Operations Management

Topics: Standard deviation, Control chart, Arithmetic mean Pages: 7 (1378 words) Published: January 16, 2012
Problem 1.
Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: |Hour |Average (inches)|R (inches) |Hour |Average[pic] |R (inches) | | | | | |(inches) | | |1 |3.25 |0.71 |13 |3.11 |0.85 | |2 |3.10 |1.18 |14 |2.83 |1.31 | |3 |3.22 |1.43 |15 |3.12 |1.06 | |4 |3.39 |1.26 |16 |2.84 |0.50 | |5 |3.07 |1.17 |17 |2.86 |1.43 | |6 |2.86 |0.32 |18 |2.74 |1.29 | |7 |3.05 |0.53 |19 |3.41 |1.61 | |8 |2.65 |1.13 |20 |2.89 |1.09 | |9 |3.02 |0.71 |21 |2.65 |1.08 | |10 |2.85 |1.33 |22 |3.28 |0.46 | |11 |2.83 |1.17 |23 |2.94 |1.58 | |12 |2.97 |0.40 |24 |2.64 |0.97 |

Develop appropriate control charts and determine whether there is any cause for concern in the cutting process. Plot the information and look for patterns.

Ten eerste moeten we eerst de boven-en ondergrens berekenen voor zowel voor een [pic] chart grafiek en R chart. Voor de grafiek met de gemiddelde inches is [pic] and [pic]: [pic][pic]
[pic]
Of(2.236, 3.728)

Voor het bereik:
[pic][pic]
[pic]
[pic]

[pic][pic]
[pic]
[pic]

In bovenste grafieken zijn af te lezen dan ze binnen het bereik vallen en daarom goed gekeurd.

Problem 2.
You are attempting to develop a quality monitoring system for some parts purchased from Warton & Kotha Manufacturing Co. These parts are either good or defective. You have decided to take a sample of 100 units. Develop a table of the appropriate upper and lower control chart limits for various values of the fraction defective in the sample taken. The values for p in this table should range from 0.02 to 0.10 in increments of 0.02. Develop the upper and lower control limits for a 99.73% confidence interval.

[pic][pic]
[pic]
[pic]
Of(–0.022, 0.0620)

| |n = 100 |
|p |UCL |LCL |
|0.02 |0.0620 |0.0000 |
|0.04 |0.0988 |0.0000 |
|0.06 |0.1312 |0.0000 |
|0.08 |0.1614 |0.0000 |
|0.10 |0.1900 |0.0100 |

 
Problem 3.
Twelve samples, each containing five parts, were taking from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were:  

|Sample |Sample mean(in.) |Range (in.) |Sample |Sample mean(in.) |Range(in.) | |1 |10.002 |0.013 |7 |10.001 |0.008 | |2 |10.002 |0.014 |8 |10.003 |0.011 | |3 |9.993 |0.005 |9 |9.995 |0.002 | |4 |10.004...
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