Control limits are occasionally mistaken for tolerances; however, they are quite different things.
Control limits provide a means for determining natural variation in a production process. They are statistical results based on sampling. Tolerances are design specifications reflecting customer re- quirements for a product. They specify a range of values above and below a designed target value (also referred to as the nominal value), within which product units must fall to be acceptable. For example, a bag of potato chips might be designed to have a net weight of 9.0 oz of chips with a tolerance of 0.5 oz. The design tolerances are thus between 9.5 oz (the upper specification limit) and 8.5 oz (the lower specification limit). The packaging process must be capable of performing within these design tolerances or a certain portion of the bags will be defective, that is, underweight or overweight. Tolerances are not determined from the production process;
they are externally imposed by the designers of the product or service. Control limits, on the other hand, are based on the production process, and they reflect process variability. They are a statistical measure determined from the process. It is possible for a process in an instance to be statistically “in control” according to control charts, yet the process may not conform to the
design specifications. To avoid such a situation, the process must be evaluated to see if it can meet product specifications before the process is initiated, or the product or service must be redesigned.
Process capabilityrefers to the natural variation of a process relative to the variation allowed by the design specifications. In other words, how capable is the process of producing acceptable units according to the design specifications? Process control charts are used for process capability to determine if an existing process is capable of meeting design specifications.
The three main elements associated with process capability are process variability (the natural range of variation of the process), the process center (mean), and the design specifications. Figure 3.5 shows four possible situations with different configurations of these elements that can occur when we consider process capability.
Figure 3.5a depicts the natural variation of a process, which is greater than the design specifi- cation limits. The process is not capable of meeting these specification limits. This situation will result in a large proportion of defective parts or products. If the limits of a control chart measuring natural variation exceed the specification limits or designed tolerances of a product, the process cannot produce the product according to specifications. The variation that will occur naturally, at random, is greater than the designed variation.
Parts that are within the control limits but outside the design specification must be scrapped or reworked. This can be very costly and wasteful. Alternatives include improving the process or re- designing the product. However, these solutions can also be costly. As such, it is important that process capability studies be done during product design, and before contracts for new parts or products are entered into.
Figure 3.5b shows the situation in which the natural control limits and specification limits are the same. This will result in a small number of defective items, the few that will fall outside the natural control limits due to random causes. For many companies, this is a reasonable quality Exhibit 3.2
Process capability:
the range of natural variability in a process—what we measure with control charts.
If the natural variability in a process exceeds tolerances, the process cannot meet design specifications.
• Excel File
Design Specifications
Process
Process
Process
Process Design Specifications
Design Specifications
Design Specifications (a) Natural variation
exceeds design specifications; process is not capable of meeting specifications all the time.
(b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time.
(c) Design specifications greater than natural vari- ation; process is capable of always conforming to specifications.
(d) Specifications greater than natural variation, but process off center;
capable but some output will not meet upper specification.
Figure 3.5
Process Capability
goal. If the process distribution is normally distributed and the natural control limits are three standard deviations from the process mean—that is, they are 3-sigma limits—then the probability between the limits is 0.9973. This is the probability of a good item. This means the area, or probability, outside the limits is 0.0027, which translates to 2.7 defects per thousand or 2700 defects out of one million items. However, according to strict quality philosophy, this is not an appropriate quality goal. As Evans and Lindsay point out in the book The Management and Con- trol of Quality, this level of quality corresponding to 3-sigma limits is comparable to “at least 20,000 wrong drug prescriptions each year, more than 15,000 babies accidentally dropped by nurses and doctors each year, 500 incorrect surgical operations each week, and 2000 lost pieces of mail each hour.”1
• Internet Exercises
1J. R. Evans and W. M. Lindsay, The Management and Control of Quality, 3rd ed. (Minneapolis: West, 1993), p. 602.
As a result, a number of companies have adopted “6-sigma” quality. This represents product- design specifications that are twice as large as the natural variations reflected in 3-sigma control limits. This type of situation, where the design specifications exceed the natural control limits, is shown graphically in Figure 3.5c. The company would expect that almost all products will con- form to design specifications—as long as the process mean is centered on the design target. Statis- tically, 6-sigma corresponds to only 0.0000002 percent defects or 0.002 defective parts per million (PPM), which is only two defects per billion! However, when Motorola announced in 1989 that it would achieve 6-sigma quality in five years they translated this to be 3.4 defects per million. How did they get 3.4 defects per million from 2 defects per billion? Motorola took into account that the process mean will not always exactly correspond to the design target; it might vary from the nominal design target by as much as 1.5 sigma (the scenario in Figure 3.5d), which translates to a 6-sigma defect rate of 3.4 defects per million. This value has since become the stan- dard for 6-sigma quality in industry and business. Applying this same scenario of a 1.5-sigma deviation from the process mean to the more typical 3-sigma level used by most companies, the defect rate is not 2700 defects per million, but 66,810 defects per million.
As indicated, Figure 3.5d shows the situation in which the design specifications are greater than the process range of variation; however, the process is off center. The process is capable of meeting specifications, but it is not because the process is not in control. In this case a percentage of the output that falls outside the upper design specification limit will be defective. If the process is adjusted so that the process center coincides with the design target (i.e., it is centered), then al- most all of the output will meet design specifications.
Determining process capability is important because it helps a company understand process variation. If it can be determined how well a process is meeting design specifications, and thus what the actual level of quality is, then steps can be taken to improve quality. Two measures used to quantify the capability of a process, that is, how well the process is capable of producing according to design specifications, are the capability ratio (Cp) and the capability index (Cpk).