Question

In a ready-mix plant, cylindrical samples are prepared and tested periodically to detect any mixture problem and to ensure that the compressive strength is higher than the lower specification limit. The minimum target was set at 5000 psi. (a) How can you use the normal distribution to guarantee strength is met 95% of the time, with process variability of σ= 600 psi. (b) Is this ready-mix plant producing a cost-effective concrete mixture? (Assumption: Concrete mixture design with a mean compressive strength of higher than 5500 psi is not cost-effective) (c) If the mixture design is not cost-effective, what parameter can be considered and improved by this ready-mix plant to produce a cost-effective concrete mixture?

Answer 1

solution-

• data given-
• the minimum target compressive strength =5000psi

a.

• we will use the normal distribution for 95% guarantee strength to set the compressive strength range by using z-value for 95%=(1.96) .
• lower limit = mean compressive strength - z*σ.
• upper limit = mean compressive strength + z*σ.
• where σ = 600psi.

b.

• minimum copressive strength = 5000psi =lower limit
• and lower limit= mean compressive strength - z*σ.

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i.e cocrete mixture has mean compressive strength higher than 5500 psi and hence it is not cost effective.

c.

• to produce the cost effiective concrete with 95% guarentee strength we should alter the target minimum strength coressponding to mean compressive strength of 5500 psi as following.
• so target minimum compressive strength = mean compressive strength - z*σ.
• here mean compressive strength = 5500psi
• z= 1.96
• σ =600psi
• minimum compressive strength= 5500-1.96*600 = 4324 psi
• so target minimum compressive strength = 4324 psi

​​​​​​​the 2 nd thing we can do alter the process variability and hence the value of standard deviation as follows if we want to keep the target minimum strength of 5000 psi

in this way by improving process variability or target minimum strenth we can produce cost effective concrete.