91Ó°ÊÓ

Is each of the following examples of a special cause most likely to result first in (i) a sudden change in level on the \(s\) or \(R\) chart, (ii) a sudden change in level on the \(x\) chart, or (iii) a gradual drift up or down on the \(x\) chart? In each case, briefly explain your reasoning. a. An airline pilots' union puts pressure on management during labor negotiations by asking its members to "work to rule" in doing the detailed checks required before a plane can leave the gate. b. Measurements of part dimensions that were formerly made by hand are now made by a very accurate laser system. (The process producing the parts does not change; measurement methods can also affect control charts.) c. Inadequate air conditioning on a hot day allows the temperature to rise during the afternoon in an office that prepares a company's invoices.

Step by step solution

01

Understanding Scenario A

The scenario involves airline pilots working to rule during labor negotiations, which means they are strictly adhering to all regulations and procedures. This increased attention to details can lead to delays, as processes may take longer to complete. Thus, this is most likely to result in (i) a sudden change in level on the \(s\) or \(R\) chart because the variability of the process increases due to these delays.

02

Analyze Scenario B

In this scenario, a new measurement method (laser system) replaces the previous hand-made measurements. This introduces a more accurate and consistent measurement process. As the measurement becomes more precise, it is likely to result in (ii) a sudden change in level on the \(x\) chart, reflecting a noticeable shift in the mean measurement due to increased accuracy, despite the production process remaining unchanged.

03

Evaluate Scenario C

The scenario where inadequate air conditioning leads to increasing temperatures in an office throughout the day exemplifies a situation where the performance might decrease gradually. The rising temperatures can slowly affect the efficiency of workers or machines over time, thus leading to (iii) a gradual drift up or down on the \(x\) chart as productivity or output quality shifts.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Special Cause Variation

Special cause variation refers to unexpected, irregular events that can cause significant changes in a process output. These variations are not part of the regular, consistent process variations.
Instead, they come from external influences that aren't usually part of the process.

• These causes are often unpredictable and can be due to sudden events, such as equipment failure, power outages, or human error.
• Special cause variations are not always bad, as they can also uncover areas for potential improvement or innovation within a process.

For instance, in the airline scenario from the original exercise, the "work to rule" approach by pilots during labor negotiations is seen as a special cause. It is because this approach isn't a regular occurrence and can create notable delays due to extra precautions, reflecting increased variability of the process outputs on control charts.

Process Variability

Process variability pertains to the predictable and natural fluctuations that occur within a process. It is often a result of many small, random factors that affect the process.
These variations are consistent and expected.

• This type of variability is termed as 'common cause variation' and is inherent in any given process.
• Understanding process variability helps in maintaining control over the process and ensuring consistent quality in outputs.

In reference to the example with the introduction of a laser measurement system, changing from manual to laser measurements drastically reduced the measurement inconsistencies. This demonstrates a decrease in process variability, although the production method itself has not changed. The laser's precision marks a shift on the control charts due to improved measurement accuracy.

Statistical Process Control

Statistical process control (SPC) is a method used to monitor and control a process to ensure it operates at its full potential.
It relies on statistical methods to identify and analyze process variations.

• Control charts are a vital tool in SPC. They help in distinguishing between common cause and special cause variations.
• By analyzing data over time, SPC aids in identifying trends or shifts that may signify underlying issues.

The original exercise examples provide a practical illustration of SPC in action. For instance, they show how having control charts allows users to track when a process shifts suddenly or gradually due to various causes such as operational changes or environmental factors. This could be seen in the airline example where process delays prompted a review of control via the charts to identify special causes of variation.

Measurement Accuracy

Measurement accuracy refers to how close a measured value is to the true value of the quantity being measured.
It is critical in maintaining quality and consistency in production processes.

• An accurate measurement system reduces errors and variations in the recorded data.
• Consistent and accurate measurements are vital for reliable statistical process control, as external or altered measurement methods can impact control chart readings.

In the example of using a laser system instead of manual measurements, measurement accuracy played a crucial role. The exactitude of the laser system compared to the subjective nature of manual measurements reduced errors and shifted the control charts, showcasing the importance of measurement precision.