a risk based approach to select and test weighing instruments

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A Risk Based Approach to Select and Test Weighing Instruments

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Page 1: A Risk Based Approach to Select and Test Weighing Instruments

� � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � ! " # ! $ % " & ' ( ) * ' ! + % $ " ' % , - . � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � - / . 0 1 � � - 2 � � � � � 3 � � � �/ 4 � � � � � � 5 � � � � 6 � � � � � 6 3 � � 7 � � � � � � �/ - � 8 � � � � � � � � 8 � 7 � � � � � � � �/ - 4 � � � 5 � � � � 6 � � � �/ - / 4 � � � 3 � � 7 � � � � � � �/ - 2 4 � � � 9 � � � �/ - : 4 � � � � � � � � � �; � < * ( + = ( % (/ - > � � � � � � � � � � ? � � � @ � � � � � � 4 � � � � 6 @ 6 A � � � � � � 3 � � � � � �2 @ 1 1 � � 6 � 0: B � � � � � �C 9 � � � � � � � � 8 � � � � � � � � �

D E E F G H I J K I L J M N O P Q I P H R S D G M T U I V O W L I X H N V O Y O Z Z N E O P K Q EV H Y H P Q I L J O L F Q H V Q I L J [ H I J K I L J I L V Q N W \ H L Q V ] O V H F E L W V H N N H ^ W I N H _\ H L Q V ` D G M T O Y Y E [ V Q E N H F W P H \ H O V W N H \ H L Q H N N E N V O L F H L V W N H VN H Y I O ] Y H [ H I J K I L J V I L O V Q N O I J K Q a E N [ O N F O L F H a a I P I H L Q [ O b `

Page 2: A Risk Based Approach to Select and Test Weighing Instruments

c d e f g h i j k h lm n o o p n q o r p n s r

t u v w w x y z{ H Y H P Q I E L E a O G H I J K I L J | L V Q N W \ H L Q. � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � - � � � � � � � � � � � � } � � � � � � � � ? � � � � � � � � � � � � � � � � } � � ~� � � � � � � � � � � � � � � � � � � � � 6 � � � 6 � B � 5 � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� = � � " � � " ' � ! $ � $ ! " % , � � ( % � � $ + � + % � $ ' % � � $ + � ( % � + & ( ( � & $ � � � ! % � % & � � " � � � � , % � � ( + �� % � � " ' " � � � � " � � % � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 7 � � � � 6 � � � � � � � � � � � � � � � � � � � ~� � � � 1 � � � 0 1 � � � � 6 � � � � ? � � � � � 6 � � � � � � � � � -� H V Q M N E P H F W N H V O L F � N H ^ W H L P I H V4 � � � � � } � } � � � � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � } � � � � B � 5 � � � � � � � 6 � � � � � � � � � ? � � � � � 1 � � � �1 � � � � 6 � � � � � � � � � � � � � 6 � � � ? � � � ? � � � � � � � � � � � � � � � � �� � $ � " � + $ % " & ' � , $ � % � & + " � � � + ( & ' ' � � $ ( + � " ! % ! � ' " ! " $ ' � � & + � $ � � � � �� + & � % " ' % ( % ( % & � ! $ + + " � & � % � , % � � ( + �� $ � % & � $ % " ! % ( % ( & + $ � � � ( % � ' % ( � � ! % � � , % � " ' ( % + � � ' % �4 � � � � � � � � � 1 � � � � 6 � � � � � 6 � � � � � � 1 � � 6 � � � � � � 7 � � � � � � � � � � � � � 6 � 6 � � B � 5 � � � � � � 6 � �� % � + � � " + � � " � � " ' � $ ! ! � + $ ! , & � % � $ � � � " ! $ % " & ' �� % � ( � + " % , & � " � � $ ! % � � � � & ' � � ( " ' ( ( � ! & ' ( � � + $ ' � ' � " + & ' � ' % � � " ' ! $ ( % � $ % % � � " � � " ' � " ' ( % + � � ' %( � & � � � ' & % � � " � + % � ! & + + ! % � " � � " ' � + ( � � % � � $ � � � ' ! % " & ' � �� % � � % ! % $ � " � " % , & � ( � ! � $ � $ � � � ' ! % " & ' �4 � � � � � � � � 6 � 6 � � � � � � � 7 � � � � � � � � � � � � � � � � 6 ? � � � � � � � � � � � � � � � � � - � - � � � � � � � � � � � � � � � 7 � � � � � � � � � � 6? � � � � � � � � � � � � � � } � � � � � � � � 1 � � � � 6 � � 6 � � � � � � 6 ? � � � 6 � � � � � � � � � � � � � � � � � � � � � � - 4 � � � � � 7 � � � � � � � � 0 � � � 6� � � ? � � � � � � � � � � 6 � � � - � � � � � � � } � � � � � � � � 6 � � � � � � � 6 � � � � � � � � � � � � � � ? � 6 � ? � � � 6 � � � � � � � � � � � 7 � � � � � � � � � � 1 � � ~ � � � � � � � � � � � � � � 6 � � � � � � � � � � � � � � � � � � � - 4 � � � � � � 6 � � � � � � � � � 6 � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � 1 � � � � � �� � � � � � � 6 ? � � � � � � � � � � � � � � � � 7 � � � � � � � � � � � � � � � � � � � � -3 � � � � � � � � � � � � � � � � ? � � � � � ? � � � � � � � � � � � � � � 6 � 6 �� � � $ + � � " � � % � + � + $ � � , � " % � $ � $ ( ( � � $ � % & % � ' & � " ' $ � ! $ � $ ! " % , & � % � � " � � " ' � " ' ( % + � � ' % � $ ' �� $ ( � $ � � � " � � % � + � + $ � � , � " % � $ � $ ( ( � � $ � % & $ � � � + ! ' % & � % � ' & � " ' $ � ! $ � $ ! " % , & � % � � " � � " ' � " ' ( % + � ~ � � � -= � � ( + % ( % ( & � ( ' ( " % " � " % , $ ' � ! ! ' % + " ! " % , ( � & � � � � ! $ + + " � & � % � " % � % � � $ + � � " � � % � % � % ( % & � + � $ % $ � " � " % ,? � � � � � � � � � ? � � � � � -4 � � � � � � � � � � � � � � � � � 6 � 6 � � B � 5 � � � � � � 6 � �� % � � " � � " ' � $ ! ! � + $ ! , + � � " + � � , % � $ � � � " ! $ % " & ' �� % � ( $ � % , � $ ! % & + ! � & ( ' � , % � � ( + � ( % $ � � " ( � " ' � $ � $ + ' " ' � � " � " % � & + % � � � $ ' ( " & ' � $ ! % & + ! � & ( ' �� % � � $ ( ( & � % � ( � $ � � ( % ( $ � � � % & � � " � � � � � � + $ � � � " ! $ � � � �� % � � $ ( ( & � % � % ( % � " � � % � ( � � � � + $ � � � " ! $ � � � ��   ¡ ¢ £ ¤ ¥ ¦ § ¨ § ¦ © ¦ ª ¥ § « ¤ £ ¬ ­ ¥ ® § ¢ § ® ¯ £ § ° ¨ ° ¢ ¯ ª ¥ § « ¤ § ¨ « § ¨ ¬ £ ± © ¦ ¥ ¨ £ § ¬ ¨ ° £ ² ¨ ° ª ¨ ³ § £ ® ¯ ¨ ´ ¥® ¯ µ ® © µ ¯ £ ¥ ¶ ¢ ± ° ¦ § £ ¬ ± ¥ ­ ¥ ¯ £ ¯ ´ § µ § £ · ¬ ­ ¥ ® § ¢ § ® ¯ £ § ° ¨ ³ ¯ ® ® ° ± ¶ § ¨ « £ °

mmin = (k/Areq)·sRP

³ ª ¤ ¥ ± ¥Areq

§ ¬ £ ¤ ¥ ± ¥ ¸ © § ± ¥ ¶ ª ¥ § « ¤ § ¨ « ¯ ® ® © ± ¯ ® · ³k

§ ¬ £ ¤ ¥ ¥ ¹ ­ ¯ ¨ ¬ § ° ¨ ¢ ¯ ® £ ° ± ³ ¯ ¨ ¶sRP

§ ¬ £ ¤ ¥ ¬ £ ¯ ¨ º¶ ¯ ± ¶ ¶ ¥ » § ¯ £ § ° ¨ ° ¢ £ ¤ ¥ ± ¥ ­ ¥ ¯ £ ¯ ´ § µ § £ · ¼

Page 3: A Risk Based Approach to Select and Test Weighing Instruments

½d e f g h i j k h lm n o o p n q o r p n s r

¾ u ¿ À ¿ Á Â Ã Ä Å Ä Æ x Ç ¿ Ã È É Ã Å È Ê Å Ë Â y v w ¿ Å ÂÌ Í Î Ï Ð Ñ Ò Ó Ô Ò Õ Ö Ó × Ø Ù Ú Û Ø Ò Ñ Ü Ö Õ Ó Ø Ö Ý� � � � � � � � � � � � � � � � � ? � � � � � 6 � � � � � � � � Þ - � � �� � � � � � � � � � � � � � � � � � � � � � � � 6 � � � � 1 1 � � � � � � � -� � � � � � � � � � � � � � � � � � � � � � � � � � 6 - � � � � � ? � � � � � � � � � � 7 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �? � � � � 1 � � � � � � Þ Þ � � 6 � � 6 � � � � � � � � Þ - � � � � � � � � � � � � � � � � � � } � 6 � � � � � � � � � � � � � � ß � � � � � � � �Þ - � � à - 4 � � � � � � � � � � � � 1 � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � 6 � � � � � � � � � � � � � � � � � � � � � � � � 7 � � } � � � � � �� � � ? � � � � � � � � � � � � � -4 � � � � � � � � } � � � 1 � � 1 � � � � � � � 7 � � � � � � � 6 � � � � � � 1 � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � 1 � � � � � ~� $ ' ! � = � � & ( % " � � & + % $ ' % $ + + � $ % $ � " � " % , � á â � � ! ! ' % + " ! " % , � ã � � � ' & ' � " ' $ + " % , � ä å � $ ' � ( ' ( " % " � " % , � � ã � � æ & �6 � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � 6 � � � � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � ç4 � � � ? � � � � � � 7 � � � � � � � � � � � � � � ß ? � � � � � � � � � � � � � � � � � à � � � � � � � � � � 6 � � � � � � � 6 - 4 � � ß � � � � � � � � � � � è � � � � � � �� � é � � � � � � � � à ê è � é ë 6 � � � � � � � � � � � � � � � � � 1 � � � � � ? � � � � � 0 1 � � � � � � � � � 6 � � 1 � � � � � � � � � � � } � � � � � � � ~� � � � � � � -4 � � ? � � � � � � � � � � � � � � � � � � � - � - � � � � � � � � � � � � � � ? � � � � � � A � � � � � ? � � � � � 6 � � ? � � � � � � � � � � � � � � � � � � � � �� � � � � � 6 � � � � � � � 1 � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � ? � � � 1 � � � � � � � � 6 � � � � � 7 � � � � � ~� � � � � � � � � � � � � � � � � � � � � � � � � ? � � � � � � ? � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � ? � � � � � � � � � � � � � � � 1 � � ~� � � � � 7 � � � � � � � � � � � � 1 � � � � � � � � 7 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � - 4 � � � � � � � � � � � � � � � � � � � � � � � �! & � � " ' � $ ! ! & + � " ' � % & ( % $ % " ( % " ! $ � � % � & � ( % & & � % $ " ' % � � " � � " ' � � ' ! + % $ " ' % , ì í * î ï �* ' ! + % $ " ' % , ! $ ' � � � + ( ( � " % � + $ ( ( % $ ' � $ + � � ' ! + % $ " ' % ,u

� � � � � � � 1 � � 6 � � � � � � � � � � � 6 � 6 6 � } � � � � � � � � � ~� � � � � � � 1 � � � � � � � � � � � � 0 1 � 6 � 6 � � � � � � � � � �U ð � - 4 � � � � � � � � � � 0 1 � 6 � 6 � � � � � � � � � � � � � � � � � 6 � 6 � � � � � � � � � � � � � � � � � � � 1 � � � 6 ? � � � � � � � 0 1 � � � � � � � � � �k

- 3 � � � � � � � � � ? � � � � � � � � � � � � � � � } � � � � � � � � � � � ? � � � � ? � � �� � � � � � 6 � � � � 6 � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � 1 � � � � � � � � � � � -ñ   ¯ µ ¬ ° ± ¥ ¢ ¥ ± ± ¥ ¶ £ ° ¯ ¬ ò © ¨ ® ¥ ± £ ¯ § ¨ £ · § ¨ £ ¥ ± » ¯ µ óRelative Weighing Uncertainty

0.0001

0.001

0.01

0.1

1

1E-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

Sample Mass mS [g]

Various Balance Models, Without Tare Load (@ k=2)

Rela

tive

Expanded W

eig

hin

g U

nce

rtain

ty

U [%

]

XP6U

XP26

XP205

XP204

XP1203S

XP4002S

XP10001S

XP64000L

ô õ ö ÷ ø ù ú û ü ù ý þ ÿ õ � ù � ù õ ö � õ � ö ÷ � � ù ø ÿ þ õ � ÿ õ ù � � � � þ ø õ � ÷ � � þ ý þ � � ù � � ø � þ � ÷ ý ÿ ø þ � õ � ø � � þ ý þ � � ù � õ ÿ � þ ø ù þ � þ � õ ý õ ÿ � � � � ú � ö ÿ � þ� ø ù � õ � õ � � � þ ý þ � � ù � õ ÿ � ú ö � � � � � � õ � ÿ � ù ø ù ý þ ÿ õ � ù ÷ � � ù ø ÿ þ õ � ÿ U � õ � � � � ù ø � ÷ � � þ � ý ù þ � �

mS � � � � � � � � � � � ! � � � � " ! � �ù � ÿ õ þ ÿ ù � � ø � ÿ � õ � þ ý � � ù � õ � õ � þ ÿ õ � � � � � ÿ � ù � þ ý þ � � ù � þ � � þ ø ù ù # � þ � � ù � � õ ÿ � þ � þ � ÿ � øk

$ % & ' � ( ( � ! " " ) * + � , � , - . � � , ! � �ý � þ � � õ � ù � ö ø � � � ý � þ � / � þ � ý ù þ � � � �

Page 4: A Risk Based Approach to Select and Test Weighing Instruments

0 d e f g h i j k h lm n o o p n q o r p n s r

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º§ ¬ ¤ ± ¥ « § ° ¨ ³ ¬ ¥ ¨ ¬ § £ § » § £ · ° ± ¥ ® ® ¥ ¨ £ ± § ® § £ · § ¨ « ± ¥ ¥ ¨ § ¬ ¤ ± ¥ « § ° ¨ ¼� � � � � � � 6 � 6 � � � 6 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � } � � � � � � � �� � � � � � � � � � � � 6 � � � - � � � � � � � � � ß 1 � � � � � � � à � � - � - � � � � � � � � � � � � � � � � � � } � � � � � � 0 � � � � � 1 � � � � � 6 � � � � � ~� � � � � � ? � � � � � � 6 � 1 � � 6 � � � � � � � � � 6 � � � � � � � � � - 4 � � � � � � � � � � � � � � � � � � � � � � � � } � � � � � � � � � � � � � } � � � �� � � � � � � � � � ? � � � � � � � � � 6 � } � 6 � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � ? � - 4 � � � � � � � � � � � � � � � � � � � � � � � � � �� 1 � � � � � � � � � � 1 � � � 6 � � � � � � � � � 6 � � � � � � � � } � � � � � � � � �� - 8 � � � � � � ? � � � � 1 � � � � � � � � � � � � � � � � � � ? � � � � � � � } � � � � � � � � ] � � � � � � � Þ � � � � � � � � 0 1 � � ^ � � � � � ~� � ? � � � � � � � � � � � � ? � � � � � � � � � � � � } � � � � � � � � � � � � � 6 � � � � � 6 � � � � 1 � � � � � � � � - @ � � � 1 � � � � � � � � � � ? � �� � � � � � � � � � � � � � � � � 6 � � � � � � � � � � � � � � � � } � � � � � � � � � � � 6 � � � � � � � � � } � � � � � � 1 � � 1 � � � � � � � � � � � � � 1 � � � � - - 8 � � � � � ? � � � � 1 � � � � � � � � � � � � � � � � � � 1 1 � � � � � � � } � � � � � � � � _ � � � � � � � Þ Þ � � � � � � � � 0 1 � � ` � �� � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � } � � � � � � � � � � � � � 6 � � � � � 6 � � � � � � � � � } � � � � � � � � � � � � � � � � � � � � � � � � � � � a � -= � + � $ % " � � ' ! + % $ " ' % " ( & � % � ( � + & � + % " ( $ + " ' � � ' � ' % & � ( $ � � � � & $ � � ! & ' ( � � ' % � , � % � ! & � � " ' �� � � � � } � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � -/ - 8 � � � � � / � � � � � � � � � � � � � � � � � � � � ? � � � � 1 � � � � � � � � � ? � � � � � � � � ? � � � 6 � 1 1 � � � � � � � } � � � � � � � � � ? � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � } � � � � 1 � � 1 � � � � � � � � � � � � � � � � � � � } � � � -é � � � � } � � � � � � � � � � � � � � � � 6 � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � � � � � � � � � } � � � � � � � � � � � � � } � � � � �� � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � b � -c ` c d V V H L Q I O Y V Q E { H Y H P Q O G H I J K I L J | L V Q N W \ H L Q� � � � � � � � � � � � � � � � � 6 � � 6 ? � � � � � � � � � ? � � 6 � � � � � � � ? � � � � � � � � � � � � � � � 7 � � � � 6 � � � � 1 1 � � � � � � � � � 6 � � � � � � � � � � � 1 � � � � � � ? � � � � � 6 � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � 6 �e   f ¯ ± « ¥ ¬ £ ¬ ¯ ¦ ­ µ ¥ ¦ ¯ ¬ ¬ ³ ¯ £ ª ¤ § ® ¤ £ ¤ ¥ ® ° ¨ £ ± § ´ © £ § ° ¨ ° ¢ ± ¥ ­ ¥ ¯ £ ¯ ´ § µ § £ · ¶ ° ¦ § ¨ ¯ £ ¥ ¬ © ¨ ® ¥ ± £ ¯ § ¨ £ · ¼g   h ¤ ¥ » ¯ µ © ¥ « § » ¥ ¨ i j k « l ¢ ° ± £ ¤ ¥ µ ° ª ¥ ± ± ° µ µ ° » ¥ ± µ § ¦ § £ ¦ ¯ ¬ ¬ § ¬ » ¯ µ § ¶ ¢ ° ± £ ¤ ¥ ¯ ¨ ¯ µ · £ § ® ¯ µ ´ ¯ µ ¯ ¨ ® ¥ ³ £ ¤ ¥ © ¨ ® ¥ ± £ ¯ § ¨ £ · ° ¢ª ¤ § ® ¤ § ¬ ¶ ¥ ­ § ® £ ¥ ¶ § ¨ ¢ § « ¼ m ¼ n £ ¤ ¥ ± ª ¥ § « ¤ § ¨ « § ¨ ¬ £ ± © ¦ ¥ ¨ £ ¬ ª § µ µ ¥ ¹ ¤ § ´ § £ ° £ ¤ ¥ ± µ § ¦ § £ ¦ ¯ ¬ ¬ ¥ ¬ ¼o   p ¦ ¯ µ µ ¥ ¬ £ ¬ ¯ ¦ ­ µ ¥ ¦ ¯ ¬ ¬ ³ ¯ £ ª ¤ § ® ¤ £ ¤ ¥ ® ° ¨ £ ± § ´ © £ § ° ¨ ¬ ° ¢ ¬ ¥ ¨ ¬ § £ § » § £ · ° ¢ ¢ ¬ ¥ £ ¯ ¨ ¶ ¥ ® ® ¥ ¨ £ ± § ® § £ · ¶ ° ¦ § ¨ ¯ £ ¥ © ¨ ® ¥ ± £ ¯ § ¨ £ · ¼q   h ¤ ¥ » ¯ µ © ¥ « § » ¥ ¨ i j k k « l ¢ ° ± £ ¤ ¥ © ­ ­ ¥ ± ± ° µ µ ° » ¥ ± µ § ¦ § £ ¦ ¯ ¬ ¬ § ¬ » ¯ µ § ¶ ¢ ° ± £ ¤ ¥ ¯ ¨ ¯ µ · £ § ® ¯ µ ´ ¯ µ ¯ ¨ ® ¥ ³ £ ¤ ¥ © ¨ ® ¥ ± £ ¯ § ¨ £ · ° ¢ª ¤ § ® ¤ § ¬ ¶ ¥ ­ § ® £ ¥ ¶ § ¨ ¢ § « ¼ m ¼ n £ ¤ ¥ ± ª ¥ § « ¤ § ¨ « § ¨ ¬ £ ± © ¦ ¥ ¨ £ ¬ ª § µ µ ¥ ¹ ¤ § ´ § £ ° £ ¤ ¥ ± µ § ¦ § £ ¦ ¯ ¬ ¬ ¥ ¬ ¼r   s « ¯ § ¨ ³ £ ¤ § ¬ § ¬ ¶ ¥ ­ ¥ ¨ ¶ ¥ ¨ £ ° ¨ £ ¤ ¥ ¦ ° ¶ ¥ µ ° ¢ ª ¥ § « ¤ § ¨ « § ¨ ¬ £ ± © ¦ ¥ ¨ £ t £ ¤ ¥ ± ¥ ¯ ± ¥ ´ ¯ µ ¯ ¨ ® ¥ ¬ ³ ª ¤ ¥ ± ¥ ¥ ® ® ¥ ¨ £ ± § ® § £ · § ¬ ¶ ° ¦ § º¨ ¯ ¨ £ ¯ ¨ ¶ ¬ ¥ ¨ ¬ § £ § » § £ · § ¬ ° ¢ § ¨ ¢ ¥ ± § ° ± § ¦ ­ ° ± £ ¯ ¨ ® ¥ ¼u   T @ 2 D E < C A I = M 6 = 5 4 6 L I 5 < ; ; ? 6 2 3 @ 2 A 3 2 A D = 5 4 E 6 A = D 7 v I ? 6 > 6 5 R = @ 6 F 5 I M < M 2 ; 2 = C = @ < = = @ 2 D < F F ; 2 6 D L I 5 < E < w I 5 2 = C I L§ ¨ ¬ £ ± © ¦ ¥ ¨ £ ¬ § ¬ ± ¯ £ ¤ ¥ ± ¤ § « ¤ ¼

Relative Weighing Uncertainty

0.00001

0.0001

0.001

0.01

0.1

1

0.01 0.1 1 10 100 1000

Sample Mass mS [g]

U_tot

U_RP

U_EC

U_NL

U_SE

Model XP204 Individual Uncertainty Contributions (@ k=2)

Rela

tive

Expanded W

eig

hin

g U

nce

rtain

ty U

[%

]

Page 5: A Risk Based Approach to Select and Test Weighing Instruments

xd e f g h i j k h lm n o o p n q o r p n s r

� - 4 � � � 1 � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 7 � � � � � � � � � � � � � � � � � � � � � 6 � � - � - � � � � � � � � � � � � � � � � 6 � 6 � � � � 1 � � � � � � � � � � � 6 � � � � � � � 6 � � 6 � � � � � 1 1 � � � � � � � - - 4 � � � � � � � � � � � � ? � � � ? � � � � � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � � � � 7 � � � � � � � � � � � � � � � � 7 � � � � 6�Areq

� � � � � � � � � � y � 1 1 � � � � � � � -� � ? � � � � � � � � � � � � � � � � � � � � � � � � � � ? � � � � 6 � � � � � � � � � � � � � 1 � � � � � 1 � � � � � � � � � � � � � � � 1 1 � � � � � � � - 4 � � � � � � � 6� � � 6 � � � � � � � � � � � � � ? � � ß � � � � ? � � � � � � � � 6 � � � � � à - 3 � � � � � � 1 � � � � � � � 1 � � � � � � � � � � � � � 6 � � � � ~� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 7 � � � � 6 � � � � � � � � � � � � � 6 � ~� � � � � � � � � � � � � � � � 6 - 4 � � � � � � � � � � � � � � � � � � � � 6 � � � ß � � � � � 1 � � ? � � � � � à � � � � � 1 � � ß � � � � ? � � � � � à - � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � ? � � � � � � � � 6 � � � � � � � 6 � � � � � 1 � � � � � � � � - z � � � � � � � � � 1 � � ? � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � �sRP

� � � � � � � � � � � � � � � 1 � � 1 � � � � � � ? � � � � � � � � � � � ? � � � � � 6 � 1 � � 6 � { � - mmin = (k/Areq)·sRP .@ � 6 � � � � � � � 6 � � } � � � � � � � � � � � � � � 6 � � � � � � � � � 6 � � � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � 1 � � � � � � � � � � � 6 � 1 � � 6 � � � � � � � � � � � � � � � ? � � � � � � 1 � � � � � � -c ` | d } O \ Z Y H� � & & � ! & � � $ ' , ' � ( $ � $ � $ ' ! � & + % � " + ~ � � � $ + % � ' % � � % $ ( � ! " � " ! � & " ' % " ' % � " ( � + & ! ( ( � % � � $ ( ( & � ( $ � ~1 � � � � � � � � Þ � � � � � � 6 � � � � � � � 6 ? � � � � � � � � } � ? � � � � � � � � � � � � � � � � � - 4 � � � � � � � � � 6 � � � � � � � 6� � � � Þ � - � � � � � � � � � � � � � � � � � 1 1 � � � � � � � ç3 � � � � � � � � � } � � � � � � � � � � � � � � � � 6 � 6 � � � � � � � � � � ? � � � � 1 � � � � � � � � Þ � � � � � � � � � � � � � � � 6 � � � ~ � ? � � � � � � 1 � � � � � � � � Þ � � � � � ? � � � � � � � � � � � � 6 � 6 � � � � � � � � � 1 1 � � � � � � � -� � � � � � � � � ? � � � � � � � � � � � � � � � ? � � � 6 � � � � � � � � ? � � � � � � 7 � � } � � � � � � 1 � � � � � � � � � � � � � � � � � � � 6� � � � � 6 - � � � � � � 0 1 � � � � � � � � � � � �

k � � � 6 � � � � � 7 � � � � 6 � � � � � � � � � � � � � � � 7 � � } � � � � � � 7 � � � � 6 � � 1 � � � � � ~� � � � �sRP = mmin

�Areq� k

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Page 6: A Risk Based Approach to Select and Test Weighing Instruments

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Page 7: A Risk Based Approach to Select and Test Weighing Instruments

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Page 8: A Risk Based Approach to Select and Test Weighing Instruments

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� § « ¼ ü ½ � ¾ ± ¥ ® ° ¦ ¦ ¥ ¨ ¶ ¬ £ ª ° £ ¥ ¬ £ ª ¥ § « ¤ £ ¬ ¼ h ¤ ¥µ ¯ ± « ¥ ª ¥ § « ¤ £ ¤ ¯ ¬ ¦ ¯ ¬ ¬ ® µ ° ¬ ¥ £ ° £ ¤ ¥ ¨ ° ¦ § ¨ ¯ µ® ¯ ­ ¯ ® § £ · ° ¢ £ ¤ ¥ ª ¥ § « ¤ § ¨ « § ¨ ¬ £ ± © ¦ ¥ ¨ £ ³ ª ¤ § µ ¥£ ¤ ¥ ¬ ¦ ¯ µ µ ª ¥ § « ¤ £ ¯ ¦ ° © ¨ £ ¬ £ ° ¯ ¢ ¥ ª ­ ¥ ± ® ¥ ¨ £° ¢ £ ¤ ¥ ¨ ° ¦ § ¨ ¯ µ ® ¯ ­ ¯ ® § £ · ¼ h ¤ ¥ µ ¯ ± « ¥ ª ¥ § « ¤ £ § ¬© ¬ ¥ ¶ £ ° £ ¥ ¬ £ ¬ ¥ ¨ ¬ § £ § » § £ · ¯ ¨ ¶ ¥ ® ® ¥ ¨ £ ± § ® § £ · ³ £ ¤ ¥¬ ¦ ¯ µ µ ¢ ° ± ± ¥ ­ ¥ ¯ £ ¯ ´ § µ § £ · i § ¢ ± ¥ ¸ © § ± ¥ ¶ ³ £ ° « ¥ £ ¤ ¥ ±ª § £ ¤ ¯ ¨ ¯ ¶ ¶ § £ § ° ¨ ¯ µ £ ¯ ± ¥ ¦ ¯ ¬ ¬ l ¼

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Æ þ ý þ � � ù Ç � � ù ý È ! + ! � � É ü ù þ � þ � õ ý õ ÿ Ê þ ø ö ù Ë ù õ ö � ÿ � þ ý ý Ë ù õ ö � ÿÌ Í Î � � � ú ö � � ú � ö x ö c � � öÏ Ð c � c c ö ú � ö c � ö ú öÏ Ð c � x c c � ö ú � � ö c � � ö ú � öÏ Ð c � 0 c c � ö � � ú ö c � � ö ú � öÏ Ð ú c � ½ � ú � c ú Ñ ö ú ö ú Ñ ö x � öÏ Ð 0 � � c � 0 � ú Ñ ö ú � ö c Ñ ö c � � öÏ Ð ú � � � ú � ú � � ú Ñ ö � � ú ö ú � Ñ ö x � � öÏ Ð � 0 � � � Ê � 0 � ú Ñ ö ú ö x � Ñ ö c Ñ öh ¯ ´ µ ¥ j t � ¹ ¯ ¦ ­ µ ¥ ¬ ° ¢ ´ ¯ µ ¯ ¨ ® ¥ ¦ ° ¶ ¥ µ ¬ ¯ ¨ ¶ ± ¥ ® ° ¦ ¦ ¥ ¨ ¶ ¥ ¶ £ ¥ ¬ £ ª ¥ § « ¤ £ ¬ ¼

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ú � d e f g h i j k h lm n o o p n q o r p n s r

8 � } � � � � � � � � � � � 0 1 � � � � � � � 6 � � � 6 � � � � � � � � � � � � � � � � � � � � 7 � � � � � � � � � � � � � � } � ? � � � � � � � � � � � � � � �Areq = 1%,? � � � � � � � � � � 1 � � � � � �

mS,min = Ò Ó Ô Õ � � � � � � � � � � � � � SF = Ò � � 6 � � 0 1 � � � � � � � � � � � �

k = Ò � � � � � � ? � � � � � � � � � 1 � � � � � � Ò Ó Ó Õ ? � � � � � � � - @ � � � � 6 � � � � � � � � � � � � � � � � � � � � ? � � � � � � � � � � � ? � � � � � � �

mT = Ò Ó Ó Õ � � 6 � � � ? � � � � � � � Ö Ó Õ � : � � � � � � � 6 � � � � � 6 � � � � � � � � � � � � � � � - 4 � � ? � � � � � � � � � � � � � � � � � � � � � �� � � � � � � } � � � � 6 � � � � � � � � � � � � � �∆WL = ½(mT·Areq/SF) = ½(200 g·1%/2) = 0.5 g

�? � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � � �sRP|WL = mS,min (Areq/k)/SF = 20 mg(1%/2)/2 = 0.05 mg

� � � � 6 � 6 6 � } � � � � � � -× Ø Ù Ú Û Ü Ý Þ ß à á â Ø ã à ã Þ Û ã ä Þ å Þ æ ã æ ç Ú è Ú ã Ù é@ � 1 � � � � � 6 � � � � � } � � � � � A � � � � � � � ? � � � � � � � � � � � 1 � � � ? � � � � � � � 1 � � � - 4 � � � � � � � � � � � � � � � � � ~� � � � ? � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � } � � � � � � � � � � 0 1 � � - � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � 1 � � � � � � � � ? � � � � � � � ? � � � � � � � � � � � � 6 � � � � � � ? 1 � � � � � � � � � � � � 1 � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � 6 � 6� � � � � � � 0 � ? � � � � � 6 � � � � � � � � � - � � � � � � � 1 � � � � � � � � � � � � � � � � � � � 6 � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � 6 �% � " ( " ' ! + $ ( " ( � ( � $ � � , � � � � $ � $ ! % & + & � � � + & � � + & � & $ � % & ' & � " ' $ � ! $ � $ ! " % , ð ` � � � & + � $ � � � � ä � + % � � ( ( �� � 1 � � � � � � � � � � � � � � � 6 � 6 � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � ? � � � � � � � � - � - � ? � � � � � � � � ? � � � � � � � � � � � 6 � � � � � � � 6 � � � � � � � � � � � � � � � � � � � 6 � � � � � � � � � � � � � � � 6 � � � � � 0 � � � � � � � � � � � � � � � � � � � � � � 1 � � � � � � � � -4 � � � � � � � � 6 � 1 � � � � 6 � � � � � � � � : - � � � � � � � � � � � � � � � � � � � � � � � � � � � � 6 � � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1 � � ? � � � � � � � � � 1 � � 6 � � � � � � 1 � � � � � �� � � � � � � � � � ð a � -� � � � 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 6 � � � � � 1 � � � � � � � � � � A � � � � � � � � � � � � � } � � � � � � � � � � � � � � - � � � � � �? � � � � � � � 1 � � � � � � 6 � � � � � � � � 1 � � � � � � � � ? � � � � � � � � � � ? � � � � � � � � � � ß ? � � � � � � 1 � � � � à - ð b �ê ë ì í î ï ð ë ñ ò ó ï ó ò ô ò õ ñ ó ö ë ð ÷ ñ ø ñ ð ñ ù ò ó ï ñ ø õ ó ð ë î ð ñ ú ð õ ñ ó ö ë ð û î ù ö ñ ù ð ë î ï ð ë ñò ó ï ó ò ô ò õ ñ ó ö ë ð üz � 6 � � � � � � � � � � � � � � ? � � � � � � � � � � � � ? � � � � � � � � � � 1 � � � � � � � � � � � ? � � � � � 6 � � � 1 � � � � � ? � � � � � } � � � � 7 � � � � 6 ? � � � � � � � � � � � � � - 4 � � � � � � � } � � � � � � � � 6 � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � ? � � � � �? � � � � � � � � � � � � 0 1 � � � � 6 � � � � � ? � � � � � � 6 6 � � � � � � � � � � � � 1 � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � ? � � �� � � � � � � � ? � � � � � - � � � � � � � � � � � � � � ? � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 7 � � � � 6 � � � � � � � � � � � � � � � � � � 1 � � � � � � � � �� � � � � � � � � � � � � � � � � � � � -4 � � � � � � � 6 � � � � } � � � 6 � � 6 } � � � � � -3 � � � � � � � � � � � � � � 1 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � 7 � � � � � � � � - 4 � � � � 6 � � � � � � � � � � � � � � � � � � � � � � 6 � � � � � � 1 � � � 6 ? � � � � � � � � � � � � ? � � � � � -� � � � � 6 � � � � � � � � � � � � � � � � � � � � � � � � � 6 � � � � � � 1 � � � 6 � � � � � � � � � � � � � � � ? � � � � � � � � � � � � ? � � � � � - � � � � � � � � � � �� � � � � � � � � � 7 � � � � � � � � � � � } � 1 1 � � � � � 6 � � 6 � � � � � � � � � � � � � � � A � � � � � � � � � � � � � - 4 � � � � � ? � � � � �� � � � � � � � � -m ý l « ± ° ¬ ¬8 þ K D 6 6 < ; D I P Z U ÿ O 8 � O � � � 6 2 3 @ 2 A 3 I A < A � A < ; C = 2 B < ; � < ; < A B 6 � R J 5 < L = 5 6 > 2 D 2 I A U 1 � � G 8 K� � < 5 B @ � � F 5 2 ; 8 N N R T < M ; 6 O 9 � Z 4 3 3 6 D = 6 J U 6 5 L I 5 E < A B 6 � 4 < ; 2 L 2 B < = 2 I A T 6 D = D �m � l ¡ £ ¬ ¤ ° © µ ¶ ´ ¥ ¦ ¥ ¨ £ § ° ¨ ¥ ¶ ¤ ¥ ± ¥ £ ¤ ¯ £ ¨ ° £ ° ¨ µ · £ ¤ ¥ ¦ ¯ ¬ ¬ ° ¢ ¯ £ ¯ ± ¥ µ ° ¯ ¶ ³ ´ © £ ¯ µ ¬ ° § £ ¬ ¶ § ¦ ¥ ¨ º¬ § ° ¨ ¬ ¦ ¯ · § ¨ ¢ µ © ¥ ¨ ® ¥ £ ¤ ¥ ± ¥ ­ ¥ ¯ £ ¯ ´ § µ § £ · ° ¢ £ ¤ ¥ ª ¥ § « ¤ § ¨ « ¼ n ¨ ¯ ¨ � � m k � ¬ ¥ ¦ § ¦ § ® ± ° ´ ¯ µ º¯ ¨ ® ¥ ³ ¢ ° ± ¥ ¹ ¯ ¦ ­ µ ¥ ³ ± ¥ ­ ¥ ¯ £ ¯ ´ § µ § £ · § ¨ ® ± ¥ ¯ ¬ ¥ ¬ ¯ ´ ° © £ � £ § ¦ ¥ ¬ ª ¤ ¥ ¨ ª ¥ § « ¤ § ¨ « ¯ ¬ ¯ ¦ ­ µ ¥ § ¨ £ °¯ » ° µ © ¦ ¥ £ ± § ® ¢ µ ¯ ¬ ² ° ¢ m � k ¦ µ ³ ® ° ¦ ­ ¯ ± ¥ ¶ £ ° ª ¥ § « ¤ § ¨ « £ ¤ ¥ ¬ ¯ ¦ ­ µ ¥ £ ° « ¥ £ ¤ ¥ ± ª § £ ¤ ¯ ® ° ¦ º­ ¯ ® £ £ ¯ ± ¥ ° ¢ £ ¤ ¥ ¬ ¯ ¦ ¥ ¦ ¯ ¬ ¬ ¯ ¬ £ ¤ ¥ ¢ µ ¯ ¬ ² i ¯ ± ° © ¨ ¶ � k « l ¼ p ¥ ¥ ¯ µ ¬ ° j � ¼

Page 11: A Risk Based Approach to Select and Test Weighing Instruments

ú úd e f g h i j k h lm n o o p n q o r p n s r

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Page 12: A Risk Based Approach to Select and Test Weighing Instruments

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Page 13: A Risk Based Approach to Select and Test Weighing Instruments

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Page 14: A Risk Based Approach to Select and Test Weighing Instruments

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Page 15: A Risk Based Approach to Select and Test Weighing Instruments

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Page 16: A Risk Based Approach to Select and Test Weighing Instruments

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