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Because data samples are random, it is unlikely that two samples from the same population will yield identical tolerance intervals. But, if you collect many samples, a certain percentage of the resulting tolerance intervals will contain the minimum proportion of the population that you specify.
The confidence level is the likelihood that the tolerance interval actually includes the minimum percentage. For example, an engineer wants to know the range within which 99% of the future product will fall, with 98% confidence. 98% is the confidence level for the tolerance interval.
The minimum percentage of the population that you want the tolerance interval to include. For example, an engineer wants to know the range that will include 95% of the future product, with 98% confidence. 95% is the minimum percent of population in the tolerance interval.
The probability the population coverage exceeds p* is the probability that the interval contains more of the population data than p*. Common values include 0.01, 0.05, and 0.1. Larger values can result in a tolerance interval that covers a much larger percentage of the population than the target, p.
Suppose you want to calculate a tolerance interval that covers 90% of the population. Using the default probability the population coverage exceeds p* of 0.05 (5%), you determine that the maximum acceptable percentage of population in interval is 92%. Together, these statistics indicate that there is only a 5% chance that your interval will include 92% or more of the population.
The maximum acceptable percentages of population is the additional percentage of the population that might be included in the interval (beyond the target of p*).
Suppose you want to calculate a tolerance interval that covers 90% of the population. Using the default probability the population coverage exceeds p* of 0.05 (5%), you determine that the maximum acceptable percentage of population in interval is 92%. Together, these statistics indicate that there is only a 5% chance that your interval will include 92% or more of the population.
The sample size is the number of observations in the sample that Minitab uses to calculate the tolerance interval. If you specify one or more sample sizes, Minitab calculates the maximum acceptable percentages of population in the interval that you can achieve with those sample sizes. If you specify one or more values for the maximum acceptable percentages of population in the interval, Minitab calculates the sample sizes that are required to achieve those percentages.
If the sample size is small, then the maximum acceptable percentages may be too large and the tolerance interval may greatly overestimate the variability in the process. A more precise tolerance interval is more useful and more informative, but smaller maximum acceptable percentages require larger sample sizes. If a tolerance interval is not sufficiently precise, it can be too wide and include a much larger percentage of the population than you specify.
Tolerance intervals are a range of values for a specific quality characteristic of a product that likely covers a specified percentage of future product output. Use the normal method tolerance interval if you can safely assume that your sample comes from a normally distributed population.
If your data follow a normal distribution, then the normal method is more precise and economical than the nonparametric method. The normal method allows you to achieve smaller maximum acceptable percentages of population for the interval with fewer observations.
The normal method is not robust to severe departures from normality. If you are unsure of the parent distribution, or you know that the parent distribution is not normal, then use the nonparametric method.
If you specify one or more values for the maximum acceptable percentages of the population in the interval, Minitab calculates the sample sizes that are required to achieve those percentages. If you specify one or more sample sizes, Minitab calculates the maximum acceptable percentages of the population in the interval that you can achieve with those sample sizes. Minitab performs calculations for the normal and the nonparametric method. For calculations for other distributions, use Tolerance Intervals (Nonnormal Distribution).
In these results, Minitab calculates the sample sizes required to create a tolerance interval for the normal and nonparametric methods. The sample size for the normal method is 1395.
| P* | Normal Method | Nonparametric Method | Achieved Confidence | Achieved Error Probability |
|---|---|---|---|---|
| 92.000% | 1395 | 2215 | 95.0% | 0.049 |
In these results, Minitab calculates the maximum acceptable percentages of population for the interval associated with particular sample sizes for the normal and nonparametric methods. When the sample size is 1000, the maximum acceptable percentage for the normal method is 96.5124%. When the sample size is 1500, the maximum acceptable percentage is 96.2603%, and when the sample size is 2000, the maximum acceptable percentage is 96.1047%.
| Sample Size | Normal Method | Nonparametric Method | Achieved Confidence | Achieved Error Probability |
|---|---|---|---|---|
| 1000 | 96.5124% | 97.0544% | 95.7% | 0.050 |
| 1500 | 96.2603% | 96.7379% | 96.1% | 0.050 |
| 2000 | 96.1047% | 96.5124% | 95.8% | 0.050 |
Tolerance intervals are a range of values for a specific quality characteristic of a product that likely covers a specified proportion of future product output. If you cannot safely assume that your sample comes from a normally distribution population, you must use the nonparametric method tolerance interval.
The nonparametric method requires only that the data are continuous. However, the nonparametric method requires large sample sizes for the results to be accurate. If your sample size is not large enough, the nonparametric interval is a non-informative interval that ranges from negative infinity to infinity. In this case, Minitab displays a finite interval based on the range of your data. As a result, the achieved confidence level is much lower than the target confidence level.
If you specify one or more values for the maximum acceptable percentages of the population in the interval, Minitab calculates the sample sizes that are required to achieve those percentages. If you specify one or more sample sizes, Minitab calculates the maximum acceptable percentages of the population in the interval that you can achieve with those sample sizes. Minitab performs calculations for the normal and the nonparametric method. For calculations for other distributions, use Tolerance Intervals (Nonnormal Distribution).
In these results, Minitab calculates the sample sizes required to create a tolerance interval for the normal and nonparametric methods. The sample size for the nonparametric method is 2215.
| P* | Normal Method | Nonparametric Method | Achieved Confidence | Achieved Error Probability |
|---|---|---|---|---|
| 92.000% | 1395 | 2215 | 95.0% | 0.049 |
In these results, Minitab calculates the maximum acceptable percentages of population for the interval associated with particular sample sizes for the normal and nonparametric methods. When the sample size is 1000, the maximum acceptable percentage for the nonparametric method is 97.0544%. When the sample size is 1500, the maximum acceptable percentage is 96.7379%, and when the sample size is 2000, the maximum acceptable percentage is 96.5124%.
| Sample Size | Normal Method | Nonparametric Method | Achieved Confidence | Achieved Error Probability |
|---|---|---|---|---|
| 1000 | 96.5124% | 97.0544% | 95.7% | 0.050 |
| 1500 | 96.2603% | 96.7379% | 96.1% | 0.050 |
| 2000 | 96.1047% | 96.5124% | 95.8% | 0.050 |
For the nonparametric method, Minitab calculates the achieved confidence level. This is the exact confidence level obtained from your sample. It will generally be greater than or equal to the target confidence level, unless your sample size is too small.
In these results, the achieved confidence levels are 95.7%, 96.1%, and 95.8%, which are greater than the desired value of 0.05.
| Confidence level | 95% |
|---|---|
| Minimum percentage of population in interval | 95% |
| Probability the population coverage exceeds p* | 0.05 |
| Sample Size | Normal Method | Nonparametric Method | Achieved Confidence | Achieved Error Probability |
|---|---|---|---|---|
| 1000 | 96.5124% | 97.0544% | 95.7% | 0.050 |
| 1500 | 96.2603% | 96.7379% | 96.1% | 0.050 |
| 2000 | 96.1047% | 96.5124% | 95.8% | 0.050 |
For the nonparametric method, Minitab calculates the achieved error probability. This is the exact margin of error probability that is associated with the specified sample size. The achieved error probability is usually close to your desired level.
In these results, the achieved error probabilities are 0.05 for each sample size, which equal the desired value of 95%.
| Confidence level | 95% |
|---|---|
| Minimum percentage of population in interval | 95% |
| Probability the population coverage exceeds p* | 0.05 |
| Sample Size | Normal Method | Nonparametric Method | Achieved Confidence | Achieved Error Probability |
|---|---|---|---|---|
| 1000 | 96.5124% | 97.0544% | 95.7% | 0.050 |
| 1500 | 96.2603% | 96.7379% | 96.1% | 0.050 |
| 2000 | 96.1047% | 96.5124% | 95.8% | 0.050 |
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