Procedure for calibration of the calculator
OBJECTIVE
To lay down the Procedure for Calibration of the calculator.
SCOPE
This SOP provides guidance to calibrate the calculators, which are used for simple and complex calculations of analysis in the quality control department.
Scientific calculator
Desktop calculator
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 the calculator as per the 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^{–}, M^{RC}), Percentage (%).
Verify the functions calculated using a calculator with manual calculations.
Verify Subtraction using input values as given below and report the result.
Verify Addition using the set of values given below and report the result –123456789 + 987654321.
Verify Multiplication using the set of values given below and report the result
a) 12345679 X 8
b) 12345679 X 9.
Verify Division using the input values of 22 ¸ 7 and report the displayed value.
Press the ‘p’ key and report the displayed value. (This test is significant in verifying the standard values that are stored in the calculator’s memory).
Verify the 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
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.
Verify the standard deviation function using the input values as 1,2,4,4,4.
For manual calculation of standard deviation using the following formula
Std. deviation =
Where x = individual sample, ∑ x^{2 } = sum of squares of x, n = sample size, (∑x)^{ 2 }= square of the sum of an individual sample.
Upon simplifying the equation the result yields √2 = 1.4142 (this requires logarithmic application).
Verify Sequential group calculations like multiplication, division, subtraction, and additions using the known conversion factor (°F – 32) (5/9) = °C. Verify the values of 0°F, 32°F, 77°F, 104°F, and 140°Fand report the results.
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, and 60°C and report the results in annexure –1.
(Note: Compare the values with USP 28 pharmacopeia under reference tables – thermometric equivalents (Centigrade to Fahrenheit.)
Verify the memory functions M^{+ }and M^{– }by 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 (M^{RC}) 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 (M^{RC}) 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 | Subtraction | 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 a 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
- Subtraction:
- by the 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 the calculator: 12345679 x 8 =
b) manual calculation: 12345679 x 8
- Acceptance criteria: display value and calculated value = “98765432”
a) by the calculator: 12345679 x 9 =
b) manual calculation: 12345679 x 9
Acceptance criteria: display value and calculated value = “111111111”
Division:
a) by the calculator: 22 ÷ 7 =
b) manual calculation: 7) 22 (
(calculate upto 5^{th} decimal)
- “p” value:
- by the calculator: p =
- Reference value: p =
- (B.P 2004- volume IV Supplementary Chapter IV G A 525)
- Acceptance criteria: p = 3.141592653589793238… ( match upto decimal indication of the calculator)
- Square root:
- a) by the 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: the result is “10”
- Standard deviation:
- a) by the calculator: press mode & 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 Sx^{2} = ( sum of squares of all samples)
- 3. Shift (Sx)^{2 }= (square of the sum of all samples)
- 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 the table –1 of SOP BA(II)QA414-00 up to two digits.
- Memory functions:1) M^{+ }calculations: a) by the calculator:
- input values are 1,2,3,4,5 ( at each entry press M^{+})
- The result is (M^{RC}) = _______________________________.
- b) manual calculation: 1+2+3+4+5 = _______________________________.
- 2) M^{– }calculations:
- a)by the calculator:
- input values are 1,2,3,4,5 ( at each entry press M-)
- The result is (M^{RC}) = _______________________________.
- b) manual calculation: 1+2+3+4+5 = _______________________________.
- Percentage Calculations:
- a) by the 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: ——————————