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Chapter 31: Problem 12

A large chain of coffee shops records a number of performance measures. Among them is the time required to complete an order for a cappuccino, measured from the time the order is placed. Suggest some plausible examples of each of the following. (a) Reasons for common cause variation in response time. (b) s-type special causes. (c) \(\mathrm{x}^{-} \bar{x}\)-type special causes.

Short Answer

Expert verified
Common causes: daily variability; S-type: equipment failures; X虅-type: increased demand from promotions.

Step by step solution

01

Understand Common Cause Variation

Common cause variation refers to the inherent variability in a process that is stable over time. It is the natural fluctuation observed in a system. When considering order completion at a coffee shop, examples of common cause variation might include fluctuations due to the time of day (e.g., slower in the early morning), slight differences in employee skills and experiences, or small inconsistencies in equipment performance.
02

Identify s-type Special Causes

S-type special causes, or systematic causes, are deviations from the normal process that can be identified and corrected. For example, an s-type special cause in the order response time could be a malfunctioning espresso machine that intermittently slows down the process. Another example could be a sudden shortage of a key ingredient, leading to delays in preparation.
03

Determine x虅-type Special Causes

X虅-type special causes are unexpected variations that cause a shift in the process average. An example might be a new promotional event leading to a sudden increase in customer orders, thereby extending the response time across shifts. Another example could be a change in staff, such as replacing experienced baristas with new hires, altering the average time to complete an order.

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Key Concepts

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

Common Cause Variation
In the world of statistics, common cause variation refers to the inherent and natural fluctuations that occur within any stable process. Imagine a bustling coffee shop where variations in the time it takes to prepare a cappuccino happen regularly. These variations are not due to any specific fault, but rather the expected small differences that arise in day-to-day operations. Consider these plausible examples:
  • The time of day affects order completion time. Early mornings might be busier, leading to minor delays as staff adjusts to peak customer influx.
  • Employee skills vary slightly. No two baristas are exactly the same, so their individual techniques and experiences cause tiny variations in order time.
  • Equipment performs differently. Even well-maintained machines like espresso makers can show slight inconsistencies over long periods.
These common cause variations illustrate that subtle changes in environment and operation are normal and expected. Understanding them helps businesses maintain consistent quality without unnecessary adjustments.
Special Cause Variation
Special cause variation occurs when there are specific, identifiable factors causing deviations from the normal process. Unlike common cause variation, these variations are not inherent but are due to unusual occurrences or faults that disrupt the system's stability. Let's consider an example in a coffee shop setting:
  • S-type Special Causes: These systematic issues can be identified and fixed. Imagine a malfunctioning espresso machine that occasionally slows service down. Once noticed, it can be repaired to restore normal operations. Another scenario could be a sudden shortage of coffee beans, requiring immediate action to prevent long-term delays.
  • \( \bar{x} \)-type Special Causes: These causes refer to unexpected shifts in the process average. A new marketing campaign could draw a large crowd, unexpectedly increasing the average wait time for everyone. Alternatively, if seasoned baristas are replaced by new hires, their lack of experience might result in a generalized increase in preparation time.
Identifying and addressing these special causes is crucial for maintaining the efficiency and reliability of a process.
Statistical Process Control
Statistical Process Control (SPC) is a method that monitors, controls, and improves a process to ensure consistent output quality. Through SPC, patterns in data are analyzed to distinguish between common and special cause variations, enabling better process management.
For the coffee shop scenario, SPC might involve using control charts to track order completion times.
  • Control charts can highlight when variations are typical, indicating that the process is stable and predictable.
  • They also help in detecting when there is special cause variation, prompting necessary interventions to address specific issues before they affect customer experience.
By employing SPC techniques, businesses can engage in continuous improvement, enhancing service speed and customer satisfaction. This proactive approach helps identify trends and potential issues early on, making it easier to maintain a smooth-running coffee shop or any other type of business.

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Most popular questions from this chapter

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 \(\mathrm{x}^{-} \bar{x}\) chart, or (iii) a gradual drift up or down on the \(\mathrm{x}^{-} \bar{x}\) 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.

John recently lost weight, and during this time, he charted the number of calories consumed each day. His calorie consumption varied each day but was generally stable. There were some days when his calorie count was unusual. Sometimes his calorie intake was much higher and sometimes it was much lower than expected. Give several examples of special causes that might significantly increase or decrease John's calorie consumption on a given day.

The inside diameter of automobile engine piston rings is important to the proper functioning of the engine. The manufacturer checks the control of the piston ring forging process by measuring a sample of five consecutive items during each hour's production. The target diameter for a ring is \(\mu=74.000\) millimeters. The process has been operating in control with center close to the target and \(\sigma=0.015\) millimeter. (a) What center line and control limits should be drawn on the \(s\) chart? On the \(\mathrm{x}^{-} \bar{x}\) chart? (b) A different manufacturer creates the pistons in which the rings will be fit. This manufacturer has a target value of \(73.945 \mathrm{~mm}\) for the piston diameter. The manufacturer checks control of the piston diameter four times each hour. Recently, the process has been running high with \(\mu=74.000\) millimeters and a \(\sigma=0.005\) millimeter. Do you see any issues that might arise for the manufacturer of the engine when the two parts from the different manufacturers are assembled?

Each weekday morning, you must get to work or to your first class on time. Make a flowchart of your daily process for doing this, starting when you wake. Be sure to include the time at which you plan to start each step.

You manage the customer service operation for a maker of electronic equipment sold to business customers. Traditionally, the most common complaint is that equipment does not operate properly when installed, but attention to manufacturing and installation quality will reduce these complaints. You hire an outside firm to conduct a sample survey of your customers. Here are the percents of customers with each of several kinds of complaints: $$ \begin{array}{lc} \hline \text { Category } & \text { Percent } \\ \hline \text { Accuracy of invoices } & 27 \\ \hline \text { Clarity of operating manual } & 6 \\ \hline \text { Complete invoice } & 25 \\ \hline \text { Complete shipment } & 16 \\ \hline \text { Correct equipment shipped } & 15 \\ \hline \text { Ease of obtaining invoice adjustments/credits } & 34 \\ \hline \text { Equipment operates when installed } & 5 \\ \hline \text { Meeting promised delivery date } & 11 \\ \hline \text { Sales rep returns calls } & 3 \\ \hline \text { Technical competence of sales rep } & 12 \\ \hline \end{array} $$ (a) Why do the percents not add to \(100 \%\) ? (b) Make a Pareto chart. What area would you choose as a target for improvement?
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