Exam 16: Quality Control Methods

Subgroups of power supply units are selected once each hour from an assembly line, and the high-voltage output of each unit is determined. a. Suppose the sum of the resulting sample ranges for 30 subgroups, each consisting of four units, is 84. Calculate control limits for an R chart. b. Repeat part (a) if each subgroup consists of eight units and the sum is 105.

Consider the control chart based on control limits $\mu _ { 0 } \pm 2.575 \sigma / \sqrt { n }$ a. What is the ARL when the process is in control? b. What is the ARL when n = 4 and the process mean has shifted to $\mu = \mu _ { 0 } + \sigma$ ? c. How do the values of parts (a) and (b) compare to the corresponding values for a 3-sigma chart?

Which of the following statements are not true?

The c control chart for the number of defectives in a single item (e.g., one automobile) or a group of items (e.g., blemishes on a set of four tires) is based on the __________ probability distribution.

Which of the following statements are true?

If Y is a Poisson random variable with parameter $\theta$ then E(Y) = __________, V(Y) = __________, and also has approximately a __________ distribution when $\theta$ is large $\text { ( } \theta \geq 10 \text { will suffice for most purposes) }$

An $\bar { x }$ control chart is based on control limits $\mu \pm 2.5 \sigma / \sqrt { n }$ When the process is in control, then the probability that a point falls outside the limits is __________.

In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a __________ and two__________.

Suppose there are 25 samples obtained at equally spaced time points, and n=5 observations in each sample. If the sum of the 25 sample standard deviations is 50, then the center line of the S chart will be at height equals to __________.

Sources of variation that may have a pernicious impact on the quality of items produced by some process, such as contaminated material, are referred to as __________ in the quality control literature.

The two control limit for 3 sigma $\bar { x }$ chart have been calculated. If the variable of interest is normally distributed, and 3 is replaced by 3.09 in the control limits formulas, then probability of Type I error $( \alpha )$ __________, but for any fixed n and $\sigma$ , probability of Type II error $( \beta )$ will __________.

Which of the following statements are true?

When an in-control process yields a point outside the control limits (an out-of-control signal), a type __________ error has occurred.

Consider a 3-sigma control chart with center line at $\mu _ { 0 }$ and based on n = 5. Assuming normality, calculate the probability that a single point will fall outside the control limits when the actual process mean is a. $\mu _ { 0 } + .5 \sigma$ b. $\mu _ { 0 } - \sigma$ c. $\mu _ { 0 } + 2 \sigma$

There are two equivalent versions of a cumulative sum procedure for a process mean, one __________ and the __________.

A sample of ROM computer chips was selected on each of 30 consecutive days, and the number of nonconforming chips on each day was as follows: 30 16 17 22 19 18 16 23 13 21 18 19 13 25 31 17 12 21 15 29 11 19 25 18 38 20 8 26 12 25 Determine control limits for a 3-sigma p chart and specify any out-of-control points.

In acceptance sampling, the risk of rejecting a good quality lot is considered a

A sample of 50 items is to be selected from a batch consisting of 5000 items. The batch will be accepted if the sample contains at most one defective item. Calculate the probability of lot acceptance, P(A), for p = .01, .02,…, .10, and sketch the OC curve.

A manufacturer of dustless chalk instituted a quality control program to monitor chalk density. The sample standard deviations of densities of n = 8 chalk specimens, were as follow: .165 .231 .073 .165 .292 .371 .179 .234 .408 .207 .170 .249 .296 .138 .111 .076 .224 .335 .116 .204 .250 .232 .342 .307 Calculate limits for an S chart, and check for out-of-control points. If there is an out-of-control point, delete it and repeat the process.

The 3-sigma lower control limit (LCL) for an R chart is given by LCL = $\bar { r } - 3 c _ { n } \bar { r } / b _ { n }$ where the values of $b _ { n } \text { and } c _ { n }$ 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 = __________.