarding distributions of the mean bias and

delay deviation between telephone calls, both components of uncertainty are

treated as rectangular distributions. Since the resolutions of digital and analog

stopwatches have known, discrete quantities, their distribution is also rectangular

[12]. All other data are considered to be normally distributed.

5.C.4.D. Method of Evaluation

Even though the data provided in previous sections were treated statistically, they were collected from previous measurements, and not during the actual stopwatch

calibration. Because the metrologist does not have statistical data based on a

series of observations to support these uncertainties, they are identified as Type

B.

37
Stopwatch and Timer Calibrations

5.C.4.C. Combination of Uncertainties

In the following examples, the uncertainty budgets were developed for a calibration using traceable land lines (Table 8 and Table 9), and for a calibration

using a cellular phone or satellite signal (Table 1 0) based upon the data previously

provided. The human reaction time was based on the worst case data presented

in Section 5.C.2. The uncertainties are rounded to the nearest millisecond. The

uncertainty components are considered to be uncorrected, so they are combined

using the root sum of squares method.

Table 8 - Uncertainty analysis for direct comparison method (digital DUT)

using a land line.

Source of Magnitude, Method of Distribution Standard

uncertainty ms evaluation uncertainty, ms Human reaction time bias Human reaction time standard

deviation

Telephone delay

deviation

XA DUT resolution

120

230

30

TypeB

Octangular

Normal

TypeB (k= 1)

TypeB

TypeB

Rectangular

Rectangular

69

230

17

Combined uncertainty

Expanded uncertainty (k = 2, representing approximately a 95 %

level of confidence)

241

482

38
i he Direct Comparison I e t 3d

Table 9 - Uncertainty analysis for direct comparison method (digital DUT)

using a cell phone.

Source of

uncertainty

Magnitude, Method of Distribution Standard ms evaluation uncertainty, ms

Human reaction time bias Human reaction time standard

deviation Telephone delay

deviation

Vi DUT resolution Combined uncertainty

120

230

150

5

TypeB

TypeB

TypeB

TypeB

Rectangular

Normal

Rectangular

Rectangular

Expanded uncertainty (k = 2, representing approximately a 95 %

level of confidence)

69

230

87

3 255

511

Table 10 - Uncertainty analysis for direct comparison method (analog

DUT) using a land line.

Source of

uncertainty

Magnitude, Method of . & A. Standard

Distribution A . A ms evaluation uncertainty, ms

Human reaction time bias Human reaction time standard

deviation Telephone delay

deviation

Vz DUT resolution Combined uncertainty

Expanded uncertainty (k = 2, representing approximately a 95 %

level of confidence)

120

230

30

100

TypeB

TypeB

TypeB

Type B

Rectangular

Normal

(*=i)

Rectangular

Rectangular

69

230

17

58

248

495

39

Section 6

The Totalize Method

The totalize method partially eliminates the measurement uncertainty from human

reaction time, but requires two test instruments: a calibrated signal generator,

and a universal counter.

6.A. Calibration Procedure for the Totalize Method

The counter is set to TOTALIZE, with a manual gate. A signal from a calibrated

synthesized signal generator is connected to the counter's input, and the

laboratory's primary frequency standard is used as the external time base for the

synthesizer and the counter (Figure 13). The frequency should have a period at least one order of magnitude smaller than the resolution of the stopwatch. For

example, if the stopwatch has a resolution of0.0 1 s ( 1 ms); use a 1 kHz frequency

(1 ms period). This provides the counter with one more digit of resolution than

the stopwatch.

Laboratory Frequency

Reference Standard

©

Frequency Synthesizer

0—1

Universal Counter

Connect to Synthesizer

and Counter

External

Time Base

Inputs

Figure 13. Block diagram ofthe totalize method.

41
Stopwatch and Timer Calibrations

To begin the measurement, start the stopwatch and manually open the gate of

the counter at the same time. One way to do this is by rapidly pressing the start- stop button of the stopwatch against the start button on the counter (Figure 14).

Another method is to press the start/stop button of the stopwatch with one hand

and simultaneously pressing the start/stop button of the counter. After a suitable

period of time (determined by the calibration requirements of the stopwatch or timer being calibrated), use the same method to simultaneously stop the stopwatch

and close the gate of the counter.

Figure 14. Using the start-stop button ofthe stopwatch to start the counter. Once the counter and stopwatch are stopped, compare the two readings. Use the

equation At/T to get the results, where At is the difference between the counter

and stopwatch displays, and T is the length ofthe measurement run. For example,

if At = 100 ms and T = 1 hour, the time uncertainty is 0.1 s / 3600 s or roughly

2.8 x 10-5 (0.0028 %).
The Totalize Method >

6.A.I. Advantages of the Totalize Method

When using the stopwatch's start/stop button to open and close the counter's

gate, this method partially eliminates human reaction time, and therefore has a lower measurement uncertainty than the direct comparison method.

6.A.2. Disadvantages of the Totalize Method

This method requires more equipment than the direct comparison method.

6.B. Uncertainties of Totalize Method

The factors that contribute to the measurement uncertainty of this method are discussed below.

6.B.I. Uncertainty of the Frequency Input

A synthesized signal generator that was recently calibrated typically has a frequency uncertainty ranging from 1 x 10~6 to 1 x 10~9

. If the signal generator

time base is externally locked to a laboratory frequency standard such as a cesium

oscillator or a GPS disciplined oscillator, the frequency uncertainty can be much

smaller, typically parts in 10 12 or less.

6.B.2. Uncertainty Due to Human Reaction Time

This source of uncertainty is due to any difference between the starting of both

the stopwatch and counter, and the stopping of both the stopwatch and counter. In order to estimate this source of uncertainty, a study was conducted at Sandia

National Laboratories. Four individuals were selected and asked to calibrate a standard stopwatch using the totalize method, using one hand to start and stop

the stopwatch, and one hand to start and stop the frequency counter. The time

base of the stopwatch was measured before and after each test (using the time

base method), and its offset from nominal was found to be small enough so that

it would not influence the test. Therefore differences in readings between the

stopwatch being tested and the standard would be due only to the operator's

reaction time.

Each operator was asked to repeat the measurement process 10 times, and the

resulting difference between the standard and the stopwatch were recorded.

43
Stopwatch and Timer Calibrations

Reaction Time Measurements for Totalize Method (Two Hands)

0.10

0.08

0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06

-0.08

-0.10 4 6 Run Number

10

Figure 15. Measured reaction times (four operators, 10 runs each) for totalize

method.

As shown in Figure 15, the average reaction time was usually less than 40 ms. The largest deviation was about 90 ms. The mean and standard deviations for

each operator were computed and graphed in Figure 16. The data demonstrates

that the worst case mean reaction time was 27 ms, and the worst case standard

deviation was 10 ms, which is a significant improvement over the direct

comparison method. Subsequent measurements of human reaction time were made by placing the start/stop button of the stopwatch directly against the start/

stop button of the frequency counter (as shown in Figure 12) so that both buttons were pushed at the same time. The experimental data showed that this method

provided no significant advantage over using one hand to start the stopwatch and

the other hand to start the frequency counter.

44
The Totalize Method

Mean Reaction Time for Totalize Method (Two Hands)

2 3 Operator Number

Figure 16. Mean reaction times (four operators, 10 runs each) for the totalize

method.

6.B.3. Uncertainty Due to the Counter

For this method, the uncertainty ofthe counter is related to the counter resolution.

The internal time base ofthe counter is not used, because the gate time is controlled

by the manual start/stop function. This method does not use the counter gate or

trigger, so the uncertainties associated with these functions are also eliminated.

The counter is simply used as an event counting device, and the uncertainty is equivalent to ±1 least significant digit on the display.

6.B.4 Device Under Test (DUT) Resolution Uncertainty

Since the totalize method involves observing data from the DUT, the resolution

of the DUT must also be considered. For digital indicating devices, resolution

uncertainty is understood to be half ofthe least significant digit, with a rectangular

45
Stopwatch and Timer Calibrations

distribution. A rectangular distribution is also used for analog timers, since these

devices move in discrete steps from one fraction of a second to the next.

6.B.5 Method of Evaluation

Since the sources of uncertainty in this calibration are different types, such

as the absolute accuracy specification for reaction time, the relative accuracy

specification for the frequency source, and an absolute specification of ±1 count

for the counter, it is necessary to define the calibration conditions and convert all specifications to a common format.

The uncertainty example in Table 1 1 assumes that the synthesized signal generator can produce a 1 kHz signal with an uncertainty of 1 x 10"8 or less. The stopwatch

is compared to the counter for 3 hours (10 800 s). The stopwatch is started and

stopped with one hand, and the counter is started and stopped with the other. The

stopwatch is digital and the resolution is 0.01 s. As in the previous uncertainty

example, all sources of uncertainty are combined by root sum of squares, and

uncertainties are rounded to the nearly millisecond.

Table 11 - Uncertainty analysis for totalize method.

Source of Magnitude, Method of

uncertainty ms evaluation

Distribution

Standard

uncertainty, ms Human reaction time bias Human reaction time standard

deviation

Synthesizer accuracy

Totalize counter

resolution

XA DUT

resolution

27

10

1

5

TypeB

TypeB

TypeB

TypeB

TypeB

Rectangular

Normal

(k=l)

Rectangular

Rectangular

Rectangular

Combined uncertainty

Expanded uncertainty (k = 2, representing approximately a 95 %

level of confidence)

16

10

1

3

1938

46
I he Totalize Method

6.C. Photo Totalize Method

An alternative measurement technique to the totalize method previously discussed

involves using a high speed camera (digital or film type). The equipment is set up

in the same manner as in Section 6. A. In this method, both the stopwatch being

calibrated and the universal counter are started in no particular order. When

both instruments are counting, a photo is taken of the two instruments. Under

appropriate shutter and lighting conditions, the resulting photo will clearly show

the time displayed on both the stopwatch and counter. Both readings are recorded

as the initial measurements in the calibration. After an appropriate amount oftime

has elapsed, a second photo is taken and the displays are recorded as the closing

measurements. The difference in elapsed time for the stopwatch is compared to the difference in elapsed time for the counter to determine the measured offset

of the stopwatch.

Figure 17 shows that the initial counter reading is 53.980 s and the stopwatch

is at 57.52 s. Figure 18 shows that the counter reading is 82.049 s and the

stopwatch is at 1 minute 26.18 s (86.18 s). The elapsed time on the counter is 82.049 - 53.980 = 28.069 s, and likewise the elapsed time on the stopwatch is 86.18 - 57.52 = 28.66 s. This would indicate that over the 28 s interval, the

stopwatch was in error by 0.59 s or approximately 1820 s per day.

Figure 1 7. Photo totalize start reading.

47
Stopwatch and Timer Calibrations

HEWLETT „„,...„- «U*ABO MPM COUNTER 8? 049

QQ CZ

Figure 18. Photo totalize stop reading.

WARNING NOTE - In order for this method to provide accurate results, the

photo system must be set up in a manner that captures the stopwatch and counter

display correctly. If the shutter speed is too slow, the images will not produce

discernable information, as Figure 1 9 shows for the stopwatch. We could interpret

this stopwatch reading with the 1/10 s digit as 9, 7, 3, or 4, and the 1/100 s digit as 3, 5, or 6. Additionally, often when the photo yields a very clear display as in Figures 17

and 18, the resulting measurement is not valid. This stopwatch was previously

calibrated using other methods described in this book and was found to have an

offset of less than 1 second per day, which is significantly different from the photo

totalize method results indicated above. For this example and photo equipment

setup, the method produced false results. Anyone using the photo totalize

method must validate the measurement results of their measurement process

by comparing results obtained for a particular instrument to other measurement

methods discussed in this book.

48
Figure 19. Ambiguous photo totalize reading.

Section 6.C1. Advantages of the Photo Totalize Method

Using this measurement method, all uncertainty due to human reaction time is reduced to zero. This makes the estimate of measurement uncertainty smaller,

and the amount of time needed to complete a calibration shorter than the direct

comparison or totalize method. This method also makes it possible to calibrate

multiple stopwatches at the same time, and then maintain the photos as archival

data.

Section 6.C.2. Disadvantages of the Photo Totalize Method

This method can VERY EASILY produce erroneous results. As previously

stated, the measurement results for the particular cameras used by the laboratory

should always be compared to measurement results of the same unit under test using other methods described in this book.

49

Th€ : Base Method <« Section 7

The Time Base Method

The time base measurement method is the preferred method for stopwatch and

timer calibrations, since it introduces the least amount ofmeasurement uncertainty.

Because the DUT's time base is measured directly, the calibrating technician's

response time is not a factor. The exact method of measuring the stopwatch's time base depends upon the type

of stopwatch or timer being calibrated. If the unit has a quartz crystal time base, an inductive or acoustic pickup is used to monitor the stopwatch's 32 768 Hz

time base frequency on a calibrated frequency counter (the pickup is fed into an

amplifier to boost the signal strength). If the unit is an older LED-type stopwatch,

the frequency is usually 4.19 MHz. An inductive pickup can even be used to sense the stepping motor frequency of analog mechanical stopwatches, or the

"blink rate" of a digital stopwatch display. Or, an acoustic pickup can be used to measure the "tick" of a mechanical stopwatch.

7.A. References for the Time Base Method

The reference for a time base calibration is the time base oscillator ofthe measuring

instrument. For example, if a frequency counter is used, the measurement

reference is the time base oscillator ofthe frequency counter. In order to establish

traceability, the frequency counter time base must have been recently calibrated

and certified. However, a better solution is to have the laboratory maintain a

traceable 5 MHz or 1 MHz signal that can be used as an external time base for

the frequency counter and all other test equipment. If an external time base is used and its measurement uncertainty is known, it is unnecessary to calibrate the

internal time base oscillator.

7.B. Calibration Procedure for the Time Base Method

Two methods of calibrating a stopwatch time base are described below. One

uses a commercially available measurement system; the other uses a frequency

counter with an acoustic pickup. Note that neither calibration method requires

opening the case of the stopwatch or timer. Keep in mind that you should never

disassemble a stopwatch or timer and attempt to measure the time base frequency

by making a direct electrical connection. The crystal oscillators in these units are very small, low-power devices. Their frequency can dramatically change if they

are disturbed or loaded down by the impedance of a frequency counter, and in

some cases they can even be destroyed by incorrect electrical connections.

51
Stopwatch arid Timer Calibrations

7.B.I. Using a Commercial Time Base Measurement System

Time base measurement systems are available from several vendors. One

example of a commercially available time base measurement system (Figure 20)

is described here for the purposes of illustration. This unit measures the frequency

of the time base oscillator, and converts this information to a display of seconds

per day, or seconds per month. This same function could be performed with a sensor (acoustic or inductive pickup), a frequency counter, and the conversion

formula described in the next section.

Figure 20. Time base measurement system for stopwatches and timers.

The example unit uses a 4.32 MHz quartz time base oscillator as a measurement

reference. In a 2 s measurement period (the shortest period used by the instrument),

the oscillator produces 8 640 000 cycles, a number equal to the number of 0.01

s intervals in one day. Therefore, the instrument resolution is 0.01 s per day.

Cycles from the DUT time base are counted by a sensor that is connected to the

measurement system. The sensor uses the cycle count from the DUT to start and stop the cycle count from the reference time base. For a 2 s measurement

interval, a 32 768 Hz DUT would stop the cycle count from the reference time

base after counting to 65 536 (32 768 x 2). If the reference time base counted to 8 639 900 during this same interval, then the system would estimate that the DUT

would gain about 1 s per day (100 x 0.01 s). The time base measurement system shown in Figure 20 allows the measurement

interval to be set from 2 s to 960 s. Selecting an interval longer than 2 s is

52
The Time Base Method

effectively the same thing as increasing the gate time on a frequency counter. It

is important to measure for a long enough period to get an accurate and stable

reading. When testing a 32 768 Hz quartz stopwatch, a 10 s to 12 s measurement

is normally sufficient to obtain a reading stable to ±1 count. When testing an

older mechanical (Type II) stopwatch, a longer measurement of 120 s or more

may be required. Table 12 shows the effect that the length of the measurement

time has on the stability of the stopwatch calibrator's readings.

Table 12 - The effect of the length of the measurement time on stability

(based on 25 readings).

Measurement time 2s 10 s 12 s 20 s Mean -0.03 -0.06 -0.06 -0.06 Standard deviation of the mean 0.0050 0.0012 0.0011 0.0006

Maximum 0.00 -0.05 -0.05 -0.06 Minimum -0.09 -0.07 -0.07 -0.07 Range 0.09 0.02 0.02 0.01

To support 0.01 s resolution, the instrument's 4.32 MHz time base oscillator

must be calibrated to within 1.16 x 10~7

. If the instrument is calibrated to within

specifications, the display uncertainty is ±0.05 s per day (maximum time base

frequency offset of about 6 x 10~7 ). In all cases, the uncertainty of the time base

oscillator relative to UTC must be known in order to establish traceability. The

system can be calibrated by applying either a traceable 1 pulse per second (pps)

signal to a pin connector on the back ofthe unit or a traceable 32 768 Hz reference

signal to the sensor, or by extracting and measuring the 4.32 MHz signal directly

with a traceable frequency measurement system.

The DUT can be a Type 1 stopwatch (both 32 768 Hz and 4.19 MHz devices can

be measured), or a Type 2 mechanical stopwatch. The 32 768 Hz signal is picked

up with an acoustic sensor, and then compared to the time base oscillator. A 1 Hz

offset in the 32 768 Hz signal translates to a time offset of about 2.6 s per day. A

capacitive sensor is used to detect the 4.19 MHz frequency of quartz time base

oscillators, an acoustic or inductive pickup is used to sense the stepping motor

frequency of analog mechanical stopwatches, and an inductive pickup is used to sense the "blink rate" of digital stopwatches.

Front panel switches allow the operator to select the type of device being tested,

53
Stopwatch and Timer Calibrations

the measurement interval, and whether the time offset should be displayed as seconds per day or seconds per month. Once these parameters have been chosen,

the device is measured by simply positioning it on top of the sensor until a usable

signal is obtained, waiting for the measurement interval to be completed, and

then recording the number from the display. It is always a good idea to allow

the stopwatch calibrator to complete at least two complete measurement cycles

before recording a reading.

Figure 21 shows a more elaborate time base measurement system with some

additional features. This device has a small LCD display with graphics capability,

built-in temperature measurement capability, an RS-232 interface that allows

measurement results to be transferred to a computer, and an optional Global

Positioning System (GPS) satellite receiver that corrects and calibrates the quartz

time base oscillator. Like the system shown in Figure 20, this system can measure

the 32 768 Hz quartz crystal frequency of Type 1 stopwatches, the stepping motor

frequency of analog stopwatches, and the "blink rate" of digital stopwatches. As

an additional benefit, this system can measure the quartz crystal frequency and

the stepping motor frequency at the same time. This can be useful if the device

under test compensates for the frequency offset of the quartz crystal by applying

corrections to the stepping motor, thus making the analog display more accurate

than the time base (a common practice in analog quartz wristwatches).

Figure 21. A time base measurement system for stopwatches and timers with an integrated graphics display.

54
TheTis r i

; is ;

7.B.2. Using a Frequency Counter and an Acoustic Pickup

If an acoustic pickup and amplifier are available, you can measure the frequency

of a stopwatch time base directly with a frequency counter. The reading on

the counter display can be used to calculate the frequency offset using this

equation:

f - f

/(offset) = measured nominal

^nominal

where f , is the reading displayed by the frequency counter, and f . . is J measured c r j j i j j nominal the frequency labeled on the oscillator (the nominal frequency it is supposed to produce).

If f , is 32 768 Hz and f ^ is 32 767.5 Hz, then the frequency offset is J nominal J measured ~ J -0.5 / 32 768 or -1.5 x 10~5 or -0.0015 %. To get time offset in seconds per day,

multiply the number of seconds per day (86400) and the frequency offset:

86 400 x (-1.5 x 10 5 ) = -1.3 s per day , which means the stopwatch can be expected to lose 1.3 s per day. You might find

it easier to note that a 1 Hz error in a 32 768 Hz device equates to a time offset of

about 2.64 s, since 86 400 / 32 768 = 2.64. Therefore, a 2 Hz offset is about 5.3

s / day, a 3 Hz offset is about 7.9 s / day, and so on. If the acceptable tolerance is 10 s/ day, then you'll know that 3 Hz is well within tolerance.

These results show that even a low cost eight-digit frequency counter will

provide more measurement resolution than necessary when measuring 32 768

Hz devices. The last digit on an eight-digit counter represents 0.001 Hz (1 mHz),

and a 1 mHz frequency offset represents a time offset ofjust 2.6 ms per day. Very

few stopwatches or timers can perform at this level.

7.B.3. Advantages of the Time Base Method

The time base method completely eliminates the uncertainty introduced by

human reaction time. The measurement uncertainty can be reduced by at least

two orders of magnitude when compared to the direct comparison method, often

to 1 x 10 6 or less. This method is also much faster. The measurement can often

be performed in a few seconds, as opposed to the several hours often required for

the direct comparison method.

55
Stopwatch and Timer Calibrations

7.B.4. Disadvantages of the Time Base Method

This method requires more equipment than the direct comparison method, and

does not easily work on some electrical, mechanical, or electro-mechanical units.

It also does not test the functionality of the stopwatch or timer, only the time base.

Function tests need to be performed separately by starting the unit, letting it run

for a while (a few minutes to a few hours, depending on how the unit is used), and

stopping the unit. If the unit appears to be counting correctly, the displayed time

interval will be accurate.

7.C. Uncertainties of Time Base Method

This method utilizes either a time base measurement system or a frequency counter

with an acoustic or inductive pickup to measure the frequency of the device's

internal time base oscillator. If we use the time base measurement system shown

in Figure 20 as an example, and take into account its specified accuracy of ±0.05

s/day and its resolution of 0.01 s, then the measurement uncertainty equals 0.05 s/ day (50 ms/day). There is no uncertainty contributed by human reaction time, and

the resolution uncertainty of the stopwatch calibrator is insignificant compared to

its accuracy specification. Resolution uncertainty does not need to be considered,

since data are not observed from the DUT's display. Since there is only one

uncertainty component, we did not include an uncertainty analysis table.

56
Required Uncertainty

Section 8

How to Determine if the Calibration Method Meets the

Required Uncertainty

The preceding sections have provided estimates of expanded measurement

uncertainty associated with various types ofstopwatch calibrations. It is important

to ensure that the achievable measurement uncertainty is relatively small when

compared to the stopwatch tolerance we are attempting to verify. For example,

if we use the direct comparison method to calibrate a stopwatch with an accuracy

of 5 s per day (0.01 s resolution), and we decide to use a calibration period of 5

minutes, the accuracy of the stopwatch over the 5 minute interval would be about

17 ms. The first problem arises in that the resolution of the stopwatch is 0.01

s, and cannot display 0.017 s, making the specification impossible to verify for

this time period. Furthermore, the measurement uncertainly for the calibration

process is 480 ms, approximately 28 times larger than the accuracy that we are

trying to verify! Clearly a 5 minute calibration period for this stopwatch and

calibration method is not adequate. Even a 1 hour calibration is inadequate,

because the quantity required to be measured, now about 208 ms, is still less than

half of the measurement uncertainty.

As stated in ISO/IEC 17025 [4], when a statement of compliance to a metrological specification is made (for example, is the DUT "in tolerance" or "out of tolerance" based on the manufacturer's specifications), the laboratory

must take the measurement uncertainty into account. It is the responsibility of the

calibration laboratory to decide whether the measurement uncertainty associated

with the calibration method is small enough to comply with the metrological

requirement. Calibration laboratories generally use some sort of decision rule

for determining whether the uncertainly associated with the calibration method is adequate. Examples of such rules are the N: 1 decision rule (where the tolerance

of the instrument to be tested is N times larger than the calibration uncertainty

and is mostly commonly stated as 4:1 or 3:1), or some form of guardbanding

(where the calibration uncertainty or some fraction of it is subtracted from the

DUT accuracy specification and the calibration results are acceptable only if the measured offset was within the guardband limit). Whatever the case, it is important to compare the calibration measurement uncertainty to the tolerance of

the DUT, in order to ensure that the calibration process is valid.

57
Stopwatch and Timer Calibrations

To illustrate this, assume that a laboratory employs a 4:1 rule for acceptable

uncertainty. This means that the expanded measurement uncertainty of the

calibration must be four times smaller than the acceptable tolerance of the DUT

in order to declare the unit in or out of tolerance. The laboratory is calibrating a

digital stopwatch to a tolerance of 0.02 %, using the direct comparison calibration

method via a telephone landline (Table 8). The estimated expanded measurement

uncertainty for this method was 482 ms. In order for 482 ms to be one quarter

of the tolerance of the DUT, the tolerance must be 1928 ms. The amount of time

required to elapse on the stopwatch during the calibration would be at least:

1,928 S =Xs = 9640 s = 2 h 41 minutes

0.02 %

For the same scenario, if we were trying to verify the stopwatch shown in Figure

8 to the manufacturer's specification of 0.0003 %, the stopwatch would have to run for more than 1 week (178 hours, 31 minutes, and 7 s). This is impractical,

and the laboratory that is testing to 0.0003 % would clearly want to consider the

time base method as a much faster, more appropriate method.

58
OtherTopics Related to Measurement Uncertainty

Section 9

Other Topics Related to Measurement Uncertainty

This section discusses other important topics related to measurement uncertainty.

The first involves estimating the uncertainty of a field calibration, where a reference standard stopwatch is brought into the field and used to calibrate another

device. Next, the stability and aging of 32 768 Hz quartz crystal oscillators used

in stopwatches and timers is discussed, followed by discussions of how the

performance of a stopwatch can change when a new battery is installed, and how

extreme temperature conditions can affect stopwatch performance.

9.A. Uncertainty Analysis of Using a Calibrated Stopwatch to

Calibrate another Device

A calibrated stopwatch is often used to perform field calibrations of other timing

devices, such as an industrial timer or parking meter. In this example (Table

13), we are calibrating an industrial timer with 1 s resolution. The reference

for the calibration is a stopwatch that has a specified accuracy of 5 s per day

(about 208 ms per hour), 0.01 s resolution, and a calibration uncertainty of 0.2

s per day (roughly 8 ms per hour). As previously discussed in Section 5.C.2,

the human reaction time bias is 120 ms, and the human reaction time standard

deviation is 230 ms. The measurement time for the calibration is 1 hour (3600

s). Using these values and the analysis provided in Table 13, the uncertainty of

the industrial timer when measuring a 1 hour interval is 789 ms, or 0.02 %. All

values in Table 1 3 are rounded to the nearest millisecond.

When performing this analysis, it is important to include the specified accuracy

of the reference stopwatch, which takes into account long-term sources of error during the calibration interval that may not have been noticeable during the time

of calibration. It is also important to consider the uncertainty of the stopwatch

calibration as part of the budget when using a stopwatch as a reference, because

it may be relatively large when compared to the other sources of uncertainty in

the measurement process.

59
Stopwatch and Timer Calibrations

Table 13 - Uncertainty analysis of using a calibrated stopwatch to calibrate

another device.

Source of Magnitude, Method of

uncertainty ms evaluation

Standard

Distribution uncertainty,

ms

Unit under test resolution

lA digit

Human

reaction time

bias

Human

reaction time

standard

deviation

Stopwatch

accuracy

Stopwatch

resolution

lA digit

Stopwatch

calibration

uncertainty

Combined uncertainty

500

120

230

208

TypeB

TypeB

TypeB

TypeB

TypeB

TypeB

Rectangular

Rectangular

Normal

(k=\)

Rectangular

Rectangular

Normal

{k=2)

289

69

230

120

Expanded uncertainty (k = 2, representing approximately a 95 % level of confidence)

394

789

9.B. The Effects of Stability and Aging on Calibrations of 32 768 Hz

Crystals

Aging is the systematic change in frequency over time due to internal changes

in an oscillator. All quartz oscillators are subject to aging, and the rate at which

they age is often a key factor in determining their calibration interval. The aging

rate of a quartz crystal oscillator often depends upon its surface area to volume

ratio, and small, low frequency crystals generally have low aging rates [18].

Thus, the 32 768 Hz crystals found in stopwatches and timers usually tend to age

slowly and have very good long term stability, and their frequency changes by a

surprisingly small amount over time.

60
OtherTopics Related to Measurement Uncertainty

Frequency Stability of Two Low-Cost Stopwatches

1.0E-07

* 8.0E-08 C

«

7.0E-08 £ 6.0E-08 tn>

jjj 5.0E-08

0)3

CT

I! 4.0E-08

3.QE-Q8

„4 L

' - ft 1

I «A

jj /—

r

q /

f

\ >t

r

t i i

i i i

> i i \V

\

t

j

j

j

i

Stopwatch A

\ s Stopwatch B

V

j

i

i I r

! ! !

,.. .i. —l~ _»TM___L . ,. 4 Days

Figure 22. Graph ofthe frequency stability oftwo stopwatches.

To illustrate this, Figure 22 is a graph ofthe frequency stability oftwo stopwatches

that were continuously measured over a period of more than one month using

a previously described (Section 7.B.1) time base measurement system. Both

stopwatches were low cost devices; stopwatch A had a suggested list price of

about $25 USD, and stopwatch B sells for about $55 USD. The laboratory

temperature during the measurement was about 23 °C ± 1 °C. The graph shows

the Allan deviation (ADEV) of each stopwatch for averaging times ranging from

0.5 days to 7 days. ADEV is a commonly used statistic for estimating frequency

stability [19]. It differs from the conventional standard deviation because it does

not use the average frequency as a point of reference. Instead, it compares the

frequency offset of the DUT during each measurement period with its frequency

offset during the previous measurement period. By doing so, it reveals how the

frequency of an oscillator changes over time due to effects such as aging.

Stopwatch A had an average frequency offset (accuracy) during the test of about

8 x 10"6

. As indicated in Figure 22, the stability (ADEV) was slightly better than

1 x 10"7 after one week, or about 80 times better than the accuracy. Stopwatch

B had an average frequency offset (accuracy) during the test of about 5 x 10~7

. 61
Stopwatch arid Timer Calibrations

Its stability as estimated with ADEV was near 7 x 10~8 after one week, or about seven times better than its accuracy.

Because of their slow aging rate, stopwatches tend to produce very repeatable

results over long periods of time. When compared to the requirements for

stopwatch calibrations discussed in Section 3, the small changes in frequency

due to aging are usually insignificant. This makes it possible for a laboratory to allow long intervals (perhaps exceeding one year) between calibrations.

9.C. Factors That Can Affect Stopwatch Performance

Many factors can cause a quartz crystal oscillator to change frequency. Some of

these are shown in Figure 23. Sharp temperature changes, vibration, and shock

are some of the more common phenomena that can affect the time base on a dayto-day basis. Also, if power is removed from an oscillator and later restored, there can be a shift in the frequency. This is true of quartz crystal stopwatches when

the battery is changed. This frequency change is usually small when compared

to the stopwatch's time base specifications, usually less than 10 to 20 parts in

106 (-10 to 20 ms/day) and usually short-term, with the time base returning to

its original frequency after a period ranging from a few hours to a few days.

Oscillator Turn Off Vibration Shock &

Figure 23. Factors that can change the quartz time basefrequency.

62
Other Topics Related tc >yrament Uncertainty

Temperature is perhaps the most important factor that affects quartz crystal time

base performance. The quartz crystals used in wrist watch time bases are cut in

such a way as to make them most stable near body temperature. The time base

acts as a thermally stable oscillator while it is on a person's wrist. Stopwatches, on the other hand, use quartz crystals that have been cut to be stable at or near room temperature. If they are used in very hot or very cold environments, the

time base can vary by over 20 parts in 1

6

. Figure 24 shows the accuracy of a

typical stopwatch over a temperature range of 0° C to 50° C (32° F to 122° F).

As can be seen for the figure, the flat portion of the performance curve is near room temperature (23° C or 73° F), and drops off as the temperature increases

or decreases.

Stopwatch Frequency Offset Versus Temperature

<

\ \

-V—

R oom Temperature (23° C)

-5

-10

-15

-20

-25 10 20 30 Temperature (° C)

40 50

Figure 24. Stopwatch accuracy versus temperature.

63

Appendix A

Appendix A

Calibration Certificates

If a calibration certificate is issued for a stopwatch or timer, it should contain the

information listed in Section 5. 10 of ISO/IEC 1 7025 [4]. Some of the necessary

elements are the name and address of the laboratory, the name and address of the

client, the identification of the method used, and a description of the item being

calibrated. A sample calibration certificate that is compliant with ISO/IEC 1 7025

is shown in Figure Al.

XXX CALIBRATION LABORATORY

XXX dlitmuioo UtvniUTv, Cif>. Slats. Z»p

TIMER-CLOCK

Fisher Scientific I4.64X-J

1X1456*. Timing i'esi Labs. 123 TcaUbLmx

Amlimn. I s A

CERTIFICATE

CtfJMUTlON

Fsk: 4782!

Manufacturer. Model Number

Serial Number

Submitted In

\> ! mind Condition: m Tolerance As left Condition' Idl At Found

Certified N*< vcrotv? IS. 2002

This unit was unled using the I ahoratnn V Sli<fmatch Tinier C»ltbni<i»<« Sun ton. MMS f ^4i#»

utilizing procedure #LAB 991 2 The calibration data imbcaies a devialum from ifw reftusnee

Kiandiird in seconds per da> (• -). tolerance oflhe Device t "ntler Test, and Fvpsnded ? 'memttty

of Measurement tK 2, tefresenting apprimmiikfv 95»« confidence).

Measured V ahie TL29*d

Tolerance

S.64 vd

( ttUbntti<m n».tu

l-.vpjnded I nccrtainty 0S64sd

Calibration fiocedare; Laboratory Tetapeiature Laboratory Ilinindily Certificate Number,»apwat£b.Timcr Version L03-' 1 1, IW

23.0 c tie c

40,(1 **- 5 ,0«n 146316

Itteftrtogtss: Calibration M. Tcefwiciaii Approved Iw J M.

K&mtpk Cal Cert Page I of 2

Figure Al. Sample calibration certificate, (page 1)

65
Stopwatch and Timer Calibrations

\\\ Calibration 1 1 burn lor? C tty. Stale

lile: -17X21 Dale: \ov ember IS 2009

CgggCgl If atvabilHv Mauntrue V jiucs and I be associated uncertainties supplied b> the* XXX

Calihraaoti I jlMii,iiti> me iiiivcahlc to one 01 m«»c Offfcc loU-ncma

1, Tine val*iv» of the units ((j Ihcr lv*sc <>t ckn\«.dt i*n.nnt J-ncd and divw-rntnatvd b> the N.itMirul lifWlCt <»t ManiLiidv and icthnologY (I nikd SUiv» <4 Aidokj) »n. m spcvial easts jnd vsheiv

appti-pN.iic. In the National Standards I ablators ,>| amrthcT n.ifi-m 2 The accented valucis) of fimdamcnlal physical phenomena (infringe nandar*):

3. K3!KK*i<<roih^no»>-maint3incd*undard»crtaNishcdb> cither a Kll-t»Uhrauoo »nd <t a direct ealilnalion UchnKiuv:

i. Standards inainlaiacd and disseminated by the \.V\ Calibration laboratory in special cases and where wan anted,

5 V alues and uncertainties wising from participation in a National Measurement Svttcnt Because «»l inherent eomptvAilx in 11k <.aiinralit>n prtn.es* and the isKefUmrx wowtributM* b> rath aundaidi and calibrabng instruments, traccabilay always toquues ev aluation or a "ira-jcabilii) bee * V *fmc£ah(litv tree" *nah su can he assembled lor a specific calibration and \alid (or a particular and

IgMSlfifi poinl m bine, The "iravcabtlily tree" isill include copies o( relevant ecruticates and reports, vvcvrplcd an .ippn>|*t.»li. Im brevity. However, the >.-•*{ nt preparation nl tin "baccabilits ttce" vsill bj

.iui v.il to the requester.

?Solf. 1 This certificate or report shall not be reproduced except in lull without the advance written approval ol the \\\ Calibration I aKrraton

.Not^.2: Ibe as rcsci*. cd <.t-ndiUnn of the standard, set Of standards, or measurement equipment described

herein was a* expected, unless olbenvtsc noted in the tuvdy ot the ccttificaic or report

Example Cal Cert

Figure Al. Sample calibration certificate, (page 2)
Appendix B

Appendix B

References

[I] B. N. Taylor and A. Thompson, (Eds.), "The International System of Units (SI),"

Natl. Inst. Stand. Technol. Special Publication 330, 2008 Edition, March 2008.

[2] BIPM/IEC/IFCC/ISO/IUPAC/IUPAP/OIML, Guide to the Expression of

Uncertainty in Measurement (GUM), 1995.

[3] International Organization for Standardization (ISO), International Vocabulary of

Metrology - Basic and General Concepts and Associated Terms (VIM), 2008.

[4] International Organization for Standardization (ISO), General Requirements for

the Competence of Testing and Calibration Laboratories, 2005.

[5] R. J. Anderson and G. L. Harris, "Specifications and Tolerances for Field Standard

Stopwatches," Natl. Inst. Stand. Technol. Handbook 105-5, October 1997.

[6] Robbins, Michael, "Electronic Clocks and Watches," Howard W. Sams Co.,

Indianapolis, IN, 1975.

[7] J. R. Vig, "Introduction to Quartz Frequency Standards," Army Research and

Development Technical Report, SLCET-TR-92-1, October 1992

[8] North American Electric Reliability Council (NERC), "Time Error Correction,"

Standard BAL-004-0, April 2005.

[9] T. Butcher, L. Crown, L. Sebring, R. Suiter, J. Williams, editors, "Specifications,

Tolerances, and other Technical Requirements for Weighing and Measuring Devices,"

Natl. Inst. Stand. Technol. Handbook 44, 2007 edition (updated annually).

[10] M. A. Lombardi, "Legal and Technical Measurement Requirements for Time and

Frequency," Measure: The Journal of Measurement Science, 1(3): 60-69, September

2006.

[II] State of Pennsylvania code, 67 § 105.71(2), 2005.

[12] R. M. Graham, "Calibration Techniques for Stopwatches and Timers," Proc. 2003

National Conference of Standards Laboratories (NCSLI), 6 p., August 2003.

67
Stopwatch and Timer Calibrations

[13] M. A. Lombardi, "NIST Time and Frequency Services," Natl. Inst. Stand.

Technol. Special Publication 432, 71 p., January 2002.

[14] International Telecommunications Union (ITU), "One-way Transmission Time,"

ITU Recommendation G. 1 14, May 2003.

[15] International Telecommunications Union (ITU), "The Control of Jitter and

Wander within Digital Networks Which are Based on the 1544 kbit/s Hierarchy," ITU

Recommendation G.824, March 2000.

[16] D. W. Allan, D. D. Davis, J. Levine, M. A. Weiss, N. Hironaka, and D. Okayama,

"New Inexpensive Frequency Calibration Service from NIST," Proc. 1990 IEEE Freq.

Cont. Symp., pp. 107-116, May 1990.

[17] S. D. Phillips, K. R. Eberhardt, "Guidelines for Expressing the Uncertainty of

Measurement Results Containing Uncorrected Bias," Natl. Inst. Stand. Technol. J. Res., 102(5): 577-585, September-October 1997.

[18] J. R. Vig and T. R. Meeker, "The Aging of Bulk Acoustic Wave Resonators,

Filters, and Oscillators," Proc. 1991 IEEE Freq. Cont. Symp., pp. 77-101, May 1991.

[19] IEEE, "IEEE Standard Definitions of Physical Quantities for Fundamental

Frequency and Time Metrology - Random Instabilities," IEEE Standard 1139-1999,

March 1999.

68