Question 4.DS.17: Control charts can be utilized to keep track of manufacturin......
Control charts can be utilized to keep track of manufacturing failures. Presented below are data collected over time showing fastening torque defects, evaluating both over and under-torque conditions found per month on a vehicle assembly line. Twelve months of data were obtained for the first year and 10 months of data have been collected to date for the second (or current) year. It is important to note that each data point should be posted as soon as its value is determined.
You are asked to develop a control chart to assess the reliability of the fastening torques.
| w | J | F | MA | AP | MY | JN | JL | AU | S | O | N | D |
| Year1 | 92 | 70 | 81 | 87 | 89 | 93 | 97 | 79 | 105 | 86 | 89 | 81 |
| Year2 | 70 | 57 | 80 | 60 | 79 | 65 | 74 | 62 | 61 | 61 |
Approach:
Since there is no previous data upon which to base your analysis, you decide to establish a control chart based on Year 1 data. Year 2 (and subsequent) are to be charted and evaluated based upon Year 1 guidelines. The charting shall be performed on the basis that n is large. Note that for n large, we consider the value of s to approach the value of σ.
From Year 1 data you find:\overline{x}_{YR1}=87.42 \sigma _{YR1}=9.13
Yielding:
UCL (95%) = 87.42 +1.96(9.13) = 105.13
LCL (95%) = 87.42 −1.96(9.13) = 69.52
UCL (99%) = 87.42 + 2.576(9.13) = 110.94
UCL (99%) = 87.42 − 2.576(9.13) = 63.90
Analysis:
In Year 1, we note from the chart that there are four points in a row monotonically increasing above the mean line. This should be the cause for some concern. Indeed, the data for the remainder of Year 1 indicate significant swings, leading ultimately to “out of control” points in February of Year 2.
The Year 2 data appears to be entirely different than that of Year 1 data. Year 2 data appears to have been displaced “downward” to out of control conditions and/or to form a new base. This data would require either a careful examination of the process to determine the cause of the shift or a reevaluation of the data, or both. Additionally, the Year 2 data displays a different cycle characteristic than that of Year 1 data.
