## Controlling Food Qualities

Much of the application of food technology is for the purpose of producing uniform output from variable input. This is a significant difference from fabricators who assemble parts into a product. Such assembly presumes interchangeable inputs (parts). By contrast food processors assume that the inputs are variable. Milk from farm A is different from milk from farm B. Peas harvested on Monday are different from peas harvested on Tuesday. The challenge and opportunity is to control the quality of the output product by controlling the processing steps applied to the inputs.

Consistently reproducing a food quality implies that this quality is somehow measurable. From a consumer perspective this is usually not the case. Even articulating the nature of a food quality may be difficult for a consumer. Although there are words like sweetness and saltiness, more often the expressions describing quality are much more generalâ€”"it tastes good" or "it doesn't taste right." This problem for quality measurement is further complicated by the variability among consumers of what is considered a good quality for food to have. Preferences vary. For control to be possible the consumer's perception of quality must be separated from the measurable qualities of food materials. The food technologist seeks desirable effects through variables that are controllable. The underlying assumption is that controlling ingredient amounts, processing times and temperatures, holding times, and the like will produce a food product that meets the consumer's quality expectations. The connection between processing variables that can be measured and replicated and the consumer's perception of the qualities of a food product is real, but it is indirect. Many intervening factors influence this connection and most of them are not measurable.

For a given product the best hope of consistent qualities is to control what can be measured as carefully as possible. Keeping in mind that the inputs are intrinsically variable and that processes also vary, "control" must be defined statistically. If a quality measure of an ice cream product is its gross weight, then the ideal is that the gross weight of every container comes from the same distribution of such weights. Because we cannot eliminate variability entirely, the best we can do is to make sure that the underlying distribution does not change. In these situations a distribution is said to have "changed" if its center (mean) or its dispersion (standard deviation) changes. A manufacturing step is said to be "in control" if the measurements taken are scattered according to the same distribution.

Deciding whether an operation is in control or not can be done by routinely sampling the output from the operation and measuring the target quality for each item in the sample. Sample statistics can be computed, including typically the mean of the sample, the range of the sample, and the standard deviation of the sample. These numbers have their own distributions, but these distributions are related to the target quality measurement in well-known ways. The easiest connection to describe is the one between the mean of the measurements and the mean of the sample. The mean of the sample means has the same value as the mean of the target measurements, and the standard deviation of the sample means (also called the standard error of the mean) is the standard deviation of the measurements divided by the square root of the sample size. Furthermore, the distribution of the sample means is distributed approximately normally, provided the sample size is big enough (in practice big enough typically means four or more items in the sample). This fact is true even if the distribution of the measurements is not normal. This enables a method for making the in control decision.

W. A. Shewhart (1) developed a strategy and a graphic that made this decision making feasible for a wide variety of situations. He proposed that if the sample mean fell more than three standard deviations from the empirically established mean of the process (established when the process was in control), this was evidence that the operation producing the measurement was not in control. If the sample mean was less than three standard deviations from the established process mean, the operation was deemed in control. Because the distribution of the sample means is approximately normal, the probability of the sample mean falling beyond three standard deviations by chance (ie, without the distribution of the individual measurements changing) can be computed and is quite small (less than 0.003).

The graphic that Shewhart developed is called a control chart (Fig. 1). This consists of three equally spaced parallel lines (or sometimes two lines for the range chart). The centerline corresponds to the process mean that is also the mean of the sample distribution; the upper and lower lines correspond to the mean plus three standard deviations and the mean minus three standard deviations of the sample distribution, respectively. Sample means and sample

Sample means

### Sample means

Figure 1. An example control chart for means and ranges of sample size four for gross weights of quarts of ice cream. There is one out-of-control point in the sample means chart.

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