# Capability Analysis (Variable Data)

#### Description

Capability analysis offers a way of measuring and quantifying the voice of the customer (specification limits) in relation to the voice of the process (control limits). Most processes have some performance limits and variation that will be acceptable to the customer. The extent to which the “expected” values fall within these limits determines how capable the process is of meeting requirements.

#### Benefits

• Offers a key measure of process performance
• Provides a visual representation that is easily understood by management
• Applicable to all spheres of business: service, manufacturing, logistics, etc.
• Widely available data analysis through statistical software or add-ins to Microsoft Office or other applications

#### How to Use

• Step 1.  Determine the voice of the customer specifications (lower and upper specifications if both are applicable).
• Step 2.  Collect variable data (time, distance, cost, speed, etc.). You will need at least 30 data points.
• Step 3.  Check the distribution. If normally distributed, use standard capability analysis. If not, you will need more advanced analysis and statistical software. Normal distribution can also be easily checked with a statistical application.
• Step 4.  Review the Cp and Cpk values. Review the histogram and the data distribution in relation to customer specifications.
• Step 5.  Draw your conclusion: Is the process capable, marginal, or not capable?

#### Relevant Definitions

Normal distribution: A set of data that follows a normal curve or bell curve where the height in relation to the width is proportionate and looks like a bell (higher than wider). Several statistical software applications will provide the p value to confirm your hypothesis.

Cp: The ratio of total variation allowed by the specification to the total variation actually measured from the process. A capable process has a Cp >1.33.

Cpk: The ratio or index that indicates if a process is capable of meeting product or service specification limits (lower or upper). It measures the ratio of the total variation and the distance of the mean from the closest limits. Cpk>1.33 is an indication of a capable process.

#### Example

A manager at a luxury hotel has received many complaints regarding the temperature in one of the large meeting rooms used by corporate customers. Many group leaders have complained about the room being too cold in the morning and too hot in the afternoon.

The manager asks the maintenance supervisor to start recording the temperature in the room every 15 minutes, starting when a group enters the room and ending when it leaves. Customers have stated that if the room stays between 67 degrees Fahrenheit and 72 degrees they are comfortable.

Data are collected for several days. The onsite mechanical engineer who supervises the data collection obtains results showing that the average temperature of the room is 70.1 degrees Fahrenheit, which should be ideal. Using a statistical package to determine the capability analysis (graph), he shows the following graphs for morning and afternoon temperature:

As the morning graph clearly shows:

• The mean value of the temperature is close to the lower specification limit of 67 degrees.
• The temperature is below the lower threshold 37% of the time during this period, which explains why customers say they are freezing.
• Cp=0.58 and Cpk=0.11 – a good indication of poor capability.

The afternoon graph shows:

• The mean value of the afternoon temperature is close to the upper specification limit of 72 degrees.
• The temperature is above the upper threshold 38% of the time during this period, which explains why customers say they are sweating.
• Cp=0.47 and Cpk=0.10 – a good indication of poor capability.

With these data on hand, the hotel manager obtains approval to invest in new and more modern air handling equipment in order to maintain the temperature with little variation throughout the day (mean of 70 +/- 2 degrees).

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