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Magazine Chapter 2: Q7OQ (page 339)
Question:Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table:
Sample | n | Number Of Defective Items In The Sample | Sample | n | Number Of Defective Items In The Sample |
1 | 15 | 3 | 6 | 15 | 2 |
2 | 15 | 1 | 7 | 15 | 0 |
3 | 15 | 0 | 8 | 15 | 3 |
4 | 15 | 0 | 9 | 15 | 1 |
5 | 15 | 0 | 10 | 15 | 0 |
a. Develop a p-chart for 95 percent confidence (1.96 standard deviations).
b. Based on the plotted data points, what comments can you make?
Short Answer
Answer
Statistical quality control(SQC) is a process that includes some various techniques designed to evaluate quality from a conformance view; that's, how well are we doing at meeting the specifications that have been set during the planning of the parts or services that we are providing. Managing quality performance using SQC techniques usually involves the periodic sampling of a process and analysis of those data using statistically derived performance criteria.
Step by step solution
(a) P-chart for 95 percent confidence
In statisticalquality control, the p-chartmay be atype ofcontrol chartaccustomedmonitor the proportion of nonconforming unitsin asample, where the sample proportion nonconforming is definedbecause of theratio ofthe numberof nonconforming units to the sample size, n.
Thep-chartonly accommodates "pass"/"fail"-type inspection as determined by one or more go-no-go gauges or tests, effectively applying the specifications tothe databeforethey'replotted on the chart. Othervarieties ofcontrol charts display the magnitude ofthe standardcharacteristic under study, making troubleshooting possible directly from those charts.
As per available data, we can have the P-chart as follows:
Formulas used:
P-bar = Average of fraction defective
Upper Control Limit = p-bar + z*sqrt(p-bar*(1-p bar)/n)
Lower Control Limit = p-bar 鈥� z*sqrt(p-bar*(1-p bar)/n)
P- CHART
(b)Comments
From the plotted p-chart, we can conclude that theprocess is out of control as some of the sample defects fall outside the control limits.
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