Exam 16: Quality Control Methods

At time r, a process is judged out of control if any of the cumulative sum plotted values $\left( 1 , S _ { 1 } \right) , \left( 2 , S _ { 2 } \right) , \ldots \ldots , \left(y , S _ { \mathrm { r } } \right)$ lies outside the __________; either above the upper arm or below the lower arm.

Let the random variable X denote the number of defective items in the lot, A denote the event that the lot is accepted, and p denote the proportion of defective items in the lot. Which of the following statements is not true?

The accompanying observations are numbers of defects in 25 1-square-yard specimens of woven fabric of a certain type: 3, 7, 5, 3, 4, 2, 8, 4, 3, 3, 6, 6, 2, 3, 2, 4, 7, 3, 2, 3, 4, 1, 5, 4, 6. Determine control limits for a 3-sigma c chart for the number of defects, and discuss the behavior of the chart.

For a sample of size 5, the tabulated value of $a = .94$ If the population standard deviation $\sigma = 2.50$ then the standard deviation of the sample standard deviation S is $\sigma _ { 2 } =$ __________, rounded to 3 decimal places.

The behavior of a sampling plan can be nicely summarized by graphing P(A); the probability that the lot is accepted, as a function of p; the proportion of defective items in the lot. Such a graph is called the __________ for the plan.

Suppose there are 28 samples obtained at equally spaced time points, and n=7 observations in each sample. If the sum of the 28 sample ranges is 98, and that the tabulated values of $b _ { 7 }$ and $c _ { 7 }$ are 2.706 and .833, respectively, then the 3-sigma control limits LCL and UCL for an R control chart are respectively

__________ are now used extensively in industry as diagnostic techniques for monitoring production processes to identify instability and unusual circumstances.

When n = 180, what is the smallest value of $\bar { P }$ for which the LCL in a 3-sigma p chart is positive?

If the points on a control chart all lie between the two central limits, the process is deemed to __________.

In acceptance sampling, the risk of accepting a poor quality lot is considered a

Suppose there are 10 sample obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 20 sample standard deviations is 42, and that the tabulated value of $a _ { 4 }$ is .921, then the 3-sigma control limits LCL and UCL for an S control chart are respectively

Consider the single-sample plan that utilizes n = 50 and c = 1 when N = 2000. Determine the values of AOQ and ATI for selected values of p and graph each of these against p. Also determine the value of AOQL.

When the out-of-control ARL corresponds to a shift of 1 standard deviation I the process mean, what are the characteristics of the CUSUM procedure that has ARL of 250 and 4.8 for the in-control and out-of-control conditions, respectively?

Which of the following statements are true?

Which of the following statements are not true?

The 3-sigma lower control limit (LCL) for an S chart is given by LCL = $\bar { s } - 3 \bar { s } \sqrt { 1 - a _ { n } ^ { 2 } } / a _ { n }$ where the values of $a _ { n }$ for n=3, ….., 8 are tabulated in your text. This expression for LCL will be negative if $n \leq$ __________, in which case it is customary to use LCL = __________.

The accompanying table gives sample means and standard deviations, each based on n = 6 observations of the refractive index of fiber-optic cable. Calculate the control limits for an $\bar { X }$ chart based on the sample standard deviations given, and comment on the behavior of the chart. [Hint: $\sum \bar { x } _ { 2 } = 2317.07 \text { and } \sum s _ { 2 } = 30.34$ ]

On each of the previous 25 days, 100 electronic devices of a certain type were randomly selected and subjected to a severe heat stress test. The total number of items that failed to pass the test was 570. a. Determine control limits for a 3-sigma p chart. b. The highest number of failed items on a given day was 40, and the lowest number was 12. Does either of these correspond to an out-of-control point? Explain.

Which of the following are not examples of assignable causes of variation?

Which of the following statements are not true?