At Isogen Pharmaceuticals, the filling process for its asthma inhaler is set to

Question

At Isogen Pharmaceuticals, the filling process for its asthma inhaler is set to dispense 150 milliliters (ml) of steroid solution per container. The average range for a sample of 6 containers is 6 ml. Use the accompanying table to establish control limits for sample means and ranges for the filling process.

The UCL Upper RUCLR equals ____ ml and the LCL Subscript Upper RLCLR equals ____ ml. (rounded to two decimal places.)

The UCL UCLx equals _____ ml and the LCLLCLx equals ____ ml. (rounded to two decimal places.)

Explanation / Answer

To be Calculated:

a) Upper Control Limit of Range Chart, UCL-R

b) Lower Control Limit of Range Chart, LCL-R

c) Upper Control Limit of X-bar Chart, UCL-X

d) Lower Control Limit of X-bar Chart, LCL-X

Given Values:

a) Average of X, X-bar = 150 ml.

b) Average of Ranges, R-bar = 6 ml.

c) Number of Samples, N = 6 containers

Solution:

a) Upper Control Limit of Range Chart, UCL-R can be calculated as;

UCL-R = (D4 x R-bar)

Using, the accompanying table, control limits can be established as;

D4 (for N = 6) = 2.004

UCL-R = 2.004 x 6 = 12.024

UCL-R = 12.02 ml.

b) Lower Control Limit of Range Chart, LCL-R can be calculated as;

LCL-R = (D3 x R-bar)

Using, the accompanying table, control limits can be established as;

D3 (for N = 6) = 0

LCL-R = 0 x 6 = 0

LCL-R = 0 ml.

c) Upper Control Limit of X-bar Chart, UCL-X can be calculated as;

UCL-X = X-bar + (A2 x R-bar)

Using, the accompanying table, control limits can be established as;

A2 (for N = 6) = 0.483

UCL-X = 150 + (0.483 x 6) = 150 + 2.898 = 152.898

UCL-X = 152.90 ml.

d) Lower Control Limit of X-bar Chart, LCL-X can be calculated as;

LCL-X = X-bar - (A2 x R-bar)

Using, the accompanying table, control limits can be established as;

A2 (for N = 6) = 0.483

LCL-X = 150 - (0.483 x 6) = 150 - 2.898 = 147.102

LCL-X = 147.10

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.