Suppose the accuracy of a compounder was described as ±5% or ±10%. What does this mean to you? In many ways, this description is lacking. First, what percentage of dispenses would you expect to be in this range? Is it 100%? Is it 50%? Does this statement describe the typical performance or a guaranteed level of performance such as a design requirement? How are the accuracy measurements to be made? Differences in interpretation and expectations can lead to different individuals having widely different views as to what an accuracy statement like ±5% or ±10% really means and whether such a claim is met. This article clarifies the assumptions associated with an accuracy statement and describes how compounder accuracy relates to the total system accuracy.

**ASSUMPTION 1: Percentage in Interval**

For many, the natural interpretation is that 100% of dispenses would fall within the interval as shown to the left. However, when performing accuracy measurements, a histogram of the values tend to take the shape of a bell-shaped curve called the normal distribution as shown below.

There is no interval that contains 100% of dispenses. There are intervals that come close such as containing 99.999% or all but 1 in 100,000. The following accuracy statements are roughly equivalent:

±3% contains 50% of dispenses

±10% contains 99% of dispenses

±18% contains 99.999% of dispenses.

An accuracy statement that does not specify the percentage of dispenses it contains has little meaning.

**ASSUMPTION 2: Typical Performance or Design Requirement**

An accuracy statement also means little if it is not stated how this accuracy statement is to be verified. If the accuracy statement is intended to reflect typical performance, it represents the performance of across a large pool of compounders. Individual compounders may perform slightly better or worse. If the accuracy statement is intended as a design requirement, then each individual compounder is expected to meet this requirement. The difference between these two interpretations can be huge.

Suppose a design spec of ±15% is set for accuracy. Each individual compounder is expected to meet this requirement. To pass final acceptance, the compounder is tested to demonstrate with 95% confidence 99% of dispenses are within this range. Compounders that have accuracies of ±15% or worse are expected to fail. Compounders that pass must exceed this requirement. Occasionally a compounder may pass that barely meets this requirement. However, most compounders that pass exceed this requirement. The typical performance of the released compounders might meet an accuracy range of ±10% or better.

**ASSUMPTION 3: Measurement Method**

Determining compounder accuracy requires the ability to measure the delivered dosage. The delivered dosage can be measured based on the solution weight, solution volume, a chemical assay of concentration using any number of ingredients as well as several other methods. The estimated accuracy is really a combination of the compounder accuracy and the measurement accuracy. If the measurement errors are small relative the compounder accuracy, the resulting estimated accuracy will accurately reflect the compounder’s performance.

It is assumed that accuracy statements like ±5% or ±10% are for the actual delivered dosage. Some measurements methods will actually measure a larger percentage of units outside these limits than truly are. Thus verification that an accuracy statement is met should be based on a measurement method whose error is considerably less than the compounder accuracy or the estimate of compounder accuracy should be corrected to account for measurement error.

**COMPLETE SPECIFICATION FOR ACCURACY**

A complete specification of accuracy should include a clear definition and a stated method for verifying accuracy including:

- The percentage of values expected to be within this interval
- A statement as to whether it is for typical performance or for a guaranteed level of performance such as a design specification.
- The method of measurement

Without this level of detail, controversy will continue on how to interpret it, how to verify the accuracy statement is met, and whether certain suppliers of equipment do or do not meet the stated accuracy claim.

**TOTAL SYSTEM ACCURACY**

A compounder is part of an overall system for ensuring the right dosage is delivered to the patient. The accuracy required of the compounder can only be addressed in the context of its effect on the total system accuracy. The total system consists of:

- Patients
- Metabolism
- Condition

- Patient Blood Values
- Sampling Accuracy
- Lab Testing Accuracy
- Time Delay

- Prescription
- Right Dosage to Have Desired Effect
- Prediction of Change in Clinical Status
- Prediction of Interactions

- Formulation
- Compounded Volume
- Source Solution Concentration of Ingredients

- Amount of Solution Delivered to a Patient
- Rate Accuracy
- Total Time
- Therapy Interruptions

To determine the total system accuracy based on the accuracy of the individual components, the root-sum-of-squares formula shown below is used.

For example, suppose there are 5 components; 4 which accuracies of ±10% and one with an accuracy of ±20%. Then the total system accuracy is:

When improving system accuracy, attention must be focused on the largest components. For example, assume it was possible to reduce the accuracy of one of the ±10% components to ±5%. Then the new total system accuracy would change to:

This result is little overall improvement. Specifying the required accuracy for a component should be done in light of its effect on total system accuracy. Specifying an accuracy for a component of less than half the total system accuracy generally does little to improve the overall system accuracy.

**Presented at 39th ASHP Midyear Clinical Meeting, December 2004**

**Copyright © 2004 Taylor Enterprises, Inc.**

#### Further information can be found in:

- Book: Optimization and Variation Reduction in Quality
- Book: Statistical Procedures for the Medical Device Industry, STAT-11, Statistical Techniques for Setting Specifications
- Blog Category: Spec Setting, Tolerance Analysis and Robust Design