I have some 2 drugs that I want to determine their nature of interaction against a tropical disease parasite. I need to plot an isobologram to achieve this. How do I go about doing this?
hello
following the 8 steps below you will have a robust way to monitor the stability of your process.
1. Determine Sample Plan
Determine the sample size, n, and frequency of sampling. Consider the cost of sampling, required resources, and balance with minimizing time (and produced units) between measurements. Of course, more samples and more frequent measurements is better statistically.
2. Collect initial set of samples
Shewhart recommended 100 individual units in 25 samples of 4 each. Basically, we want enough samples to create reasonable estimates of the mean values of ˉX and R. Keep the data in time sequence following the time of the sample selection, which should be in the same order of manufacture.
3. Calculate ˉX
Calculate the average for each set of samples. This is the ˉX for each sample.
4. Calculate R
Calculate the range of each set of samples. This is the difference between the largest and smallest value in the sample.
5. Calculate ˉˉX
Calculate the average of the ˉX’s. This is the centerline of the ˉX control chart.
6. Calculate ˉR
Calculate the average of the R values. This is the centerline of the R control chart.
7. Calculate Control Limits
First, calculate the R chart limits.
UCLR=D4ˉR
LCLR=D3ˉR
Note: for a sample size, n, of less than 7 the lower limit is zero.
The D3 and D4 constants are found in tables or calculated with the following formulas.
D3=1−3d3d2
D4=1+3d3d2
where,
d2=∫∞−∞[1−(1−αl)n]dxl
d3=√2∫∞−∞∫xl−∞[1−αnl−(1−αn)n+(αl−αn)n]dxndxl−d22
and,
αl=1√2π∫xl−∞e−(x22 )dx
αn=1√2π∫xn−∞e−(x22 )dx
n = sample size
A Table of Constants speeds up the calculations.
n
A2
D3
D4
2
1.880
0
3.267
3
1.023
0
2.575
4
0.729
0
2.282
5
0.577
0
2.114
6
0.483
0
2.004
7
0.419
0.076
1.924
8
0.373
0.136
1.864
9
0.337
0.184
1.816
10
0.308
0.223
1.777
Be sure to plot the data on the R chart and if not in control, before continuing with building the control chart, work to bring the variability of the process under control.
For the ˉX chart limits use
UCL=ˉˉX+A2ˉR
LCL=ˉˉX−A2ˉR
where,
A2=3d2√n
8. Plot the data
With the control limits in place, gather samples, and plot the data. Look for special or assignable causes and adjust the process as necessary to maintain a stable and in control process.
formulas from 2002, Manual on presentation of data and control chart analysis, ASTM International, West Conshohocken, PA.
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