Exam 26: Statistical Process Control

Repeated sampling of a certain process shows the average of all sample ranges to be 2.3 cm. The sample size has been constant at n = 6. What are the 3-sigma control limits for this R-chart?

A small, independent amusement park collects data on the number of cars with out-of-state license plates. The sample size is fixed at n = 25 each day. Data from the previous 10 days indicate the following number of out-of-state license plates: Day Out-of-state Plates 1 6 2 4 3 5 4 7 5 8 6 3 7 4 8 5 9 3 10 11 (a) Calculate the overall proportion of "tourists" (cars with out-of-state plates) and the standard deviation of proportions. (b) Using ± 3σ limits, calculate the LCL and UCL for these data. (c) Is the process under control? Explain.

Calculate the C_p and C_pk scores from the following information. Upper tolerance limit 0.57 Lower tolerance limit 0.022 Mean (optional) 0.034 Standard deviation 0.02

When a lot has been accepted by acceptance sampling, we know that

A Type II error occurs when

A p-chart is appropriate to plot the number of typographic errors per page of text.

A manager wants to build 3-sigma control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 6. If samples of size 9 are to be taken, the UCL and LCL will be

A retail store manager is trying to improve and control the rate at which cashiers sign customers up for store credit cards. Suppose the manager takes 10 samples, each with 100 observations. P-bar is found to be .05, and the manager does not want a lower limit below .0064. What z-value would this imply, and how confident can he be that the true lower limit is greater than or equal to .0064?

The Central Limit Theorem states that when the sample size increases, the distribution of the sample means will approach the normal distribution.

A lot that is accepted by acceptance sampling is certified to be free of defects.

A car mechanic is thinking of guaranteeing customers that an oil change will take no more than 15 minutes with a 99.73% confidence level. He takes a few samples of size 5 and finds the process mean to be 13 minutes with a standard deviation of .2 minutes and average sample range of 1.2 minutes. Find the A₂, D₂, and D₃ values and use them to compute the upper and lower limits for an x-bar chart. Use the upper limit to determine if the mechanic can offer a 15 minute guarantee. Assume the mechanic plots the samples on the x-bar control chart and finds the process is in control, is there anything else the mechanic is missing to ensure the process is in control?

The probability of rejecting a good lot is known as consumer's risk.

The specification for a plastic handle calls for a length of 6.0 inches ± .2 inches. The standard deviation of the process is estimated to be 0.05 inches. What are the upper and lower specification limits for this product? The process is known to operate at a mean thickness of 6.1 inches. What is the C_p and C_pk for this process? Is this process capable of producing the desired part?

A process is operating in such a manner that the mean of the process is exactly on the lower specification limit. What must be true about the two measures of capability for this process?

The x-bar chart indicates that a gain or loss of uniformity has occurred in dispersion of a production process.

What is the difference between natural and assignable causes of variation?

Ten samples of a process measuring the number of returns per 100 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, 11. Find the standard deviation of the sampling distribution. (Hint- Use p-bar formula)

Some degree of variability is present in almost all processes.

Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend?

An operating characteristics curve shows