Write a paper of no more than 1,050 words in which you explanation of the control limits, including the calculations and data used to determine them. (I expect everyone to use the data that they have collected and create a control chart for your process. I want to see your calculations for the upper and lower control limits as well as the raw data).
In collecting data for 7 days between day 27 and 33, the following were observed. On day 27th, hair length was 15". 4 umbers of products were used that day and it took 20 minutes to style the hair. On day 28th, hair length was reduced by 1", resulting in using 3 products and taking 18 minutes. On day 29th, hair length still at 14", but with no haircut, the number of hair products used increased to 4 from the previous day and the resultant time spent to style it up was 20 minutes. On day 30th, hair was cut 2" shorter to a length of 12". Time spent on styling hair that day reduced to 17 minutes. On the 31st day, 32nd, and 33rd day, hair length remained at 12". No of products used on those 3 consecutive days were 3, 2 and 3 respectively. Time spent was 16, 16 and 15 minutes respectively.
Hence, in calculation of control limits, in taking 91 divided by 7, then, the average control limit then is C.L.= Total hair length = 91 = 13
Total no. of days 7
Hence in getting Upper control limit (U.P.L.) = c + z √c where c represents the average control limit and z=3
Hence U.P.L= 13 + 3√13= 23.82
In getting the Lower control Limit (L.C.L) = c+ z√c where c represents the average control limit and z=3
Hence L.C.L= 13-313=2.18
C-Control chart showing time taken in minutes against hair length
Discuss the effect of any seasonal factors using the process performance data collected each week?
There are often a number of seasonal factors that affect the performance of the process. The main target of the observation was to determine which hair length resulted in less time taken in styling hair. From the data collected, the following could be deduced. Less time was spent styling hair when it was cut short (12") compared to when it was 15". In addition, as hair length reduced, so did the number of hair products used to style up hair. Seasonal factor in this case was trimming the hair (Doty, 2003). A shorter hair proved to consume fewer products and take lesser time compared to longer hair that consumed more products and took more time (Oakland, 2012). Another seasonal factor which upon change could affect the outcome of the whole performance process is the type of product used (Stapenhurst, 2012) In changing to a new product that has multiple functions instead of using multiple products can be more advantageous in assisting to reduce time spent on styling.
Discuss the confidence intervals and their usefulness based on the number of data points.
In calculating the Standard deviation
Hence list of deviation 2, 1, 1, -1, -1, -1, and 1
Squares of deviation 4, 1, 1, 1,1,1,1
Sum of deviations 10
Hence square root of 1.67=1.29
Doty, L. A. (2003). Statistical Process Control. New York: Industrial Press Inc.
Oakland, J. S. (2012). Statistical Process Control. New York: Routledge.
Stapenhurst, T. (2012). Mastering Statistical Process Control. New York: Routledge.