Ch 13 - Statistically quality control Flashcards
What is statistically quality control?
In general, 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 we are providing? Managing quality performance using SQC techniques usually involves periodic sampling of a process and analysis of these data using statistically derived performance criteria.
As you will see, SQC can be applied to logistics, manufacturing, and service processes. Here are some examples of 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-thru 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. What are the two types of variation that can occur?
- 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 random variation and may be the result of the type of equipment used to complete a process, for example.
In SQC terminology, what is sigma (σ) often used to refer to?
The sample standard deviation. As you will see in the examples, sigma is calculated in a few different ways, depending on the underlying theoretical distribution (i.e., a normal distribution or a Poisson distribution).
However, engineers also know that it is impossible to have zero variability, so how do they manage it?
For this reason, designers establish specifications that define not only the target value of something but also acceptable limits about the target. For example, if the target value of a dimension is 10 inches, the design specifications might then be 10.00 inches ± 0.02 inch. This would tell the manufacturing department that, while it should aim for exactly 10 inches, anything between 9.98 and 10.02 inches is OK. These design limits are often referred to as the upper and lower specification limits.
What is capability index?
The capability index (Cpk) shows how well the parts being produced fit into the range specified by the design specification limits. If the specification limits are larger than the three-sigma allowed in the process, then the mean of the process can be allowed to drift off-center before readjustment, and a high percentage of good parts will still be produced.
We say that a process is capable when the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits.
What is the Z-score?
Recall from your study of statistics that the Z score is the standard deviation either to the right or to the left of zero in a probability distribution. a z-score is the number of standard deviations from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.
Interpreting this information requires understanding exactly what the NORMSDIST function is providing. NORMSDIST is giving the cumulative probability to the left of the given Z value. Since Z = –7.2289 is the number of standard deviations associated with the lower specification limit, the fraction of parts that will be produced lower than this is 2.43461E-13.
Interpreting the Z score?
We add the two z score associated with the upper and lower limit. This fraction defective above the upper spec is 1 – .99999928 = .00000072 of our parts. Adding these two fraction defective numbers together we get .00000072000024361. We can interpret this to mean that we expect only about .72 parts per million to be defective. Clearly, this is a great process. You will discover as you work the problems at the end of the chapter that this is not always the case.
“Probability of a can less than 55 psi or more than 65 psi Probability = 0.001349898 + 0.022750132 = .024100030 Or approximately 2.4 percent of the cans will be defective.
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What is process control and what does statistical process control concern?
Process control is concerned with monitoring quality while the product or service is being produced. Typical objectives of process control plans are to provide timely information about whether currently produced items are meeting design specifications and to detect shifts in the process that signal that future products may not meet specifications. Statistical process control (SPC) involves testing a random sample of output from a process to determine whether the process is producing items within a preselected range.
What is sampling by attribute?
The examples given so far have all been based on quality characteristics (or variables) that are measurable, such as the diameter or weight of a part. Attributes are quality characteristics that are classified as either conforming or not conforming to specification. Goods or services may be observed to be either good or bad, or functioning or malfunctioning. For example, a lawnmower either runs or it doesn’t; it attains a certain level of torque and horsepower or it doesn’t.
How is process control with attributes carried out? (p-chart)
Measurement by attributes means taking samples and using a single decision—the item is good or it is bad. Because it is a yes or no decision, we can use simple statistics to create a p-chart with an upper process control limit (UCL) and a lower process control limit (LCL). We can draw these control limits on a graph and then plot the fraction defective of each individual sample tested. The process is assumed to be working correctly when the samples, which are taken periodically during the day, continue to stay between the control limits.
- Size of the Sample The size of the sample must be large enough to allow counting of the attribute. For example, if we know that a machine produces 1 percent defective units, then a sample size of five would seldom capture a bad unit. A rule of thumb when setting up a p-chart is to make the sample large enough to expect to count the attribute twice in each sample. So an appropriate sample size, if the defective rate were approximately 1 percent, would be 200 units.
- Number of samples can be eg. 10. Each sample number of factions of defective parts should be between the LCL and UCL.
How is process control with attributes carried out? (c-chart)
In the case of the p-chart, the item was either good or bad. There are times when the product or service can have more than one defect. For example, a board sold at a lumberyard may have multiple knotholes and, depending on the quality grade, may or may not be defective. When it is desired to monitor the number of defects per unit, the c-chart is appropriate. The underlying distribution for the c-chart is the Poisson, which is based on the assumption that defects occur randomly on each unit.
How is process control with attributes carried out? (X and R-chart (range))
In attribute sampling, we determine whether something is good or bad, fits or doesn’t fit— it is a go/no-go situation. In variables sampling, however, we measure the actual weight, volume, number of inches, or other variable measurements, and we develop control charts to determine the acceptability or rejection of the process based on those measurements. For example, in attribute sampling, we might decide that if something is over 10 pounds, we will reject it, and under 10 pounds, we will accept it. In variables sampling, we measure a sample and may record weights of 9.8 pounds or 10.2 pounds. These values are used to create or modify control charts and to see whether they fall within the acceptable limits. There are four main issues to address in creating a control chart: the size of the samples, number of samples, frequency of samples, and control limits.
Sample size?
Sample sizes of four or five units seem to be the preferred numbers. The means of samples of this size have an approximately normal distribution,
Number of samples?
To set up the charts, however, prudence and statistics suggest that 25 or so sample sets be analyzed.
