Samples of five metal washers are taken periodically, and their thickness (in mm

Question

Samples of five metal washers are taken periodically, and their thickness (in mm) are measured. The following table presents the means and standard deviation for 10 consecutive samples. Data are in vasher.xlsx. The means are X^= 2.-166, S^bar = 0.058. Calculate the 3 sigma control limits for the S chart. Is the process variation under control? If not, delete the samples that are out of control and recompute X^, s^bar and the 3 sigma limits for the S chart. Based on the sample deviation S, calculate the 3 sigma control limits for the X^chart. Based on the 3 sigma limits, is the process mean in control? If not, when is it first detected to be out of control.

Explanation / Answer

(a) Central line sbar = 0.058

Upper control Limit UCL = B4 sbar = 2.089 * 0.058 = 0.121162

Lower Control LImit LCL = B3 sbar = 0 * 0.058 = 0

so control Limits = ( 0, 0.121162)

I have picked B3 and B4 value from the Control Chart table for sample size = 5

Yes, the process variation is under control.

(ii) 3 sigma control limits for the Xbar chart

Here CL = xbar-bar = 2.466

UCL = xbar-bar + A3 sbar = 2.466 + 1.427 * 0.058 = 2.5488

LCL = xbar-bar + A3 sbar = 2.466 - 1.427 * 0.058 = 2.3832

Yes, all the sample means are under control limits that means process mean in contol.

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