 The following questions and answers can be used to test your personal understanding of process capability and statistical control. There are 8 questions each aiming to focus on a different aspect of statistical process control and statistical methods of process improvement.

# Question 1

A QC scheme is in operation for a process producing ball-bearings. Samples of 6 bearings are taken every hour and diameters measured. The mean diameter the process delivers is 2 cm. A bearing meets specification within the range 1.998cm – 2.002cm.

USL = Upper Specification Limit.

LSL = Lower Specification Limit.

δ = Standard deviation of the process.

µ = Process mean.

If the USL is µ + 1δ, the LSL is µ – 1δ.

(i) Calculate δ?
(ii) Calculate the process capability?
(iii) What value of δ will deliver a six sigma process?

# Question 2

You measure the height of members of your family as follows:
Heights recorded: 6; 6.1; 5.8 and 5.2 feet respectively.

a) Are there enough measurements to record a variance? Explain.
If yes, what is the sample variance?

# Question 3.

A machine is newly installed in a factory to fill bags of flour. The standard weight of each bag of flour is 2000 g’s. The installing company operate the machine  for one day in order to test and five samples of the output from the machine are recorded every hour. The average results for each of the five samples are as follows: 1996, 2090, 2010, 2008, 1835, 1820, 2180, 2118 grams. The specification is nominal +/- 10%. The installers complete the installation based on the above measurements.

a) Are all the samples within specification?
b) What is the mean, variance, standard deviation of the samples?
c) How many sigma is the process?
d) What is the capability of the process (Cpk)? Is it capable?
e) Is the machine acceptable?

# Question 4. Process Temperature.

In a manufacturing process, temperature readings are recorded every hour over an eight hour day. The average readings are as follows: all in degrees C.
10,12,13,15,12,11,14,10,18,12.

Changes are made to the process which results in the following set of recordings:
10,13,16,17,14,15,15,18,19,20.

The specification for the process temperature is 9 to 25 degrees C.

What has been the result of the process change in terms of:

a) Centering of the process performance within the process specifications?
b) The variability inherent within the process, both before and after the process change?
c) The capability of the process?
d) What has improved/deteriorated as a result of the process change?

# Question 5. Data Distribution.

Why might you think it would be acceptable to make an assumption that the data obtained from a process would be “Normally” distributed?

Identify four other potential distributions.

# Question 6. Which of the following is correct and why ?

To measure Cpk a process must be:

a) Predictable
b) Stable
c) In control
d) have a standard capability of < 1
e) none of the above

# If you obtained a negative Cpk, what would your opinion be?

a) The mean is a negative number
b) One process specification is a negative number
c) Both process specifications are negative numbers
d) The standard deviation is negative
e) Process mean is outside specifications
f) Error in the calculations

# Question 8:

If you implement a change to a process with the result that the mean comes closer to the center between the specifications and the variability reduces, which of the following would you expect to happen ?

a) The Cpk will decrease towards zero.
b) The Cpk is independent of mean and variability so will not be affected.
c) The Cpk will stabilize at 1.
d) None of the above. Current Best Practice.

## SPC & Statistical Methods for Process Improvement.

• Process Capability. Variability Reduction. Statistical Process Control.
• Pre-Control. R&R Studies.
• Process capability indices Cp, Cpk, Cpm, Capability ratio.
• Performance indices Pp and Ppk.
• Variable Control Charts.
• Attribute Charts.
• Pareto Charts.
• Individual – X Charts.
• Histograms / Process Capability Analysis.
• Scatter Diagrams.
• Etc. … Etc. …