Question

Chapter 6 - Question 02 Homework. Unanswered The weights of large Nacho Cheese Doritos (sold to Sam's Club) within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means (Z=3) and given is the population (process) standard deviation, which is 1. You are in charge of randomly selecting nine (n=9) boxes each hour, for twelve hours (k=12). Then find the overall mean and compute the control limits using an x-bar chart. The data you collected is in the table below: What are the upper and lower control limits? Hour UWN Avg. of 9 bags 16.1 16.8 15.5 16.5 16.5 16.4 15.2 16.4 16.3 BBB00 14.8 14.2 17.3 [] Fulls FOTO

Answer 1

Solution:

Given, Z = 3

Process standard deviation ($\sigma$) = 1

Sample size (n) = 9 boxes

Number of samples = 12

Overall mean (X-double bar) is calculated as,

X-double bar = Sum of hourly average / Number of hours

X-double bar = (16.1 + 16.8 + 15.5 + 16.5 +...........+ 14.2 + 17.3) / 12

X-double bar = 192 / 12

X-double bar = 16

Upper and Lower control limits are calculated as,

Upper control limit (UCL) = X-double bar + [Z x $\sigma$/SQRT(n)]

Lower control limit (LCL) = X-double bar - [Z x $\sigma$/SQRT(n)]

Putting the given values in the above formula,

UCL = 16 + [3 x 1/SQRT(9)]

UCL = 16 + 1

UCL = 17

LCL = 16 - [3 x 1/SQRT(9)]

LCL = 16 - 1

LCL = 15

Answer: (B) UCL = 17, LCL = 15