Frequently Asked Questions

This page will contain questions submitted by at least two students and the instructor's response to those questions.


If we know we are trying to achieve a Cpk of 1.33 or greater, why don't we have the customer use specification limits that are outside the 3 sigma limits of the process?
Customers set specifications which satisfy their requirements--not to meet the current status of our process.  Our job is to design a process that will manufacture product to meet their specifications--i.e. to provide a Cpk of 1.33 or higher.  To increase the Cpk, process variation must be reduced.  This reduces the numerical value of the denominator in the Cpk calculation and thus increases the magnitude of Cpk.
How do I determine which factors to use in calculating the control limits for x-bar and range charts?  I am confused about n and k.
The number of observations in each sample (subgroup) is n.  The number of samples (subgroups) is k.  Use n to determine the factors to use (A2, D4, D3) from Table 4.1 on page 58 of the text in calculating the control limits for x-bar and range charts.
Example:  You have 5 samples each containing 4 observations.  k = 5; n = 4.  Locate 4 in the n column; read 0.729 as the value of A2, 0 as the value of D3, and 2.282 as the value of D4.
What is the difference between control limits and specification limits.  I just saw a chart in a company labeled a control chart which had only specification centerline and limits.
Specification limits are the desired extremes that can be tolerated in a product.  They are usually set during the design process and are the "words from the designer."  Control limits are statistically derived from data taken from the process.  They are usually determined during a capability study of a process.  They are the "words from the process."  It can be useful to think of specification limits as "what is desired," and control limits as "what is possible for a given process."  Statistically derived control limits are used for control charts--generally it is not a good practice to show specification limits on a control chart.  Specification limits are used on precontrol charts.
What is the difference between a process being in control and capable?
In control means that the process is predictable.  The control chart for the process shows no sign of the presence of assignable cause variation.  Think of this as the process telling you what it can do when running as designed.
Capable means that the in control process is capable of meeting the specifications for the product being produced.  Generally this means that the value of Cp or Cpk is at least 1.33.  Think of this as comparing what the process told you it could do (6 sigma) with what you want it to do (USL -LSL).
How do I know when to use a c-chart instead of a p-chart?
A p-chart is used to record the proportion of defective units in a sample.  A c-chart is used to record the number of defects in a sample.  Consider the following example:
A process produces jelly beans.  Small spots on a jelly bean are defects.  The specification allows a jelly bean to have 4 or fewer defects (spots) and still be considered acceptable.  If we use a p-chart to record the proportion of defective jelly beans we could miss spotting a trend where the number of defects is increasing but since no jelly beans contain more than 4 defects, none are defective.  The p-chart would show 0 proportion defective for all samples.  The c-chart, however, would show an increasing number of defects over time.
Do I approach problem 5 on page 75 in the text as demonstrated in the slide presentation?
Yes.  Calculate your deltas (difference from nominal) and use those to calculate the control limits for the Delta and range charts.
I'm having trouble getting the "estimated standard deviation" for the Lesson 8 assignment. My "n" is larger than the chart on page 58, so I can't get a d2 value. Should I use a smaller sample size, or am I overlooking something? I used all 75 numbers in the sample (replacing the out of control data points), calculated a mean, and then got hung up on the estimated sigma, as the chart doesn't have an "n" higher than 16.
The sample size used in Eq. 4.22 on p. 70 is the number of observations in the subgroups (samples) used to come up with your range.  If you have 25 samples each with 3 observations, you do indeed have a total of 75 observations (3 x 25 = 75).  But your n is 3 -- the number of observations in each sample.  Therefore, d2 = 1.693 from Table 4.1 on p. 58 of the text.