# Essay on Production and Operation Management

1145 Words Dec 8th, 2014 5 Pages
Plastic key chains are being produced in a company named Hot Shot Plastics. The plastic material is first molded and then trimmed to the required shape. The current curetimes (which is the time for plastic to cool) during the molding process affect the edge quality of the key-chains produced. The aim is to achieve statistical control of the curetimes using Xbar and R-charts
Curetime data of 25 samples, each of size 4 have been taken when the process is assumed to be in control. These are shown below. Sample no | Observations | 1 | 27.34667 | 27.50085 | 29.94412 | 28.21249 | 2 | 27.79695 | 26.15006 | 31.21295 | 31.33272 | 3 | 33.53255 | 29.32971 | 29.70460 | 31.05300 | 4 | 37.98409 | 32.26942 | 31.91741 | 29.44279 | 5 | 33.82722 |
The plastic material is first molded and then trimmed to the required shape. The curetimes (which is the time for the plastic to cool) during the molding process affect the edge quality of the keychains produced. The aim is to achieve statistical control of the curetimes using X̅- and R-charts.
Questions:
1. Prepare X̅- and R-charts using these data with the method described in the chapter.
Solution:
Factor for Determining from R̅ the Three-Sigma Control Limits for X̅- and R-Charts
| | Factors for R-Chart |
Number of observations in each samplen | Factor for X̅-ChartA2 | Lower Control LimitD3 | Upper Control LimitD4 |
4 | 0.73 | 0 | 2.28 |
X̅̅ = 30.40289
R̅ = 5.932155
Upper control limit for X̅ = X̅̅ + A2 R̅ = 30.40289 + 0.73 (5.932155) = 34.73336315
Lower control limit for X̅ = X̅̅ - A2 R̅ = 30.40289 - 0.73 (5.932155) = 26.07241685
Upper control limit for R = D4 R̅ = 2.28 (5.932155) = 13.5253134
Lower control limit for R = D3 R̅ = 0 (5.932155) = 0
Exhibit 1
LCL 26.07241685
X̅̅=30.40289
UCL 34.73336315
Exhibit 2
LCL 0
LCL 13.5253134
R̅ = 5.932155
Sample number
2. Analyze the charts and comment on whether the process appears to be in control and stable.
Solution:
Exhibit 1 and 2 shows the X̅-chart and R-chart with a plot of all sample means and ranges of the samples. All the points are well within the control limits, although sample 24 is close to the X̅ lower control limit and samples 17 through 22 are above the target.
3.

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