Cost Effects of Accuracy, Repeatability, and Resolution

Modern advances in technology have effected the lives of many people in the world today. In some cases this technology has brought about an improved life style, or has changed the manner in which human interrelationships are conducted.


In many instances these new improvements have made it possible for products and services to be delivered more efficiently and with less cost. In some others these changes have added complexity and provide clever marketers the opportunity to justify many unnecessary features and their associated costs. In this article we will consider the overall design goals of the AFAB Enterprises PR-111 In-Line Process Refractometer. We believe that in doing so it will provide us with the opportunity to discuss the effects of Accuracy, Repeatability and Resolution on product cost.

The first section of the definition of our goals was relatively simple.

1. It will be a Refractometer of the critical angle type to provide us with the most flexibility.

2. It will be an in-line continuous measuring system and will be industrially hardened for continuous service on the process plant floor.

3. It should have a 4-20 milliamp output to allow the unit to interface with a PC, PLC, or other SCADA type control or DAQ systems.

4. It should be small and easy to use yet low in cost.

These are the things that we knew about and could manage, but... what about the issues of Accuracy, Repeatability and Resolution? How could it be possible to deal with all of the issues surrounding these variables in one instrument without creating an incredibly complex device?

The accuracy of a device, as you remember from our last article, is defined as the ability of the device to conform to a standard. Refractive Index (RI) is defined as: “The ratio of the velocity of light in a vacuum, to the velocity of light in a material”(usually based on air though, not on vacuum for practical reasons). The change in the angle of the light (velocity change) occurs at the interface of two materials as the light passes between them. There is also an angle of light propagation at which refraction no longer occurs and the light beam is reflected back into the original material. This is called the Critical Angle.

A critical angle refractometer uses this reflected light and focuses it on a measurement cell to determine RI. As the mixture of the material changes so to does the angle of light (RI) change direction. This also changes the amount of reflected light on the measurement cell and thus it’s output signal to the instrument. So the instrument actually infers RI through the changes in reflected light it sees on the measurement cell. Well, having said all of that, one can begin to realize how this measurement can be affected by many independent variables. Some of these are: the intensity of the light source, it’s frequency, temperature of the measured medium (density), the type of materials involved in the medium, the number of different materials involved in the measurement medium etc. Basically, any variable which may cause the light velocity to change, as the light passes between the two mediums. This includes the variable that we want to measure, as well as those that we do not.

Think about the costs associated with putting all that capability into one instrument! Think about the complexity of that instrument! What about the standards that would be necessary for our customers to maintain to insure that the instrument was kept in calibration and the standards we would have to purchase in order to calibrate it in the first place? What about the training requirements for those folks having to interface with this device? A rather costly project to be sure. It would certainly not be easy to use and probably would not be too small. Indeed... not a tool for the plant floor.

If the instrument could be designed as a “specialist” it would make things a lot simpler. This became our focus. To design the instrument so that it could be configured for each application.

1) Calibrate it using a sample of the product (or products if they were similar) to be measured.

2) Calibrate the instrument to the specific range required by each customer.

3) Temperature compensate it for the customer’s operating temperature range.

4) Set the back-scatter compensation to deal with color differences and/or suspended solids in the solution if they were present.

5) Automatic Gain Control (AGC) to handle variations in light intensity (aging of the light source etc.) would be made standard.

We could even conduct product evaluations for our customers before the sale to be sure that our unit would function properly with their process liquid. After all this was going to be an “in-line process Refractometer”. Of course, it should have provisions for re-calibration in the field should our customers choose to do this. Creating a “specialist” instrument like this certainly limited it’s flexibility, (the ability to interface with other mediums without re-calibration) certainly reduced the overall costs of the instrument and indeed made it much easier to use. Because of the experience of our design staff we felt sure that we could provide an accuracy specification of +/- 5% of the instrument calibrated span. We knew that certain non-linear characteristics were inherent with some solutions and that 5% was a realistic number. We also knew that there would be cases where our customers would require the linearization of the measurement response to improve the overall accuracy. We decided to provide this additional measurement capability as an option. We could accomplish this with an add-on instrument utilizing the 4-20 milliamp output provided with the PR-111. This accuracy specification could be set at +/- 1% of instrument span. Added cost to be sure, but not to the basic unit and yet available to those requiring this accuracy.

Repeatability of the instrument now had to be set at better than +/- 1% of instrument span to insure the integrity of the instrument with the improved accuracy specification. This would be made standard with all instruments and all ranges and would not add any significant costs to the design of the instrument.

Measurement resolution could be adjusted to the needs of each customer with out any accompanying cost impact. The strategy would be to adjust the calibrated range of each instrument so that is was as narrow as possible (maximum resolution) yet would be sufficiently wide enough to cover the area of measurement interest.

It was difficult to make the decisions associated with our above goals. “One cannot be all things to all people” it has been said. It was the goal to provide a quality, dependable, low cost instrument that would be easy to install and use. The “specialist “ instrument seemed the right way to go. In each application our customers are faced with a similar decision. What are my exact needs? Specify the operating parameters, define the goals and purchase the most cost-effective solution.


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