Exam 20: Statistical Methods for Quality Control

The quality control department of a company has decided to select a sample of 20 items from each shipment of goods it receives and inspect them for defects.It has been decided that if the sample contains no defective parts,the entire lot will be accepted. a.What is the probability of accepting a lot that contains 10% defective items? b.What is the probability of accepting a lot that contains 5% defective items? c.What is the probability of rejecting a lot that contains 15% defective items?

A production process is considered in control if it processes at least 98.5% non-defective items.Samples of size 400 are used for the inspection process.Determine the upper and lower control limits for the P chart of defective elements.

A control chart that is used when the output of a production process is measured in terms of the percent defective is

Normal or natural variations in process outputs that are due purely to chance are

Producer's risk is

A production process that is in control has a mean (µ)of 200 and a standard deviation ( $\sigma$ )of 22.Determine the lower and the upper control limits for sample sizes of 49.

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

A production process is considered in control if no more than 4% of the items produced are defective.Samples of size 100 are used for the inspection process. a.Determine the standard error of the proportion. b.Determine the upper and the lower control limits for the P chart.

The upper and lower control limits of the mean of a process are 606 and 594.Samples of size 225 are used for the inspection process.Determine the mean and the standard deviation for this process.

A production process is considered in control if no more than to 6% of the items produced are defective.Samples of size 300 are used for the inspection process. a.Determine the standard error of the proportion. b.Determine the upper and the lower control limits for the P chart.

If the lower-control limit of a P chart is negative,

Brakes Shop,Inc. ,is a franchise that specializes in repairing brake systems of automobiles.The company purchases brake shoes from a national supplier.Currently,lots of 1,000 brake shoes are purchased,and each shoe is inspected before being installed on an automobile.The company has decided instead of 100% inspection to adopt an acceptance sampling plan. a.Explain what is meant by the acceptance sampling plan. b.If the company decides to adopt an acceptance sampling plan,what kinds of risks are there? c.The quality control department of the company has decided to select a sample of 10 shoes and inspect them for defects.Furthermore,it has been decided that if the sample contains no defective parts,the entire lot will be accepted.If there are 50 defective shoes in a shipment,what is the probability that the entire lot will be accepted? d.What is the probability of accepting the lot if there are 100 defective units in the lot?

A graph showing the probability of accepting the lot as a function of the percent defective in the lot is

The upper and lower control limits of the proportions of defectives of a process are 0.33 and 0.27. a.What has been the proportion of defectives in this process? b.What has been the sample size?

The results of inspection of samples of a product taken over the past 10 days are given below.Sample size for each day has been 140. Determine the 97% upper and lower control limits for the p-chart.

Chocolate,Inc.manufactures 4 ounce chocolate bars.Random samples of size four were taken and weighed.Eight hours of observation provided the following data. a.Determine the 3 sigma upper and lower control limits for the x-bar chart. b.Determine the 3 sigma upper and lower control limits for the R-chart.

A soft drink filling machine is set up to fill bottles with 12 ounces of soft drink.The standard deviation s is known to be 0.4 ounces.The quality control department periodically selects samples of 16 bottles and measures their contents.Assume the distribution of filling volumes is normal. a.Determine the upper and lower control limits and explain what they indicate. b.The means of six samples were 11.8,12.2,11.9,11.9,12.1,and 11.8 ounces.Construct an X bar chart and indicate whether or not the process is in control.

The results of inspection of samples of a product taken over the past 8 days are given below.Sample size for each day has been 120. Determine the 97% upper and lower control limits for the p-chart.

The maximum number of defective items that can be found in the sample and still lead to acceptance of the lot is

The upper and lower control limits of the mean of a process are 66 and 54.Samples of size 16 are used for the inspection process.Determine the mean and the standard deviation for this process.