The Canine Gourmet Company produces delicious dog treats for canines with discri
ID: 359112 • Letter: T
Question
The Canine Gourmet Company produces delicious dog treats for canines with discriminating tastes. Management wants the box-filling line to be set so that the process average weight per packet is 46 grams. To make sure that the process is in control, an inspector at the end of the filling line periodically selects a random box of 10 packets and weighs each packet. When the process is in control, the range in the weight of each sample has averaged 7 grams.
a. Design an R- and an x chart for this process.
The UCLr equals { ??? grams} and the LCL r equals {??? grams}
Factors for calculating three-sigma limits for the x-chart and R-chart Size of Sample Factor for UCL and LCL for x-chart (A2) 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 Factor for LCL for R-Chart (D3) 0 0 0 0 0 0.076 0.136 0.184 0.223 Factor for UCL for R-Chart (D4) 3.267 2.575 2.282 2.115 2.004 1.924 1.864 1.816 6 9 10Explanation / Answer
Given are following data :
Process average = Xbar-bar = 46 grams
Average of Range values = Rbar = 7 grams
Sample size = n = 10 packets
As given in the chart, following are the relevant values of constants for n = 10 packets :
A2 = 0.308
D4 = 1.777
D3 = 0.223
Construction of X chart :
Upper Control Limit = Xbar-bar + A2.Rbar = 46 + 0.308 x 7 = 46 + 2.156 = 48.156 grams
Lower Control Limit = Xbar-bar – A2.Rbar = 46 – 0.308 x 7 = 46 – 2.156 = 43.844 grams
Construction of R chart :
Upper Control Limit = D4 x Rbar = 1.777 x 7 = 12.439 grams
Lower Control Limit = D3 x Rbar = 0.223 x 7 = 1.561 grams