Stats

Process Control

Using Individuals and a Moving Range chart, initial analysis was conducted to determine if the manufacturing process for making the soles was stable (shown below). On the left sole there was initially one special cause (point 20) on investigation, which we have decided not to remove. While recognising that the I chart control limits are based on the average moving range, the special cause is only XXX above the upper control limit.

Moving range and Individuals chart for Left sole

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Moving Range and Individuals chart for Right sole

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When assessing the left and right soles individually, both left and right processes are stable but the averages vary significantly (by how much) against the specification target of 77.10.

It is only when combined, does the process show instability. It is also when combined that the specification target aligns with the average of the left and right soles. | | UCL | LCL | Av X |

Left | 86.32 | 74.20 | 80.26 |

Right | 80.21 | 67.68 | 73.95 |

Combined | 83.32 | 70.89 | 77.10 |

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Moving Range and Individuals chart for Combined shoe soles

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While the MR chart indicates stability, there are 11 special causes in the I chart (which is checked after the MR Chart), 4 (at points 20, 49, 79 and 82) for the left sole and 7 for the right. These are removed and the MR and I charts are reproduced. This has resulted in an unstable MR chart with 2 points now to be removed.

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The MR chart is now in control but the I chart is once again unstable. This is likely to continue to given the close proximately of the data points. The removal of these data points has also had an impact on the Average (now 77.22) which is 0.12 points above the target of 77.10.

Alternative charting option

There are six observations per subgroup and while the Central Limit theorem states n>30 so 30 observations per subgroup, groups of 4-5 are common so the distribution of averages should...