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Numerical Example of Statistical Process Control

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One of the stages in the process of making denim cloth at the Southern Mills Company is to spin cotton yarn onto spindles for subsequent use in the weaving process. Occasionally the yarn breaks during the spinning process, and an operator ties it back together. Some number of breaks is considered normal; however, too many breaks might mean that the yarn is of poor quality. In order to monitor this process, the quality-control manager randomly selects a spinning machine each hour and checks the number of breaks during a 15-minute period. Following is a summary of the observations for the past 20 hours:

Sample Number of Breaks Sample Number of Breaks
 1 3 11 3
 2 2 12 4
 3 4 13 6
 4 1 14 7
 5 5 15 8
 6 3 16 6
 7 2 17 5
 8 4 18 7
 9 0 19 8
10 2 20 6

Construct a -chart using limits for this process and indicate if the process was out of control at any time.

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The process is considered to be out of control when the observed values are higher than the upper control limit (UCL) or lower than the Lower Control Limit (LCL)
Here UCL = mean + 3*Standard Error (i.e. Standard Deviation / Sqrt (no. of observations))
LCL = Mean - 3*Standard Error
For the present set of observations, the control limits are calculated as follows
Mean = (3+2+4.....+7+8+6)/20 = 4.30
Standard ...

Solution Summary

The writeup shows the numerical calculation of upper and lower control limits as per the theory of Statistical Process Control and uses it to determine if the process is out of control

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