MICROBIOLOGICAL QUALITY AND SAFETY IN DAIRY INDUSTRY

Module 2. Food safety and quality management systems

Lesson 12
STATISTICAL QUALITY CONTROL

12.1 Introduction

Product wholesomeness and uniformity can be more effectively maintained through a QA program that incorporates available scientific and mechanical tools. Quality is considered to be the degree of acceptability by the user. These characteristics are both measurable and controllable. The major ingredients needed for a successful QA program are education and cooperation. The HACCP approach can be incorporated in a QA program because it applies to a zero defects concept in food production. Effective surveillance of a QA program can detect unsanitary products and variations in production.

Statistical QC techniques make inspection more reliable and eliminate the cost of 100% inspection. The principal tool of a statistical QC system is the control chart. Trends of control charts provide more information than do individual values. Values outside the control limits indicate that the production process should be closely observed and possibly modified.

12.2 Role of Statistical Quality Control

Statistical quality control is the application of statistics in controlling a process for the betterment. Measurements of acceptability attributes are taken at periodic intervals during production and are used to determine whether or not the particular process in question is under control-that is, within certain predetermined limits. A statistical QA program enables management to control a product. This program also furnishes an audit of products as they are manufactured. The samples taken for analysis are destroyed; thus, only SQC is practical for monitoring food safety. The greatest advantage of an SQC program is that it enables management to monitor an operation continuously and to make operating a closely controlled production process.

Sample selection and sampling techniques are the critical factors in any QC system. Because only small amounts (usually less than 10 g) of a product are used in the final analysis, it is imperative that this sample be representative of the lot from which it was selected. Statistical quality control also referred to as operations research, operations analysis, or reliability, is the use of scientific principles of probability and statistics as a foundation for decisions concerning the overall acceptability of a product. Its use provides a formal set of procedures in order to conclude what is important, and how to perform appropriate evaluations. Various statistical methods can determine which outcomes are most probable and how much confidence can be placed in decisions.

12.3 Central Tendency Measurements

Three measurements are commonly used to describe data collected from a process or lot. These are the arithmetic mean or average, mode or modal average and median. The mean is the sum of the individual observations divided by the total number of observations. The mode is the value of observations that occurs most frequently in a data set. The median is the middle value present in collected data. By using these values, the manufacturer can represent characteristics of central tendencies of the measurements taken. Table 12.1 illustrates calculated values for the mean, mode and median from a collection of sample data.

Table 12.1 Central tendency values

12.4 Variability

There must be a uniformity and minimal variation in microbial load or other characteristics between the products manufactured. Two measures of variation are the range and standard deviation. Measuring variability by means of the range, R, is accomplished by subtracting the lowest observation from the highest.

R = X_max − X_min

From Table 12.1 the calculation would be:

R = 43 − 13 = 30

Because the range is based on just two observations, it does not provide a very accurate picture of variation. As the number of samples increases, the range tends to increase because there is an increased chance of selecting an extremely high or low sample observation. Standard deviation is a more accurate measurement of how data is dispersed as it considers all the values in the data set. The formula for calculating the standard deviation, S, is:

Although this formula is more complicated than the range calculation, it can be determined easily by using a personal computer. As the standard deviation increases, it reflects increased variability of the data. To maintain uniformity, the standard deviation should be kept to a minimum.

12.5 Displaying Data

It is beneficial to represent data in a frequency table, especially when a large sample of numbers must be analyzed. A frequency table displays numerical classes that cover the data range of sampling and list the frequency of occurrence of values within each class. Class limitations are selected to make the table easy to read and graph. The frequency table of microbial load from raw materials (Table 12.2) displays how data is divided into each class. To help visualize how these data is arranged, one can graph it in the form of a histogram. Fig. 12.1 takes the information from Table 12.2 and displays it graphically. The histogram in Figure 12.2 depicts an important curve common to statistical analysis — the normal curve or normal probability density function. Many events that occur in nature approximate the normal curve. The normal curve has the easily recognizable bell shape and is symmetrical about the center. The area underneath the curve represents all the events described by the frequency distribution. From Figure 12.2, the mean is the highest point on the curve. The variation of the curve is represented by the standard deviation. It can be used to determine various portions underneath the curve. This is illustrated in the figure where one standard deviation to the right mean represents roughly 34% of the sample values. Consequently, 68.27% of the values fall within ±1 standard deviation from the mean. Similarly 95.45% fall within ± 2 standard deviations. Virtually all of the area (99.75) is represented by ± 3 standard deviations. The information thus far can be used to establish control limits in order to determine whether a process is in a state of statistical control.

Table 12.2 Frequency table for microbial load (CFU/ g)

Fig. 12.1 Histogram of microbial load

12.6 Control Charts

Control charts offer an excellent method of attaining and maintaining a satisfactory level of acceptability. The control chart is a widely used industry technique for on-line examination of materials produced. In addition to providing a desired safety level, it can be useful in improving sanitation and in providing a sign of impending trouble. The primary objective is to determine the best methodology, given the available resources, then to monitor control points. This variation can be classified as either chance-cause variation or assignable-cause variation. In chance-cause variation, the end products are different because of random occurrences.

Fig. 12.2 Normal curve

They are relatively small and are unpredictable in occurrence. There is a certain degree of chance-cause variation present. Assignable-cause variation is just what the name implies. Cause can be ‘assigned’ to a contributing factor, such as a difference in microbial load of raw materials, process, and machine aberration, environmental factors, or operational characteristics of individuals involved along the production line. This variation, once determined, is controlled through appropriate corrective action. When a process shows only variation due to chance causes, it is “under control.” Quality control charts were developed in order to differentiate between the two types of variation and to provide a method to determine whether a system is under control. Fig. 12.3 illustrates a typical control chart for a quality characteristic. The y-axis represents the characteristic of interest plotted against the x-axis, which can be a sample number or time interval. The center line represents the average or mean value of the quality trait established by the manufactured product when the process is under control. The two horizontal lines above and below the center line are labeled so that as long as the process is in a state of control, all sample points should fall between them.

Fig. 12.3 Typical control chart for a quality characteristic

The variation of the points within the control limits can be attributed to chance cause and no action is required. An exception to this rule would apply if a substantial number of data points fall above or below the center line instead of being randomly scattered. This would indicate a condition that is possibly out of control and would warrant further investigation.
If a point falls above or below the out-of bounds lines, one can assume that a factor has been introduced that has placed the process in an out-of-control state, and appropriate action is required. Control charts can be divided into two types:

1. Control charts for measurement
2. Control charts for attributes

12.7 Measurement Control Charts

Measurement of variable control charts can be applied to any characteristic that can be measured. The X chart is the most widely used chart for monitoring central tendencies, whereas the R chart is used for controlling process variation. The following examples show how both of these control charts are used in a manufacturing environment.

A food manufacturer may monitor the microbial load of raw milk satisfy safety concerns. Five samples may be pulled after every shift during an 8-hour shift and analyzed for total bacterial count Table 12.3.

Table 12.3 X and R values for microbial load measurements

First calculate the average (X) and range (R) for each inspection sample. For example, sample calculations for sample 1 are:

From the calculated, the center line for the X and R chart can be defined to be:

X Chart center line = 4.91
R Chart center line = 0.525

In order to calculate the upper control limits (UCL) and lower control limits (LCL), the standard deviation for each sample lot must be determined. Rather than perform the lengthy calculation needed for this value, another method can be used to determine these values. The control limits for the previous charts were represented by:

UCL =X + 3δ
LCL =X + 3 δ

By substituting a factor (A2) from a statistical table into the above equation for UCL and LCL, the needed values for the control point can be obtained. In this example, the value for (A2) for a sample size of 5 is 0.525.

The new equation becomes:

UCL =Ave. X + A₂ Ave. R
LCL =Ave. X - A₂ Ave. R

Substituting,

UCL = 4.91 + 0.25(0.252) = 4.9735
LCL = 4.91 − 0.25(0.252) = 4.8464

The control limits for the R chart are determined similarly, using factors D4 and D3 from the statistical reference table.

D4= 2.11, D3= 0
UCL = D4R = 2.11 (0.252) = 0.53172
LCL = D3R = 0 (0.252) = 0

Once these calculations are complete, the values can be plotted on an X-Y chart to obtain the X and R charts (Figures 12.4 and 12.5) for microbial load detection. Figures 12.4 and 12.5 illustrate complete control charts from the sample data. Both graphs show a process currently under control, with all data points lying within the boundaries of the control limits and an equal number of points above and below the center line.

Fig. 12.4 X chart for microbial load

Fig. 12.5 R chart for microbial load

12.8 Attribute Control Charts

Attribute control charts differ from measurements charts in that one is interested in an acceptable or unacceptable classification of products. The following charts are commonly used for attribute testing:

• p charts
• np charts
• c charts
• u charts

12.8.1 p charts

The p chart, one of the more useful attribute control charts, is used for determining the unacceptable (p) fraction. It is defined as the number of unacceptable items divided by the total number of items inspected. For example, if a producer examines five samples per hour (for an 8-hour shift) from the production line and finds a total of eight unacceptable units, p would be calculated as follows:

Total number of unacceptable (dy) = 9
Total number of inspected (dx) = 5(8) = 40

Sometimes this value is represented as percentage unacceptable. In this example, percentage defective would be:

0.225 × 100 = 22.5%

An attribute control chart can be constructed from a sampling schedule by obtaining an average fraction unacceptable (p) value from a data set and using the formula , or the desired control limits. Because attribute testing follows a binomial distribution, the standard deviation would be calculated:

Where n is the number of items in a sample.
Control limits would be obtained by:

UCL = ρ + 3δ

LCL = ρ - 3δ

When these data are plotted and no points are outside of the control limits, it can be assumed that the process is in a state of statistical control, and any variation can be attributed to natural occurrences.

12.8.2 np charts

np charts can be used to determine the number of unacceptable instead of the fraction defective, and the sampling lots are constant. The formula for the number of unacceptable (np) is:

Number of unacceptable (np) = n × p,

Where n is the sample size and p is the unacceptable fraction defective. If one value is known, the other can be easily calculated. For example, if a sample lot of 50 is known to be 5% unacceptable, the number of unacceptable should be:

np = 50 × 0.05 = 2.5

The calculation for determining the control limits would be the same as for the p chart, except that the standard deviation would be:

d = np (1 - p)

12.8.3 c charts

These charts are used when the concern is the number of defects per unit of product. They are not as frequently incorporated as the p and np charts but can be effective if applied correctly. Assume that a manufacturer examines 10 lots and discovers 320 defects. The equations for the average (c) and standard deviation required for a c chart is:

12.8.4 u charts

Sometimes, a constant lot size may not be attainable when examining for defects per unit area. The u chart is used to test for statistical control. By establishing a common unit in terms of a basic lot size, one can determine equivalent inspection sample lot sizes from unequal inspection samples. The number of equivalent common basic lot sizes (k) can be calculated as:

k= size of sample lot/ size of common lot

The u statistic can be determined from c, the number of defects of a sample lot, and the k value defined in the above equation.

μ = c/k

From these values, the upper and lower control limits for the u chart can be defined as:

In addition to charting, a manufacturer may introduce other statistical analyses, such as modeling, variable correlations, regression, analysis of variance, and forecasting to the production area. These techniques provide additional statistical methods for examining processes in order to ensure maximum production efficiency.

12.9 Explanation and Definition of Statistical Quality Control Program Standards

The following terms apply to maintenance of standards:

• Standard: The level or amount of a specific attribute desired in the product.
• Quality attribute: A specific factor or characteristic of the food product that determines a proportionate part of the acceptability of the product. Attributes are measured by a predetermined method, and the results are compared against an established standard and lower and upper control limits to determine if the product attribute is at the desired level in the food product.
• Retained product: A product that is not to be used in production or sold until corrective action has been taken to meet the established standards. Retained products should not be released for production or sales use until the problem is corrected.

12.10 Rating Scales

Two rating scales have been devised for evaluation of attributes:

1. Exact measurement: For attributes that can be measured in precise units (bacterial load, percentage, parts per million, etc.).
2. Subjective evaluation: Used when no exact method of measurement has been developed. The evaluation must be conducted through sensory judgment (taste, feel, sight, smell). This is usually described numerically. Two scales have been developed for evaluating acceptability:

The number of samples to conduct at any point during production to evaluate the sanitation operation also depends on the variations of analysis of the samples. A minimum of three to five samples of approximately two kg each should be selected and pooled from each lot of incoming raw material. After a sufficient number of samples have been analyzed, control charts can be constructed for each raw material.

Sampling of the finished product should be conducted at a special step in the production sequence, such as at the time of packaging. Sampling at this stage does not need to be done on individual products for inspection or regulatory purposes because it is directed at monitoring process control, not individual product analysis. However, to be familiar with the wholesomeness and overall acceptability of each product, the preferred procedure is to analyze and maintain control charts on all products.

Sample size usually consists of three to five specimens that serve as a representative of the population sampled. Another guideline for sample size is the square root of the total units, and, for large lots, an acceptable size may be the square root of the total units divided by 2. Daily sampling is necessary to monitor process control effectively. Action limits for finished products should be as outlined under the analysis program and should be used in determining whether the process conforms to the designated specifications. If three consecutive samples exceed the maximum limit for contamination, production should cease, with further cleaning.

12.11 Cumulative Sum (CUSUM) Control Charts

Data can be plotted where greater sensitivity in detecting small process changes is required by use of the CUSUM chart. This chart is a graphic plot of the running summation of deviation from a control value. These differences are totaled with each subsequent sampling time to provide the CUSUM values. This monitoring technique can be incorporated in sanitation operations that require a higher degree of precision than obtained from a regular statistical QC chart.

The CUSUM chart gives a more accurate account of real changes, faster detection and correction of deviation, and a graphical estimation of trends. It enhances an optimum process control for various applications. Webb and Price (1987) suggested that the CUSUM chart was not developed for multiple levels and is not practical for use on production processes that drift over an extended period of time. If used, it is important that the results of the CUSUM system be kept current so that immediate corrective action may be taken.

A personal computer can rapidly perform the statistical computations and identify the points that require corrective action, thus reducing the burden of processing large quantities of data. This data can be available to promptly expedite corrective actions, project future performances and determine when and where preventive QC procedures are necessary.