Statistical Quality Control

Statistical Quality Control (or SQC) is a number of different techniques designed to evaluate quality from a conformance view. That is, how well are we doing at meeting the specifications that have been set during the design of the parts or services that we are providing? Managing quality performance using SQC techniques usually involves periodic sampling of a process and analysis of this data using statistically derived performance criteria.

SQC and Variances

SQC can be applied to both manufacturing and service processes. Some example situations where SQC can be applied:

• How many paint defects are there in the finish of a car? Have we improved our painting process by installing a new sprayer?
• How long does it take to execute market orders in our Web-based trading system? Has the installation of a new server improved the service? Does the performance of the system vary over the trading day?
• How well are we able to maintain the dimensional tolerance on our three-inch ball bearing assembly? Given the variability of our process for making this ball bearing, how many defects would we expect to produce per million bearings that we make?
• How long does it take for customers to be served from our drive-through window during the busy lunch period?

Processes that provide goods and services usually exhibit some variation in their output. This variation can be caused by many factors, some of which we can control and others that are inherent in the process. Variation that is caused by factors that can be clearly identified and possibly even managed is called assignable variation. For example, variation caused by workers not being equally trained or by improper machine adjustment is assignable variation. Variation that is inherent in the process itself is called common variation. Common variation is often referred to as a random variable and may be result of the type of equipment used to complete a process, for example.

This material requires an understanding of very basic statistics. Recall from your study of statistics involving numbers that are normally distributed the definition of the mean and standard variation. The mean is just the average value of a set of numbers.

In monitoring a process using SQC, samples of the process output would be taken, and sample statistics calculated. The distribution associated with the samples should exhibit the same kind of variability as the actual distribution of the process, although the actual variance of the sampling distribution would be less. This is good because it allows the quick detection of changes in the actual distribution of the process. The purpose of sampling is to find when the process has changed in some non-random way, so that the reason for the change can be quickly determined.

In SQC terminology, sigma is often used to refer to the sample standard deviation, and is calculated in different ways, depending on the underlying theoretical distribution, i.e. a normal distribution or a Poisson distribution.

Acceptance Sampling

Acceptance sampling is performed on goods that already exist to determine what percentage of products conforms to specifications. These products may be items received from another company and evaluated by the receiving department, or they may be components that have passed through a processing step and are evaluated by company personnel either in production or later in the warehousing function.

Acceptance sampling is a statistical method that enables us to base the accept reject decision on the inspection of a sample of items from the lot. The items of interest can be incoming shipments of raw materials or purchased parts as well as finished goods from final assembly. Typical application of acceptance sampling is for lot disposition, sometimes referred to as lot sentencing, for receiving inspection activities. Accepted lots are put into production. Rejected lots may be returned to supplier or subjected to other lot-disposition action. Sampling methods may also be used during various stages of production

Acceptance sampling may be applied where large quantities of similar items or large batches of material are being bought or are being transferred from one part of an organization to another. Unlike statistical process control where the purpose is to check production as it proceeds, acceptance sampling is applied to large batches of goods which have already been produced.

Acceptance sampling is a form of quality testing used for incoming materials or finished goods. e.g. purchased material & components. The procedure for sampling involves the following steps.

• Take one or more samples at random from a lot (shipment) of items
• Inspect each of the items in the sample
• Decide whether to reject the whole lot based on the inspection results