Statistical quality control (SQC) and statistical process control (SPC) are two powerful tools, which have different goals and requirements for successful application. By using a methodology that combines the strengths of both approaches, it is possible to overcome the individual weaknesses of each one. The volume of calculations required by this technique prohibits manual data collection in favor of computerized analysis. The specific SPC technique to be discussed in combination with SQC is the attribute control chart.

Problems Applying SQC

SQC deals with the statistics used for acceptance sampling. Based on consumer and producer risks, lot sizes and acceptable reject levels, a specific sampling plan and acceptance numbers are determined for sampling and acceptance of a given lot. One commonly used SQC technique is MIL-STD-105D, also known as the ABC standard.

Although the statistics used in SQC guarantee that the quality of delivered goods will comply with a predictable level, there are some negative aspects of SQC worthy of discussion. SQC is always applied at the end of a process, when the problems have already occurred. SQC by itself will not improve the process nor will it signal where or when a problem has appeared. It will only inform the inspector whether the lot is good enough to be shipped. In contrast, using SPC techniques, inspection is done in-process to discover possible problems as soon as they appear. As a result, the technique of SPC is more commercially useful because it is more descriptive and pre-emptive in nature.

Problems Applying SPC

The advantage of SPC is that sampling is done frequently, which increases the chance of finding a process problem in its early stages. Frequent data collection allows production to be stopped as soon as a problem is detected, so that minimum waste is generated. Further savings are enjoyed since value is not added to defective products in subsequent processes. Attribute control charts have a few disadvantages in the way they would be applied alone:

1. In traditional attribute charts, only one defect is considered. In practice, different defects are often combined in an attribute chart without distinction being made between major and minor errors. This can cause false signals from the control chart especially when the number of minor errors is significantly higher than the number of major errors or when the difference between major and minor defects is extreme. One solution would be to create separate charts for minor and major defects but, that will increase the amount of administrative work and difficulty in data collection.
2. Attribute charts most of the time have aggregated count data. The problem with this aggregated data is that this data will only follow the binomial distribution if each individual binomial variable has the same value for p. This is rarely the case. A solution to overcome this problem is to use empirical limits instead of control limits based on a theoretical model. These limits can be calculated based on the X moving range chart. This approach will produce good results as long as the number of errors in the subgroup is 1 or higher. In most attribute processes, the number of errors is lower. In cases such as this, subgroups should be combined so that an average of 1 or higher is attained.
3. The attribute control charts will give the operator information when the process is out of statistical control, but it will not give proper information when the lot should be rejected based on chosen consumer and producers risks. In the case of an out of control indication, SQC should be applied to verify whether the lot can be shipped.

Solution

By using attribute charts with special features, you can enjoy the benefits of both systems (i.e., timely feedback and pre-emptive response of SPC and the certifiable quality levels of SQC).

First, categorize the nonconformities to be entered. During data collection, each of these categories should be able to be considered separately for statistical control using separate control limits and alarms. They also can be considered separately for acceptance criteria. Categories also can be combined to yield overall SQC analysis for the lot.

Beyond that, individual categories or the whole can be analyzed and certified for a specific quality level using SQC techniques on a real-time basis. This is accomplished by using a moving calculation similar to an x moving range chart. When an individual sampling lot (subgroup) contains insufficient samples to satisfy the requirements of sampling plan, simply combine it with previously collected subgroups until the amount of data collected from the process meets or exceeds the sampling plan size required. The number of defects found from the process is compared with the acceptance number in the sampling plan. An alarm results if the acceptance number is exceeded (i.e., if the process produced too many nonconformities). This alarm indicates the combination of lots should be quarantined and should not be shipped.

Illustration

The following graphic shows an example of an attribute chart illustrating the solution. The chart shows the total number of defects for all categories at once. The table below the chart shows the number of defects per category. If a control limit for a category is exceeded the value in the table is shown in red.

Benefits

The benefits of the described methodology are obvious.

Companies applying only SQC – The benefits of SPC over SQC are obvious. A lot has been said in recent years about these benefits: Faster feedback, problems are discovered as soon as they occur, production people making the quality also are responsible for verifying the quality, and separate inspectors are removed from the warehouse. The solution described above retains all the customer requirements related to SQC, but the task is performed much more efficiently. The voice of the process can be heard with greater clarity due to the additional differentiation offered by data collection through an SPC format.

Companies applying only SPC – The benefits for companies applying SPC are less obvious. The major benefit is the fact that attribute SPC with low defect levels does not always work properly. In practice you will see that these charts are not much more than check sheets and no action is taken when control limits are violated. Implementing the solution described will make people much more aware of the problems with traditional attributive SPC and will help them to take better decisions when action is required. The second big advantage is that the solution described will guarantee a specific quality level required by customers. SPC communicates what the process is doing without regard for what the customer is expecting from the process. The use of SQC and an associated AQL, however, sets a minimum acceptable level for key product characteristics so customer expectations can be achieved.

Companies applying both SPC and SQC – If companies apply both SPC and SQC, the amount of inspection can be decreased significantly without decreasing the consumer’s risk. The minimum frequency of the SPC checks can be derived from lot size, production speed and required sample sizes prescribed by SQC.

By working smarter rather than harder, you can overlay the SQC requirements on the SPC data collection with the result that both analyses can be performed with no additional data collection. Simply use the data already collected from SPC for SQC analysis and compliance reports. You can further use the sampling plan as a control mechanism for six sigma improvement projects. When cost reduction is the goal, AQL can be referenced to ensure quality levels do not suffer as a result of process changes.

Further reading – For more about SQC, read Statistical Quality Control by Eugene L. Grant and Richard S. Leavenworth, McGraw-Hill, ISBN: 0-07-024117-1. For more about SPC, read Advanced Topics in Statistical Process Control by Dr. Donald J. Wheeler, SPC Press, ISBN: 0-945320-45-0.