Question

Let's assume that your process yields products with a mean diameter of 1.251mm with σ = 0.00083mm. The Process Specification call for a LSL=1.245mm and USL=1.255. What is the C_pk?

You are a consultant to an manufacturing company that wants to design a control chart to monitor the parts quality sourced from a supplier. The supplier guarantees an average of only 4 blemishes per part. What is the three-sigma (standard deviation) LCL control chart limit (blemishes per part)?

Over the course of the most recent production run, you have measured 20 samples with 5 units in each sample. The average part length over all 20 samples (X-bar-bar) is 10.21mm. The average of the range (R-bar) over all 20 samples is 0.60mm. What is the Upper Control Limit for the X-bar Chart?

Answer 1

1)

This is the information we have been provided in terms of the process specifications, mean and standard deviation:

Upper Specification U =	1.255
Lower Specification L =	1.2451
Process Mean Xˉ =	1.251
Process Standard Deviation σ =	0.00083

Therefore, the capability index is computed using the following formula

= 1.606

the process capability ratio is C{pk} = 1.606. Since the process capability is greater than 1, the process is capable.

2) Here c(bar) is given as 4 the lower control limit is given by LCL= c(bar)-3sqrt[c(bar)]= 4 - 3 [sqrt(4)]= 4-3*2= -2~ = 0

Hence the lower control limit is given as 0.

3) X(double bar) = 10.21 , R(bar) = 0.60.

The upper control limit is given as UCL X(bar) = X(double bar) + zσx(bar) = X(double bar) + 3σx(bar)

=X(double bar) + A2R(bar)=10.21 + 0.577*0.60= 10.21 + 0.3462= 10.5562