Challenge 1
• The upper and lower control limits for the X-bar chart will be around
34.5 and 25.5, respectively
• For the R chart, the lower control limit will always be zero because D3
is not defined for a sample size of 5
• The upper control limit for the R chart will vary around about 16.5
Challenge 2
• When Challenge 2 is run without making any interventions, the total
cost should be around $14,000 
 When equipment recalibrations and labor substitutions are made
when assignable causes are detected, the total cost is reduced
substantially, to around $4000. Around $3500 of that amount is in
external defect costs, while the rest is in internal defect costs and the
cost of making the recalibrations and labor substitutions 
 When equipment recalibrations and labor substitutions are made
when assignable causes are detected, the total cost is reduced
substantially, to around $4000. Around $3500 of that amount is in
external defect costs, while the rest is in internal defect costs and the
cost of making the recalibrations and labor substitutions 
 Challenge 4
• When Challenge 4 is run without making any investments in improving the
quality of the process, the total cost of quality is around $41,000.
• This is comprised primarily of external failure costs, with a small amount of
internal failure costs and appraisal costs for the baseline sampling plan.