3.39. The tensile strength of a metal part is normally distributed with
mean 40lb and standart deviation 5lb. If 50,000 parts are produced,
how many would you expect to fail to meet a minimum specification
limit of 35 lb tensile strength? How many would have a tensile
strength in excess of 48 lb
3.40. The output voltage of a power supply is normally distributed
with mean 5 V and standart deviation 0.02 V. If the lower and upper
specifications for voltage are 4.95 V and 5.05 V, respectively, what is
the probability that a power supply selected at random will conform
to the specifications on voltage?
3.24. A manufacturer of electronic calculators offers a one-year warranty. If
the calculator fails for any reason during this period, it is replaced. The time to
failure is well modeled by the following probability distribution:
𝑓(𝑥) = 0.125𝑒 −0.125𝑥
𝑥>0
a) What percentage of the calculators will fail within the warranty period ?
b) The manufacturing cost of a calculator is $50, and the profit per sale is $25.
What is the effect of warranty replacement on profit ?
4.1. The diameters of aluminum alloy rods produced on an extrusion
machine are known to have a standard deviation of 0.0001 in. A
random sample of 25 rods has an average diameter of 0.5046 in.
a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume
a two-sided alternative and use 𝛼 = 0,05
b) Find the P-value for this test.
c) Construct a two-sided 95% confidence interval on the mean rod
diameter.
5.23. Consider the time-varying process behaviour shown below.
Match each of these several patterns of process performance to the
corresponding 𝑥̅ and R charts shown in figures (a) to (e) below ?
Question : Apply the Western electric rules to the control charts presented below. Would
these rules result in any out of control signal ?
Xbar - chart
R-chart
Checking for out of control conditions we have the following 8 tests:
Test 1 : Extreme points -> points 8, 20, 32, 44 on x bar chart & no extreme points on
R chart.
Test 2: Two out of Three Points in or beyond Zone A -> 20, 21
Test 3: Four out of Five Points in or beyond Zone B -> 25, 26, 27
Test 4: Runs Above or Below the Centerline (Eight or more consecutive points) -> No
points satisfying this condition both on x bar and R charts.
Test 5: Linear Trend Identification (Six or more consecutive points) -> 25, 26
Test 6: Oscillatory Trend Identification( 14 or more consecutive points) -> No points
Test 7: Avoidance of Zone C (8 or more consecutive points) -> No points
Test 8: Run in Zone C (15 or more consecutive points) -> No points
We check for all of the 8 tests above for x bar chart. However for R chart, we don’t
apply tests that contain zones (tests 2,3,7 and 8), thus they are not needed to be
checked. (Only 1,4,5,6 th tests should be checked for an R chart)