. Ceramic items are “baked” in a gas-fired tubular-shaped oven is lots of 100 units. The items are lined up in a single row on a special high-temperature pallet, slid into the oven, the oven closed, and the temperature increased manually according to time-temperature scale. After cooling, a sample of five units is drawn from a lot and strength-tested by breaking them in a special testing device. To be effective in use, breaking strength must exceed 5 psi. If any item breaks at less than 5 psi, the lot from which it came is scrapped. About 10% of the lots have been scrapped in recent times. a. A decision is made to run a process capability study. Data on the next 20 lots are tested using the same procedure, and a sample sized of 5, and X-bar and R charts are drawn. At this point, ΣX = 112.00 psi and ΣR = 23.26 psi. Calculate control limits for X and R for this process and estimate σ b. Assuming a normal distribution of product, what proportion would you estimate does not meet specifications? c. Calculate the pertinent Process Capability Indexes for this process and interpret their meaning relative to your answer to part (b) d. Assuming R chart shows good control, where should the process be centered to ensure that no more than 0.1% of the items do not meet specification (assume a normal distribution)? Calculate the same Process Capability Indexes at this target mean setting
2. Ceramic items are “baked” in a gas-fired tubular-shaped oven is lots of 100 units. The items are lined
up in a single row on a special high-temperature pallet, slid into the oven, the oven closed, and the
temperature increased manually according to time-temperature scale. After cooling, a sample of five
units is drawn from a lot and strength-tested by breaking them in a special testing device. To be
effective in use, breaking strength must exceed 5 psi. If any item breaks at less than 5 psi, the lot from
which it came is scrapped. About 10% of the lots have been scrapped in recent times.
a. A decision is made to run a process capability study. Data on the next 20 lots are tested using the
same procedure, and a sample sized of 5, and X-bar and R charts are drawn. At this point, ΣX = 112.00
psi and ΣR = 23.26 psi. Calculate control limits for X and R for this process and estimate σ
b. Assuming a
specifications?
c. Calculate the pertinent Process Capability Indexes for this process and interpret their meaning relative
to your answer to part (b)
d. Assuming R chart shows good control, where should the process be centered to ensure that no
more than 0.1% of the items do not meet specification (assume a normal distribution)? Calculate the
same Process Capability Indexes at this target mean setting.
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