Manov Steel Inc. has a rolling mill that produces sheet steel with a nominal thickness of 0.125 inch. Suppose that the specification limits are given by LSL = 0.120 and USL %3D = 0.130 inch. According to historical data, the actual thickness of a random sheet produced by the mill is normally distributed with mean and standard deviation of = 0.125 and o = 0.0025.

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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Manov Steel Inc. has a rolling mill that produces sheet steel with a nominal thickness of
0.125 inch. Suppose that the specification limits are given by LSL = 0.120 and
USL = 0.130 inch. According to historical data, the actual thickness of a random sheet
produced by the mill is normally distributed with mean and standard deviation of u = 0.125
and o = 0.0025.
(a) What are the lower and upper natural tolerance limits (LNTL and UNTL) for individual
sheets of steel?
(b) What are the lower and upper control limits (LSL and USL) if we use a control chart that
plots the average thickness of samples of size n = 4?
(c) What will be the percentage nonconforming, given the above values for (LNTL, UNTL)
and (LSL, USL)? What is the process capability index C? Do you consider this process
capable of meeting its performance specifications?
(d) Suppose that the process mean suddenly shifts from 0.125 to 0.1275. What happens to
the process capability index C and the percentage nonconforming?
Transcribed Image Text:Manov Steel Inc. has a rolling mill that produces sheet steel with a nominal thickness of 0.125 inch. Suppose that the specification limits are given by LSL = 0.120 and USL = 0.130 inch. According to historical data, the actual thickness of a random sheet produced by the mill is normally distributed with mean and standard deviation of u = 0.125 and o = 0.0025. (a) What are the lower and upper natural tolerance limits (LNTL and UNTL) for individual sheets of steel? (b) What are the lower and upper control limits (LSL and USL) if we use a control chart that plots the average thickness of samples of size n = 4? (c) What will be the percentage nonconforming, given the above values for (LNTL, UNTL) and (LSL, USL)? What is the process capability index C? Do you consider this process capable of meeting its performance specifications? (d) Suppose that the process mean suddenly shifts from 0.125 to 0.1275. What happens to the process capability index C and the percentage nonconforming?
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