Spotlight: Calculated Industries QR Calc <Title>
Quick Facts
Model: 3375
Name: QR Calc
Company: Calculated Industries
Timeline: 1993
Type: Quality Control, Statistics
Operating System: Algebraic
Digits: 7
Memory: 1 general purpose memory register plus specific variable registers
Power: 1 CR-2032 battery
When I purchased the QR Calc, there was no manual with it. Normally, it wouldn’t present any issues because I can often find manuals online. That is not the case with the QR Calc. If there is any manual online, please email me. I’ll have to be more careful next time.
I apologize that I will not be able to describe all the functions but hopefully I describe enough features to give the reader a general idea. Please check out the sources below.
Features
Let’s start with the mathematical functions included: powers and roots (y^x, x². √), natural logarithm (ln), exponential function (e^x), reciprocal (1/x), arithmetic (+, -, ×, ÷), and the standard percent key which operates they people expect it to (%). The order of operations is enforced. Like a lot of calculators, the change sign (+/-) key is a shifted function.
The operating range of the calculator is 7 digits: -9,999,999 to 9,999,999. Any calculator that has a result outside of this range causes the QR calculator to display an error message.
The store key for the QR Calc is labeled [ Set ].
The function →PPM changes any number into n parts per million.
Example: 0.0014 →PPM displays 1,400 PPM.
Here are some functions I was able to find out and figure out:
Normal Distribution
The normal distribution functions calculate areas of the standard normal distribution, assuming that μ = 0 and σ = 1.
n [ nZ ]: lower tail probability (from -∞ to x = n)
n [ 2nd ] (ModZ): probability from x = 0 to x = n
One Variable Statistics
The QR handles a single set of statistics with the following key and key sequences:
[ Add ]: Add a data point (Σ+)
[ 2nd ] [ Add ] (Subtract): Subtract a data point (Σ-)
[ 2nd ] [ + ] (S←→P): Toggle between standard deviation and population deviation (σn indicator)
[ x-bar ]: Calculate the arithmetic mean.
[ R ]: Calculate the range of the data.
[ 2nd ] [ x-bar ] (N): Calculate the number of data points.
[ 2nd ] [ R ] (σ): Calculate the deviation, depending on the deviation mode set.
[ Low ]: Returns the minimum value of the data set entered.
[ 2nd ] [ Low ] (High): Returns the maximum value of the date set entered.
[ Skew ]: Skew. I’m not sure what formula the QR Calc uses because I have not been able to match results with any formula I found yet.
[ 2nd ] [ Skew ] (Kurt): Excess Kurtosis. Kurtosis measures how concentrated the data is with respect to the mean.
The formula used for Excess Kurtosis:
μ4 = 1/n * Σ((xi – mean)^4)
kurtosis = μ4/s^4 – 3
Process Capability Indices
If a process is mature, that is a process that is regular and has been executed for a period of time, we can measure the capability index.
There are two capability indices:
Cp: for a centered analysis
Cpk: for a non-centered analysis. This metric is used for potential future performance.
Generally, we want these indices to be at least 1. Capable processes have an Cp index of 1.33 or higher.
Key strokes:
Enter the mean: [ Set ] [ x-bar ]
Enter the deviation: [ Set ] [ 2nd ] [ R ] ( σ )
Enter the lower specification limit (based on the normal distribution): [ Set ] [ LSL ]
Enter the upper specification limit: [ Set ] [ 2nd ] [ LSL ] (USL)
Each variable entered will have an indicator.
Calculate Cp: [ 2nd ] [ Cpk ] (Cp)
Calculate Cpk: [ Cpk ]
Example:
LSL = - 1, USL = 1, mean = 0.05, deviation = 0.27
[ 2nd ] [ × ] (AC) to clear out the registers if needed
0.5 [ Set ] [ x-bar ] (x-bar indicator is on)
0.27 [ Set ] [ 2nd ] [ R ] ( σ ) (σ indicator is on)
1 [ 2nd ] [ - ] (+/-) [ Set ] [ LSL ] (L indicator is on)
1 [ Set ] [ 2nd ] [ LSL ] (USL) (U indicator is on)
Results:
Cp: 1.234568
Cpk: 1.17284
That is a pretty good process.
Formulas Used:
Cp = (USL -LSL) / (6 * σ)
Cpx = min((x-bar – LSL) / (3 * σ), (USL – x-bar) / (3 * σ))
Control Charts
We get to the main feature of the QR Calc: Control Charts and Capability Limits. On the back of the calculator, the QR Calc has a list of handy formulas.
The heart of the QR Calc is the table of constants that are used in control charts and limit charts. Often the chart limits are built on many samples of n data points each, where x-bar is the average of the sample averages, and R is the average of the range samples. We can also build chart limits with one sample. The QR Calc can only handle sample sizes from 3 to 25 data points.
Mean Control Chart Limits:
Lower: LCL-mean = x-bar – n * A2 * R
Upper: UCL-mean = x-bar + n * A2 * R
R Control Chart Limits:
Lower: LCL-R = n * D3 * R
Upper: UCL-R = n * D4 * R
A2, D3, and D4 are constants used in calculating control chart limits. Accessing these constants takes one argument, which is the sample size.
The A2 constant for a sample size of 3: 3 [ nA2 ] returns 1.023.
Below is a short table of constants, as determined by the QR Calc.
Sample Size n |
Constant A2 |
Constant D3 |
Constant D4 |
5 |
0.577 |
0 |
2.114 |
10 |
0.308 |
0.223 |
1.777 |
15 |
0.223 |
0.347 |
1.653 |
20 |
0.18 |
0.415 |
1.585 |
25 |
0.153 |
0.459 |
1.541 |
Standard deviation can be estimated by using the average range ( R ) and another constant d2:
σ ≈ R / d2
Sample Size n |
Constant d2 |
5 |
2.326 |
10 |
3.078 |
15 |
3.472 |
20 |
3.735 |
25 |
3.931 |
A table of constants from n = 2 to 25 can be found here:
https://sixsigmastudyguide.com/x-bar-r-control-charts/
Example:
Construct mean and range charts from a sample (n = 5):
3.995 |
4.26 |
4.37 |
4.44 |
4.58 |
Keystrokes:
(after clearing data)
3.995 [ Add ] 4.26 [ Add ] 4.37 [ Add ] 4.44 [ Add ] 4.58 [ Add ]
X-bar chart:
LCL: [ x-bar ] - 5 [ nA2 ] [ × ] [ R ] [ = ] Result: 3.991455
UCL: [ x-bar ] + 5 [ nA2 ] [ × ] [ R ] [ = ] Result: 4.666545
R chart:
LCL: 5 [ 2nd ] [ nD4 ] (nD3) [ × ] [ R ] [ = ] Result: 0
UCL: 5 [ nD4 ] [ × ] [ R ] [ = ] Result: 12.36669
The QC calc has contains the E2 constant.
Final Thoughts
The functions that I still do not know about or have figured out are: TRGa, TRGb, RS a, RS b, %Low, and %High.
This review is incomplete. I will keep searching for a manual, I may have to buy another QR Calc.
This calculator is a rarity, and one worth checking out.
Sources
Hessing, Ted. “Process Capability (Cp & Cpk)” 6σSTUDYGUIDE.COM (no specific date give, first comment on November 19, 2014) https://sixsigmastudyguide.com/process-capability-cp-cpk/. Accessed January 2025.
Hessing, Ted. “X Bar R Control Charts” 6σSTUDYGUIDE.COM (no specific date give, first comment on April 17, 2018) https://sixsigmastudyguide.com/x-bar-r-control-charts/. Accessed January 2025.
Hewlett Packard. HP-65 Stat Pac 2 Cupertino, CA. https://literature.hpcalc.org/items/975 1975
Next time, I’m going to see if a manual comes with it. Not everything has a manual online.
Eddie
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