Project 5 Quality Control By Christine Duane Jason Copyright (c) 2008 by The McGraw-Hill Companies. This material is intended solely for educational use by licensed users of LearningStats. It may not be copied or resold for profit.

Situation Commercial Cleaning Solution Manufacturing Company Works best when its acidity (pH) is 5.0 There has been some quality control problem Our team decided to look at Cycle & Oscillation Changed the sample size from 50  500  1000 Changed the magnitude of out-of-control process level from Strong  Medium  None Looked at Rules of Thumb pH level as close as 0.01 SD = 0.06

What is pH? A measure of acidity and alkalinity of a solution that is a number on a scale on which a value of 7 represents neutrality and lower numbers indicate increasing acidity and higher numbers increasing alkalinity and on which each unit of change represents a tenfold change - Webster Dictionary

What is Cycle? A cycle is a short, repeated series of high measurements followed by a series of low measurements. It is detected visually and may lead to higher-than-expected frequencies in tails of histogram. Likely Assignable Causes Industry worn threads or gears humidity or temperature fluctuations operator fatigue, voltage changes and over-adjustment Services duty rotations employee fatigue poor scheduling and periodic distractions

What is Oscillation? Alternation above and below the centerline The measurements tend to be near upper or lower edges of the chart with fewer than expected near the centerline. It is detected visually or by runs-test. Variance increases but process mean may stay near centerline. Likely Causes Industry alternating sampling of two machines, two settings, two inspectors or two gauges Services alternating task responsibility between two workers

Results – Cycle 1 Strong Out-of-Control Level with 500 Samples

Results – Cycle 2 Medium Out-of-Control Level with 500 Samples

Results – Cycle 3 No Out-of-Control Level with 1000 Samples

Results – Oscillation 1 Strong Out-of-Control Level with 50 Samples

Results – Oscillation 2 Medium Out-of-Control Level with 500 Samples

Results – Oscillation 3 No Out-of-Control Level with 1000 Samples

Conclusion – Cycle 1 When cycles were present, there were fewer centerline crossings than should have occurred for an in-control process When evidence of strong cycles was present, the histogram showing the number of data points falling within a given standard deviation of the mean was symmetrical in shape, but showed too many data points falling outside of the one- and two-standard deviation range to approximate the shape of a normal curve

Conclusion – Cycle 2 The mean for the samples would have remained very close to the historical mean, but as the number of samples increased, the data points became less normally distributed. The cyclical nature of the samples seemed to have a flattening affect on the histogram, which was less evident when the cycling was at medium severity, and was not evident in the in-control samples.

Conclusion – Oscillation 1 In the strong level of out-of-control oscillating sample, the mean chart visually shows an oscillation pattern, fails the rule for oscillation by having 14 or more consecutive data points cross the centerline, and has an extremely high negative Z-value for the run test, which denotes severe oscillation In the medium out-of-control oscillating sample, the mean chart still shows an oscillating pattern, but not as clearly defined as the severe sample, the samples also fail the oscillation rule and have a moderately negative Z-value for the run test.

Conclusion – Oscillation 2 As expected, it was very difficult to notice the oscillation in the “in-control” samples. In addition, the samples passed the oscillation rule and generated a positive Z-value for the run test.