Paste batch or test results in time order to draw an individuals and moving range (I-MR) control chart. You get the mean, ±3σ control limits, automatic Nelson-rule signals, summary statistics, and Cpk/Ppk against your specification limits. It is ideal for APQR trending and continued process verification.
What is an individuals (I-MR) control chart?
A control chart plots results in time order against a centre line (the mean) and upper and lower control limits. These limits are calculated from the data’s own variation. The individuals and moving range (I-MR) chart is used when you have one result per batch or per time point. That is typical in pharma: one assay, dissolution or hardness result per batch. Points inside the limits with no unusual patterns indicate a stable process. Signals show that something has changed and should be investigated.
Control limit formulas
Centre line (CL) = x̄ (mean of the individual results)
Moving range MRi = |xi − xi−1| · MR̄ = average moving range
σwithin = MR̄ ÷ 1.128
UCL = x̄ + 3σwithin = x̄ + 2.66 MR̄ · LCL = x̄ − 2.66 MR̄
MR chart: UCLMR = 3.267 MR̄
1.128 is the d2 constant for moving ranges of 2 consecutive points.
Control limits describe what the process does. Specification limits describe what the product must meet. They are different things: a process can be in control yet produce out-of-specification results, or meet specifications while being out of control.
Signals to investigate (Nelson rules)
| Rule | Pattern | What it may mean |
|---|---|---|
| 1 | One point beyond the 3σ control limits | A special cause affecting one batch or result |
| 2 | 9 points in a row on the same side of the centre line | A shift in the process mean, for example a new raw material lot, equipment or method change |
| 3 | 6 points in a row steadily increasing or decreasing | A trend, for example column ageing, equipment wear or drift |
| MR | A moving range above 3.267 MR̄ | A sudden jump between consecutive results |
The calculator checks these rules automatically. Other Nelson and Western Electric rules exist. Your trending SOP should define which rules you apply.
Worked example: assay trend for 20 batches
The default data in the calculator are 20 consecutive batch assay results (% of label claim). The mean is 100.15%, MR̄ = 0.72 and σwithin = 0.72 ÷ 1.128 = 0.64. That gives UCL = 100.15 + 3 × 0.64 = 102.07% and LCL = 98.23%. Batch 17 (101.9%) is the highest, but it is still inside the control limits, so there is no signal. Against specification limits of 95.0–105.0%, Cpk ≈ 2.5. That means the process is highly capable.
Process capability: Cpk and Ppk
Cpk = min[(USL − x̄), (x̄ − LSL)] ÷ 3σwithin
Ppk = min[(USL − x̄), (x̄ − LSL)] ÷ 3soverall
Cpk uses short-term (within) variation from the moving ranges. Ppk uses the overall standard deviation. A value of 1.33 or more is a common target. Only interpret capability when the process is in statistical control and the data are roughly normal.
Using control charts in pharma QC
- Annual Product Quality Review (APQR / PQR): trend assay, dissolution, related substances, hardness, weight and yields across batches.
- Continued process verification (Stage 3): monitor critical quality attributes and process parameters after validation.
- Laboratory control: trend system suitability results, check standards and control samples.
- Environmental monitoring and water: microbial counts are usually not normally distributed. Use alert and action limits or charts suited to count data.
Common mistakes
- Using specification limits as control limits.
- Calculating limits from too few points. Use about 20–25 or more results, and recalculate only after a justified, documented change.
- Plotting results out of time order.
- Calculating σ from the overall SD for the I chart. The standard method uses MR̄ ÷ 1.128, which is less affected by shifts.
- Ignoring a signal because the result is still within specification.
Frequently asked questions
How many data points do I need for a control chart?
At least 20–25 results are usually recommended for setting reliable control limits. Fewer points give only provisional limits.
What is the difference between control limits and specification limits?
Control limits are calculated from process data (±3σ) and show natural process variation. Specification limits are set by regulatory or product requirements. A result outside the specification is an OOS result. A point outside the control limits is a process signal.
Why divide the average moving range by 1.128?
1.128 is the statistical constant (d2) that converts the average range of two consecutive points into an estimate of the standard deviation.
Is a Cpk of 1.33 good?
Yes. A Cpk of 1.33 is a widely used minimum target for a capable process, and 1.67 or more is often expected for critical attributes. Always check that the process is in control first.
Related tools and guides
- RSD calculator
- Sample size calculator
- OOS procedure in pharma
- CAPA explained with examples
- Pharmaceutical Lab Toolkit: all calculators
References
- Montgomery DC. Introduction to Statistical Quality Control. Wiley.
- FDA Guidance for Industry: Process Validation: General Principles and Practices (2011).
- ICH Q10 Pharmaceutical Quality System.