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Chapter 11

Process Capability and

Improvement Studies

Learning Objectives

• To describe and illustrate performance and technical specifications, including individual unit specifications, acceptable quality level (AQL) specifications and distribution specifications.
• To define and illustrate the development of individual unit specifications in terms of nominal value, tolerance an upper and lower specification limits.
• To define and illustrate acceptable quality level specifications.
• To define and illustrate distribution specifications as a function of the Empirical Rule.

Introduction

• Process capability studies determine whether a process is unstable, investigate any sources of instability, determine their causes, and take action to eliminate such sources of instability.
• After all sources of instability have been eliminated from a process, the natural behavior of the process is called its process capability.
• Process capability compares the output of a process (called “ Voice of the Process ”) with the customer’s specification limits for the outputs (called “ Voice of the customer ”).
• A process must have an established process capability before it can be improved. Consequently, a process capability study must be successfully completed before a process improvement study can have any chance for success.

Specifications (“Voice of the Customer”)

Performance Specifications

• Performance specifications address a customer’s needs or wants.
• An example of a performance specification can be seen in restaurants rated by the Red Michelin Guide. The customers of these restaurants set their performance specifications as “a perfect dining experience.”
• Performance is measured in terms of the synergistic experience created by the interaction of food, service, ambience, and price.

Individual Unit Specifications

• Individual unit specifications state a

boundary, or boundaries, that apply to individual units of a product or service.

• An individual unit of product or service

is considered to conform to a specification if it is on or inside the boundary or boundaries; this is the goal post view of quality. USL = Nominal + Tolerance LSL = Nominal - Tolerance

Technical Specifications

An example of an individual unit specification and its three parts can be seen in the specification for the “case hardness depth” of a camshaft.

• A camshaft is considered to be conforming with respect to case hardness depth if each individual unit is between 7.0 mm ± 3.5 mm (or 3.5 to 10.5 mm).
• The nominal value in that specification is 7.0mm; the two-sided tolerance is 3.5mm; the lower specification limit is 3.5mm (7.0 mm – 3.5 mm); and the upper specification limit is 10.5 mm (7.0 mm + 3.5 mm).

Technical Specifications

• Acceptable Quality Level (AQL) specifications state a requirement that must be met by most individual units of product or service, but allow a certain proportion of the units to exceed the requirements.
• For example, cam shafts shall be acceptable if no more than 3 percent of the units exceed the specification limits of 3.5 and 10.5 mm.
• This type of specification limits is frequently referred to as an Acceptable Quality Level.
• AQL specification are much like individual unit specifications, except they have a unique negative feature: they formally support the production of a certain percentage of defective product or service.

Technical Specifications

• Distribution Specifications define an acceptable distribution for each product or service quality characteristic.
• In an analytic study, a distribution is defined in terms of its mean, standard deviation, and shape.
• However, from the Empirical Rule discussed in Chapter 5, it is not necessary to make any assumptions about the shape of the distribution. That is, virtually all data from a stable process will fall between the mean plus or minus three standard deviations.

Attribute Process Capabilities Studies

• Attribute process capabilities studies determine a process’s capability in terms of fraction defective output or counts of defects for a unit of output.
• The major tools used in attribute process capability studies are attribute control charts and the tools discussed in Chapter 10.
• The process capability for a p chart is p (the average fraction defective units generated by the process).
• The process capability for the np chart is np (the average number of defective units generated by the process for a given subgroup size, n).
• The process capability for a c chart is c (the average number of defects per unit generated by the process for a given area of opportunity).
• Finally, the process capability for a u chart is u (the average number of defects per unit generated by the process where the area of opportunity varies from subgroup to subgroup).

Variables Process Capability Studies

• Variables control charts are used to stabilize a process so we can determine meaningful upper and lower natural limits.
• Natural limits are computed for stable processes by adding and subtracting three times the process’s standard deviation to the process centerline.
• In general, for any variables control chart, the upper and lower natural limits are:

= − σ

= + σ

LNL x 3

UNL x 3

For x-bar and s charts, the upper and

lower natural limits are:

where c 4 is a constant factor based on

sub-group size

 

  

= − 

 

  

= + 

4

4

c LNL x 3 s

c UNL x 3 s

c 4 s for a normal distributi on σ

=

For individuals charts, the upper and

lower natural limits are:

where d 2 is a constant factor based on

sub-group size of 2

2

2

d LNL x 3 R

d UNL x 3 R

d 2 =Rσ for astable normal distributi on

Example: If samples of four steel ingots are drawn from an ingot- producing process every hour, and the process is stable with a process average subgroup weight of 42.0 pounds (x = 42. pounds) and an average range of 0.6856 pounds, we can say the following about the process:

• Virtually all (99.73% for a stable normal distribution) of the steel ingots produced will weigh between 41.0 and 43. pounds. This is what the steel ingot process is capable of producing; it is the identity of the process.

( )

( ) 42.0 3(0.333) 41.001 41.0 pounds

42.0 3 0. d 2.UNL x 3 R

The Process'slower natural limit is:

42.0 3(0.333) 42.999 43.0pounds

42.0 3 0. d 1.UNL x 3 R

The process'supper natural limit is:

2

2

= − = ≈

= −    

= − 

= + = ≈

= +    

= + 

Data Requirements for Process

Capabilities Studies

• Attribute Studies. In general, the study should cover at least three distinct time periods, where each time period should contain 20 to 25 samples and each sample should have between 50 and 100 units.
• Variables Studies. A separate variables study may be required for each quality characteristic that can cause a unit to be defective. - As a rule of thumb, a variables study should cover at least three distinct time periods. - The first period should contain about 50 samples of between three and five units each, and the second and third time periods should contain 25 samples of between three and five units each.