A motorcycle manufacturer produces the parts for its vehicles in different locations and transports them to its plant for assembly.In order to keep the assembly operations running efficiently,it is vital that all parts be within specification limits.One important part used in the assembly is the engine camshaft,and one important quality characteristic is the case hardness depth.Specifications state that the hardness depth must be between 3.0 mm and 6.0 mm.To investigate the process,the quality control engineer selected 25 daily subgroups of n = 5 and measured the hardness depth.The process yielded a mean of the means $\overline { \overline { x } }$

= 4)50 and an average range = 1.01.Calculate the control limits for the X-bar chart.

Question

A motorcycle manufacturer produces the parts for its vehicles in different locations and transports them to its plant for assembly.In order to keep the assembly operations running efficiently,it is vital that all parts be within specification limits.One important part used in the assembly is the engine camshaft,and one important quality characteristic is the case hardness depth.Specifications state that the hardness depth must be between 3.0 mm and 6.0 mm.To investigate the process,the quality control engineer selected 25 daily subgroups of n = 5 and measured the hardness depth.The process yielded a mean of the means

\overline { \overline { x } }

= 4) 50 and an average range = 1.01.Calculate the control limits for the X-bar chart.

= 4)50 and an average range = 1.01.Calculate the control limits for the X-bar chart.

Quizplus · Accepted Answer

To calculate the control limits for the X-bar chart, we need to use the following formulas:

Upper control limit (UCL) = $\overline { \overline { x } }$ + A2R
Lower control limit (LCL) = $\overline { \overline { x } }$ - A2R

where A2 is the control chart factor for n = 5, which is 0.577, and R is the average range, which is 1.01.

Substituting the values, we get:

UCL = 4.50 + (0.577)(1.01) = 4.92
LCL = 4.50 - (0.577)(1.01) = 4.08

Therefore, the control limits for the X-bar chart are [3.917, 5.083], which is option C.

A Motorcycle Manufacturer Produces the Parts for Its Vehicles in Different