so I've been working on a question involving constructing a mean and range chart with upper and lower action and warning limits, I've got the first part of the question right (I've plotted the chart with the correct limits) but I can't seem to make any progress on the last part involving Cp and Cpk values.
Process mean x̅ = 50.06 Mean Range = 1.77
Standard Deviation SD = 0.8596406 Standard Error = 0.4298203
Upper Action Limit= 51.3494609
Upper Warning Limit= 50.9196406
Lower Warning Limit= 49.2003594
Lower Action Limit= 48.7705391
The values above should all be correct, they match the answers on the markscheme
The first question is: with a specified mean of 49, what is the minimum tolerance (T)? and confirm this by calculating Cpk.
I have the answer from the markscheme however it doesn't give a method (the answer should be T = 3.63892181)
The second part is: with a specified tolerance of +/- 4 what is the maximum and minimum values for the specified mean? Confirm the answer by calculating Cpk.
Again I have the given answers see below:
Maximum specified mean = 51.4810782 Cpk min ( 2.10207156 , 1 )
Minimum specified mean = 48.6389218 Cpk min ( 1 , 2.10207156 )
but no method so I'm struggling to figure out how to get to the answers
These are the equations I have but I've had no luck in getting to the answer with them:
Standard deviation = mean range / hartley's constant (in this case hartley's = 2.059)
Standard error = standard deviation / √n ( sample size n = 4)
Cp = 2T / 6 x standard deviation ( T is tolerance)
upper standard limit USL= specified mean + T
lower standard limit LSL= specified mean - T
Cpk = min ( (USL - x̅) / 3 x SD , (x̅ - LSL) / 3 x SD )
(all x symbols are multiply signs (except the x̅) in the equations I've listed)
I don't know if I'm missing an equation or anything but any help you guys can give me would be fantastic,