Complete the following steps to interpret a binomial capability analysis. Key output includes the control chart, binomial plot, and the %defective.

Before you evaluate the capability of your process, determine whether it is stable. If your process is not stable, the estimates of process capability may not be reliable.

Use the P chart to visually monitor the %defective and to determine whether the %defective is stable and in control.

Red points indicate subgroups that fail at least one of the tests for special causes and are not in control. Out-of-control points indicate that the process may not be stable and that the results of a capability analysis may not be reliable. You should identify the cause of out-of-control points and eliminate special-cause variation before you analyze process capability.

Before you evaluate the capability of your process, determine whether it follows a binomial distribution. If your data do not follow a binomial distribution, the estimates of process capability may not be reliable. The graph that Minitab displays to evaluate the distribution of the data depends on whether your subgroup sizes are equal or unequal.

If your subgroup sizes are all the same, Minitab displays a binomial plot.

Examine the plot to determine whether the plotted points approximately follow a straight line. If not, then the assumption that the data were sampled from a binomial distribution may be false.

If the subgroup sizes vary, Minitab displays a rate of defectives plot.

Examine the plot to assess whether the %defective is randomly distributed across sample sizes or whether a pattern is present. If your data fall randomly about the center line, you conclude that the data follow a binomial distribution.

Use the mean %defective of the sample data to estimate the mean %defective for the process. Use the confidence interval as a margin of error for the estimate.

The confidence interval provides a range of likely values for the actual value of the %defective in your process (if you could collect and analyze all the items it produces). At a 95% confidence level, you can be 95% confident that the actual %defective of the process is contained within the confidence interval. That is, if you collect 100 random samples from your process, you can expect approximately 95 of the samples to produce intervals that contain the actual value of %defective.

The confidence interval helps you assess the practical significance of your sample estimate. If you have a maximum allowable %defective value that is based on process knowledge or industry standards, compare the upper confidence bound to this value. If the upper confidence bound is less than the maximum allowable %defective value, then you can be confident that your process meets specifications, even when taking into account variability from random sampling that affects the estimate.

Summary Stats | |
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(95.0% confidence) | |

%Defective: | 0.39 |

Lower CI: | 0.24 |

Upper CI: | 0.60 |

Target: | 0.50 |

PPM Def: | 3931 |

Lower CI: | 2435 |

Upper CI: | 6003 |

Process Z: | 2.6579 |

Lower CI: | 2.5120 |

Upper CI: | 2.8155 |

The results for binomial capability analysis include a Summary Stats table, located in the lower middle portion of the output. In this simulated Summary Stats table, the Target (0.50%) indicates the maximum allowable %defective for the process. The %defective estimate is 0.39%, which is below the maximum allowable %defective. However, the upper CI for %defective is 0.60%, which exceeds the maximum allowable value. Therefore, you cannot be 95% confident that the process is capable. You may need to use a larger sample size, or reduce the variability of the process, to obtain a narrower confidence interval for the %defective estimate.

Use the Cumulative %Defective plot to determine whether you have enough samples for a stable estimate of the %defective.

Examine the %defective for the time-ordered samples to see how the estimate changes as you collect more samples. Ideally, the %defective stabilizes after several samples, as shown by a flattening of the plotted points along the mean %defective line.