Numworks (Python): Control Charts

 Numworks (Python): Control Charts

The following Python script develops the x-bar and R control charts.

Formulas used:

mean_average = Σ(mean of each sample)

range_average = Σ(range of each sample)

x-Bar Chart:

low = mean_average - a2 * range_average

high = mean_average + a2 * range_average

R chart:

low = d3 * range_average

high = d4 * range_average

Python script (done with Numworks): ctrlchart.py

from math import *

# control chart function

# run as a defined function

# HP 65 Stat Pac 2, 1975

def ctrlchart():

  #elements

  a2=[0,0,1.88,1.02,.73,.58,.48,.42,.37,.34,.31,.29,.27,.25,.24,.22,.21,.20,.19,.19,.18]

  d3=[0,0,0,0,0,0,0,.08,.14,.18,.22,.26,.28,.31,.33,.35,.36,.38,.39,.4,.41]

  d4=[0,0,3.27,2.57,2.28,2.11,2,1.92,1.86,1.82,1.78,1.74,1.72,1.69,1.67,1.65,1.64,1.62,1.61,1.6,1.59]

  # calculation

  meansum=0

  rangesum=0

  n=int(input("number of samples? "))

  m=int(input("sample size (2-20)? "))

  for i in range(n):

    x=[]

    for j in range(m):

      # adjust to show proper numbering

      s="x("+str(i+1)+","+str(j+1)+")? "

      p=eval(input(s))

      x.append(p)

    rangesum+=max(x)-min(x)

    meansum+=sum(x)/m

  rangeavg=rangesum/n

  meanavg=meansum/n

  lowmean=meanavg-rangeavg*a2[m]

  highmean=meanavg+rangeavg*a2[m]

  lowrange=d3[m]*rangeavg

  highrange=d4[m]*rangeavg

  print("x-bar chart")

  print("L: "+str(lowmean))

  print("H: "+str(highmean))

  print("range chart")

  print("L: "+str(lowrange))

  print("H: "+str(highrange))

Example 1:

5 samples (n = 5)

Sample size: 4  (m = 4)

Sample 1:  4.3, 4.2, 4.3, 5.0

Sample 2:  4.1, 4.1, 4.6, 3.6

Sample 3:  4.0, 4.5, 4.3, 3.7

Sample 4:  3.9, 4.7, 4.4, 5.1

Sample 5:  4.2, 5.2, 4.9, 5.3

x-Bar chart:

Low:  3.7046

High:  5.1354

R chart:

Low:  0

High:  about 2.2345

Example 2:

2 samples (n = 2)

Sample Size: 7 (m = 7)

Sample 1:  48, 58, 53, 56, 57, 59, 55

Sample 2:  56, 46, 48, 49, 63, 52, 51

x-Bar chart:  

Low:  47.33428571428571

High:  59.09428571428571

R chart:

Low:  1.12

High: 26.88

Source

“x-bar and R Control Charts”. HP 65 Stat Pac 2. Hewlett Packard. 1975. pp. 98 – 101

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Dozenal RPN Calculator App for Android for Android Smartphones and Numworks Beta Firmware Version 25

 Dozenal Calculator App for Android Smartphones and Numworks Beta Firmware Version 25

Dozenal Calculator App for Android Smartphones

The Dozenal RPN Calculator app is by Unum Designum for the Android smartphones. It is a classical, four-level stack RPN (Reverse Polish Notation) app that operates in both dozenal (i.e. duodecimal, Base 12) and decimal (Base 10). The calculator app features a standard set of scientific functions:

* arithmetic, square, square root

* sin, cos, tan, and inverses

* e^x, 10^x, ln, log

* DMS/Decimal conversions and HMS/Hours conversions (not sure how there are two sets, since they seem to do the same thing)

* Pol/Rect conversions

* percent function (%)

* Stack functions: roll down, roll up, swap, last x

Originally Released: July 1, 2020

Last Updated: December 17, 2025 (as of January 22, 2026)

Version I am reviewing 1.0.11

The polar/rectangular conversions follow the conventional RPN calculator format:

	Rectangular	Polar
Y Stack:	Y	Θ
X Stack:	X	R

The percent function follows the conventional RPN calculator format:

	Before	After
Y Stack:	Y	Y
X Stack:	X	Y * X ÷ 100

However, the decimal/DMS (decimal-minute-seconds) and hours/HMS (hours-minute-seconds) follow up this format:

	Decimal/Hours	DMS/HMS
Z Stack:	0 after conversion	seconds
Y Stack:	0 after conversion	minutes
X Stack:	decimal/hours as a decimal	decimal/hours

Conversion between bases is just a matter of pressing [ f ] [ DOZ/DEC ].

Symbols:

* Upside down 2 (↊) represents 10 (Unicode 218A); commonly symbolized by X

* Backwards 3 (↋) represents 11 (Unicode 218B); commonly symbolized by E

(Unicode is from Wikipedia: https://en.wikipedia.org/wiki/Duodecimal)

Two constants provided by the Dozenal RPN app:

	Base 10 (e: 10^n)	Base 12 (e: 12^n)
π	3.141592653589793	3;184809493↋9186459↊↊
Planck	6.6206070149999999e-34	1;↊79611175↊0925342846e-27

App information: https://play.google.com/store/apps/details?id=dozecal.unumdesignum.com&hl=en_NZ#/

Numworks: Beta Firmware 25

Version 25 Information: https://www.numworks.com/calculator/update/version-25/

Nuwmorks has released a firmware update 25.1. It is a beta version software where new features are tested. To try it, Numworks is inviting Numworks users to download and become a beta test or us the beta emulator on the Numworks website.

Verison 25 Beta Emulator: https://www.numworks.com/calculator/update/version-25/

Please keep in mind that this emulator is probably only available for the testing period and may become unavaiable once the official release is made.

Major updates include:

* Data in the Statistics app can either be qualitative (data points, the way the statistics mode was always used) or categorial (data points always belong to specific categories, up to 10)

* The Grapher app can shade area of intersection for a given set of inequalities.

* The Grapher app also finds intersection points of conic sections and vertical lines.

* In the Calculations app, results with five or more decimal place will have at least a fractional approximation in the Additional Results quick tab.

* The degree and radian symbol/indicators are added to the Toolbox.

* Sequences have new notations.

* Installing this version will limit roll back deinstalls to versions 24.11 or later.

No word on any additions or changes to the Python app.

I have installed version 25 on my older Numworks calculator (N0110) so I can try them out.

HP 12C Platinum: RC Series Circuit Analysis

HP 12C Platinum: RC Series Circuit Analysis

The program was originally posted on the Museum of HP Calculators website (https://www.hpmuseum.org/forum/thread-24591-post-215436.html#pid215436).

A difference between the HP 12C Platinum and the HP 12C Classic is that the Platinum has a square function (x²). The square function is the g-shifted (blue) of the multiplication key.

Introduction and Program Code

Given the following of a RC series circuit:

Stack Z: E: voltage of the RC circuit

Stack Y: R: resistance of the resistor (R) in ohms (Ω)

Stack X: Xc: equivalent resistance of capacitor (Xc) in ohms (Ω)

What is calculated:

Stack Z: equivalent impedance of the RC series circuit in ohms (Ω), Z = √(R^2 + Xc^2)

Stack Y: current in amps (A), I = E ÷ Z

Stack X: true power in watts (W), P = I^2 * R

Program Code:

x^2	001	43, 20	beginning of the program
x<>y	002	34
STO 0	003	44, 0	store resistor
x^2	004	43, 20
+	005	40
√x	006	43, 21
PSE	007	43, 31	show impedance
ENTER	008	36
R↓	009	33
÷	010	10
PSE	011	43, 31	show current
ENTER	012	36
x^2	013	43, 20
R↓	014	33	stack manipulation (014 – 018)
R↓	015	33
x<>y	016	34
R↓	017	33
R↓	018	33
RCL 0	019	45, 0
×	020	20
GTO 000	021	43, 33, 000	finish program, show power

Example

E = 150 V

R = 19 Ω

Xc = 10 Ω

Results (to four decimal places):

Z ≈ 21.4709 Ω

I ≈ 6.9862 A

P ≈ 927.3319 W

Source

Noll, Edward M. Basic Electronics Math With a Scientific Calculator Howard W. Sams & Co, Inc. Indianapolis, IN. 1977. 0-672-21425-3 pp. 81-98

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

RPN: HP 11C: Transferring Between Bases (Common/Natural)

RPN: HP 11C: Transferring Between Bases (Common/Natural)

All algorithms were tested with the HP 11C.

Between the Exponential Function and Common-Antilog

e^α = 10^ß

Given α, what is ß?

ß = log(e^α)

RPN:

<input α>

e^x

LOG

Examples (Fix 6):

e^1.05 = 10^ß

ß ≈ 0.456009

e^(-2.2) = 10^ß

ß ≈ -0.955448

Given ß, what is α?

α = ln(10^ß)

RPN:

<input ß>

10^x

LN

Examples (Fix 6):

e^α = 10^5.4

α ≈ 12.433960

e^α = 10^0.366

α ≈ 0.842746

Between the Natural Logarithm and Common Logarithm

log α = ln ß

Given α, what is ß?

ẞ = exp(log α)

RPN:

<input α>

LOG

e^x

Examples (Fix 6):

log 17 = ln ß

ß ≈ 3.422766

log 317 = ln ß

ß ≈ 12.195405

Given ß, what is α?

α = 10^(ln ß)

RPN:

<input ß>

LN

10^x

Examples (Fix 6):

log α = ln 425

α ≈ 1,127,428.915

log α = ln 9.81

α ≈ 192.044677

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Spotlight: Casio fx-451 Calculator

Spotlight: Casio fx-451 Calculator

Quick Facts

Model: fx-451

Company: Casio

Type: Solar Scientific Algebraic

Memory: 1 (store, recall, exchange (X←→M), sum (M+), subtract (M-))

Years in Production: 1985 to 1987 per calculator.org (https://www.calculator.org/calculators/Casio_fx-451.html)

Display: 10 digits

Casio Ledudu’s page on the fx-451: https://casio.ledudu.com/pockets.asp?lg=eng&type=1016

Folding Calculator Power

The Casio fx-451 is a folding scientific calculator. On the left side, there are the arithmetic keys, the shift, mode, and on keys, the display (10 digits), and the solar panel that operates the calculator. The right side has touch, rubber-like, membrane keys. The right side has all the scientific, statistical, fraction, base conversion, and imperial/metric conversions.

You can see my review of the fx-450 from 2018 here: https://edspi31415.blogspot.com/2018/07/retro-review-casio-fx-450-calculator.html

The available modes for the fx-451 are:

. (decimal point): SD (Standard Deviation), single variable statistics. Statistics functions are marked in blue.

0: DEC. Decimal mode. This is also the calculator’s normal/computation mode.

1: BIN. Binary integer mode (base 2). Boolean logic operators are available and are marked in green.

2: OCT. Octal integer mode (base 8). Boolean logic operators are available and are marked in green.

3: HEX. Hexadecimal integer mode (base 16). Boolean logic operators and the letter digits A-F (A=10 to F=15), are available and are marked in green.

4: DEG. Degree angle mode.

5: RAD: Radians angle mode.

6: GRA: Gradians angle mode.

7: FIX: Fixed point decimal setting

8: SCI: Scientific notion decimal setting.

9: NORM: Floating point decimal setting. Numbers less than 0.01 are shown in scientific notation form.

The engineering keys, [ENG] and [←ENG], temporarily show the number in display using scientific notation where the exponents are in multiples of 3 (i.e. 10^-6, 10^-3, 10^0, 10^3, 10^6, etc.)

Like many Casio scientific calculators, the fx-451 sports the fraction key [a b/c], allowing both entry of fractions (proper and mixed), and conversions between fractions and decimal approximations.

In addition, the fx-451 has nine scientific constants. (by pressing [SHIFT] [1-9]).  The constants are:

1. Speed of Light (c)

2. Plank’s constant (h)

3. Universal gravitational constant (G)

4. Electron charge (e)

5. Mass of an electron (me)

6. Atomic mass constant (u)

7. Avogadro’s constant (Na)

8. Boltzmann constant (k)

9. Molar volume of ideal gas (Vm)

All units are in SI units, and are listed with the constant on the keyboard.

The fx-451 Adds Imperial/Metric Conversions

(fx-450 (top), fx-451 (bottom))

The fx-451 is a later version of the fx-450 and has added a set of eight imperial/metric conversions:

Temperature: degrees Fahrenheit/Celsius

Length: inches/millimeters

Volume: gallons/liters, ounces/grams

Mass: pounds/kilograms

Energy: calories/Joules

Pressure: inches of Mercury/kilopascals, atm/megapascals

Conversions are called by the two arrow keys [ ← ] and [ → ], and are they are marked in gold. I always find conversions to be a welcome addition to any calculator.

Solar Power

Like it’s cousin, the fx-450, the fx-451 operates only by solar and light power, hence no other batteries are required.

This is a fun calculator to have, and Casio does a really good job of including lots of features even in its basic scientific calculators.

Eddie

All original content copyright, © 2011-2026. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.