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# Procedure for calibration of calculator. Quality assurance

• Procedure for calibration of calculator. Quality assurance
• OBJECTIVE
• To lay down the Procedure for Calibration of calculator.
• SCOPE
• This SOP provides guidance to calibrate the calculators, which are used for simple and complex calculations of analysis in quality control department.
1. Scientific calculator
2. Desktop calculator
3. Calculator used in the computer (Windows Version 98, 2000, 2003, XP both standard and scientific)
• RESPONSIBILITY
• Officer/ Executive – Quality Control
• ACCOUNTABILITY
• Manager QC/QA
• PROCEDURE
• Before starting the calibration check the operation of calculator as per manufacturer’s manual.
• Calibrate the calculator for Subsraction (-), Addition (+), Multiplication (X), Division (÷), Square root (√), Logarithmic function (log), Inv (log) or Anti (log), Standard deviation (sd), Memory functions (M+, M, MRC), Percentage (%).
• Verify the functions calculated using calculator with manual calculations.
• Verify Substraction using input values as given below and report the result in annexure – 1
654 – 321.
• Verify Addition using the set of values given below and report the result in annexure – 1
123456789 + 987654321.
• Verify Multiplication using the set of values given below and report the result in annexure – 1
a) 12345679 X 8
b) 12345679 X 9.
• Verify Division using the input values of 22 ¸ 7 and report the displayed value in annexure – 1.
• Press ‘p’ key and report the displayed value in annexure – 1. (This test is significant in verifying the standard values           that are stored in calculator’s memory).
• Verify Square root (Ö) function using logarithmic tables and anti-log tables.

the reference equation used for manual calculation is
ÖX  =  Y                        applying log. on both sides,

½ log X = log Y           applying anti – log on both sides            anti log (½ log X) = antilog (log Y).

• The log. Values for reference are enclosed
• The complex functions like logarithmic and anti-log functions are counter verified in the square root function itself.
• For calculation consider √100 and report the values in annexure – 1.
• Verify standard deviation function using the input values as 1,2,4,4,4.
• For manual calculation of standard deviation use the following formula
• Std.deviation  =
• • Where x = individual sample, ∑ x2  = sum of squares of x, n = sample size, (∑x) 2 = square of sum of individual sample.
• Upon simplifying the equation the result yields √2 = 1.4142 (this requires logarithmic application).
• Verify Sequential group calculations like multiplication, division, subsraction and additions using the known conversion factor (°F – 32) (5/9) = °C. Verify the values of 0°F, 32°F, 77°F, 104°F, 140°Fand report the results in annexure –1.
• Further verify the group calculation using the conversion factor of (9/5)°C+ 32 = °F verify the values of  -20°C, 0°C, 25°C, 40°C, 60°C and report the results in annexure –1.
• (Note: Compare the values with USP 28 pharmacopoeia under reference tables – thermometric equivalents (Centigrade to Fahrenheit.)
• Verify the memory functions M+ and Mby using the set of values as given below, for M+ follow the steps    1   M+ ⇒ 2  ⇒  M+   ⇒     3   ⇒    M+  ⇒   4   ⇒   M ⇒   5.
• Press Memory recall (MRC) to review the final result and enter the details in annexure – 1
• Verify Memory functions in M using the following set of values  1  ⇒   M –   ⇒  2 ⇒  M  ⇒   3  ⇒   M –⇒ 4  ⇒  M  ⇒  5.
• Press Memory recall (MRC) to review the result and enter the details in annexure – 1.
• Verify the percentage (%) calculations by applying the following values 1/1 x % =. Enter the details in annexure – 1

Table 1
Acceptance Criteria For Calibration Parameters

 S.NO TEST PARAMETER ACCEPTANCE CRITERIA TOLERANCE 1 Subsraction 333 – 2 Addition 1111111110 – 3 3.1 Multiplication 98765432 – 3.2 Multiplication 111111111 – 4 Division 3.1428 – 5 ‘p’ Value 3.141592653589793238… Up to digits of Calculator 6 Square root 10 – 7 Standard deviation 1.4142 – 8 Group calculations 8.1 0°F -17.78°C 32°F 0.00°C 77°F 25.00°C 104°F 40.00°C 140°F 60.00°C 8 Group calculations 8.2 -4.0°C 24.8°F 0°C 32.0°F 25°C 77.00°F 40°C 104°F 60°C 140°F 9 9.1 M+  calculation 15 – 9.2 M–  calculation -15 – 10 Percentage 100 –
• Forms and Records (Annexures)
• Calibration format for calculator – Annexure-1
• Distribution
• Master copy –  Quality Assurance
• Controlled copies- Quality Assurance, Production, Quality Control.engineering
• History
 Date Revision Number Reason for Revision – 00 New SOP

Annexure-1

Calibration format for calculator

• Substraction:
• by calculator: 654 – 321 =
• b) manual calculation: 654 321(-)
• Acceptance criteria: display value and calculated value = “333”
• Addition:

a) by calculator:   123456789 + 987654321 =                                                                        .
b) manual calculation:

123456789

987654321 (+)

• Acceptance criteria: display value and calculated value = “1111111110”
• Multiplication:

a) by calculator:  12345679 x 8 =

b) manual calculation: 12345679 x 8

• Acceptance criteria: display value and calculated value = “98765432”

a) by calculator:  12345679 x 9 =

b) manual calculation: 12345679  x 9

Acceptance criteria: display value and calculated value = “111111111”

Division:

a) by calculator:   22 ÷ 7  =

b) manual calculation: 7)  22  (
(calculate upto 5th decimal)

• p” value:
• by calculator: p =
• Reference value: p =
• (B.P 2004- volume IV Supplementary Chapter IV G A 525)
• Acceptacne criteria:  p = 3.141592653589793238… ( match upto decimal indication of calculator)
• Square root:
• a) by calculator:   Ö 100  =
• b) manual calculation: Ö 100  =   x  ( upon applying  “log” on both sides)
• ½ x  log (100)    =       log( x )
• log(100)  (y)    =  (by using logarithmic table)
• ½ x  (y)   =  log( x )
• anti- log [½ x  (y)]    =  x  (by using anti-logarithmic table)   =  x
• Acceptance criteria: result is      “10”
• Standard deviation:
• a) by calculator:   press mode & to shift into standard deviation mode.
• Input values  = 1 shift M+ , 2 shift M+          , 4 shift M+ , 4 shift M+, 4 shift M+.
• 1. Shift ‘n’       =
• 2. Shift Sx2   =                  ( sum of squares of all sample)
• 3. Shift (Sx)2  =                 (square of sum of all sample)
• 4. n x Shift (Sx)2  =            (n= sample size)
• standard deviation = ( upon using the equation)
• calculated value  =
• manual calculation:                                                               (x)²
• input values are                           1                                               1 x 1   =

2                                                2 x  2  =

4                                                4 x 4   =

4                                                4 x 4   =

(+) 4                                       (+) 4 x 4   =

• (Σx)      sum of sample                                              Σx²  sum of squares
• (Σx)²    square of sum of sample  =
• Upon introducing the values in the above formula =
• standard deviation (s) = Ö x  =  log (s) = ½ x log( x )  = (s)  = anti log{½ x log( x )}  =
• (note: use logarithmic and anti- log tables for calculations)
• Group Calculations:
• A) (°F- 32) ( 5/9) = °C
• by calculator:
• for input values of ° F    0°F  =  °C,     32°F =  °C, 77°F = °C, 104°F = °C, 140°F = °C.
• b) manual calculations: (°F- 32) ( 5/9) = °C ( simplify the equation into i) °F –32  ii) 5/9
( the value of 5/9 is considered for calculations is 0.555556)
• For input value  0°F      i)  °F – 32 =  __________ ;
• (°F- 32) ( 5/9) = ___________________°C
• For input value  32°F      i)  °F – 32 =  __________ ;
•  (°F- 32) ( 5/9) = ___________________°C
• For input value  77°F      i)  °F – 32 =  __________ ;
• (°F- 32) ( 5/9) = ___________________°C
• For input value  104°F      i)  °F – 32 =  __________ ;
• (°F- 32) ( 5/9) = ___________________°C
• For input value  140°F      i)  °F – 32  = __________ ;
• (°F- 32) ( 5/9) = ___________________°C
• Acceptance criteria: values should match with values in table –1 of SOP BA(II)QA414-00 up to two digits.
• (9/5)°C + 32 = °F
• by calculator:
• for input values of ° C    -20.0°C  = °F,     0°C = °F, 25°C =  °F,  40°C = °F, 60°F =°F.
• b) Manual calculations:
(9/5)°C + 32  = °F (simplify the equation into i) 9/5 ii) (9/5) x °C iii) (9/5) x °C + 32
(the value of 9/5is considered for calculations is 1.8)
• For input value  -20°C     i) 1.8 x – 20°C = __________ ;
• (1.8 x – 20°C) + 32  = ___________________°F
• For input value 0°C     i) 1.8 x 0°C = __________ ;
• (1.8 x 0°C) + 32  = ___________________°F
• For input value 25°C     i) 1.8 x 25°C = __________ ;
• (1.8 x 25°C) + 32  = ___________________°F
• For input value 40°C     i) 1.8 x 40°C = __________ ;
• (1.8 x 40°C) + 32  = ___________________°F
• For input value 60°C     i) 1.8 x 60°C = __________ ;
• (1.8 x 60°C) + 32  = ___________________°F.
• Acceptance criteria: values should match with values in table –1 of SOP BA(II)QA414-00 up to two digits.
• Memory functions:1) M+ calculations:  a) by calculator:
•  input values are 1,2,3,4,5 ( at each entry press M+)
• Result is (MRC) = _______________________________.
• b) manual calculation: 1+2+3+4+5 = _______________________________.
• 2) Mcalculations:
• a)by calculator:
• input values are 1,2,3,4,5 ( at each entry press M-)
• Result is (MRC) = _______________________________.
• b) manual calculation: 1+2+3+4+5 = _______________________________.
• Percentage Calculations:
• a) by calculator:
• input values are 1 ÷ 1 (press %) =  _______________________________.
• b) Manual calculations:
• input values are   1 ) 1  (
• result  = —————- x 100 = —————–.
• Remarks: the calculator is calibrated/ not calibrated and approved for usage/ not to be used.
• Next calibration due on : ——————————

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