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A resource for data collection tools, including how to collect data, how much to collect, and how frequently to collect it.
Sampling is a tool that is used to indicate how much data to collect and how often it should be collected. This tool defines the samples to take in order to quantify a system, process, issue, or problem.
To illustrate sampling, consider a loaf of bread. How good is the bread? To find out, is it necessary to eat the whole loaf? No, of course not. To make a judgment about the entire loaf, it is necessary only to taste a sample of the loaf, such as a slice. In this case the loaf of bread being studied is known as the population of the study. The sample, the slice of bread, is a subset or a part of the population.
Now consider a whole bakery. The population of interest is no longer a loaf, but all the bread that has been made today. A sample size of one slice from one loaf is clearly inadequate for this larger population. The sample collected will now become several loaves of bread taken at set times throughout the day. Since the population is larger, the sample will also be larger. The larger the population, the larger the sample required.
In the bakery example, bread is made in an ongoing process. That is, bread was made yesterday, throughout today, and will be made tomorrow. For an ongoing process, samples need to be taken to identify how the process is changing over time. Studying how the samples are changing with control charts will show where and how to improve the process, and allow prediction of future performance.
For example, the bakery is interested in the weight of the loaves. The bakery does not want to weigh every single loaf, as this would be too expensive, too time consuming, and no more accurate than sampling some of the loaves. Sampling for improvement and monitoring is a matter of taking small samples frequently over time. The questions now become:
These two questions, “how much?” and “how often?” are at the heart of sampling.
Begin by answering the question, “How many items does this process produce during the frequency interval (per hour, week, etc.)?” When that number is determined, the sample size should be at least the square root of that number. For instance, if a purchasing department processes 100 purchase orders per week, an appropriate sample size would be 10 purchase orders per week (the square root of 100 is 10.)
The above article is an excerpt from the “Sampling” chapter of Practical Tools for Continuous Improvement: Volume 1 – Statistical Tools. The full chapter provides more details on sampling.
Tools for analyzing and interpreting data so that areas to improve become apparent.
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Consists of measurements of a characteristic, such as length, weight, density, time, or pressure.
Consists of defects per item (nonconformities) or the number of defective items (nonconforming). For example, the number of non-working parts in sample or the number of blemishes counted on an individual part.
Consists of a count of items or occurrences, such as the number of defective items, the number of scratches on a door panel, or how often a specific problem occurs.
Use this when other control charts are not effective to determine if your process is stable.
Answer “yes” or “no” to a series of questions about your control charts.
Follow these steps to interpret histograms.
A tool used to indicate how much data to collect and how often it should be collected.
A clear, concise, detailed definition of a measure.
Gage R&R refers to testing the repeatability and reproducibility of the measurement system.
Process performance indices use sigma of the individuals.
Pp for one-sided specifications
If you are using one sided specifications, use the following formulas to determine the Cp:
Upper specification
Lower specification
Where:
Zmin is the smaller of Zupper and Zlower.
Using sigma of the individuals:
Capability indices use estimated sigma.
Cp for one-sided specifications
Using estimated sigma:
T = specification target (nominal)
Xi = a given individual reading of ” i ”
n = total number of individual readings
= symbol for summation
The t-chart formula:
The g-chart formula:
The c-chart formula (for number of nonconformities, from subgroups of a constant size):
The u-chart formula (for number of nonconformities from subgroups that can vary in size):