Coverage and Usage Testing

Based on FSMs and Markov Chains

FSM-Based Testing

FSM:

• State: operations/ functions
• Transition: link int a chain
• Input/output associated with transition
• Complete operation: chain

Three representations of FSMs

• Graphical
• Tabular
• list

1. define state

{Power-Up, Mobile Station Initialization, Mobile Station Idle, System access, Mobile station control or Traffic channel}

{A, B, C, D, E}

2. define transitions

{A -> B; B-> C; C->D (paging channel message); C-> B (unable to receive paging channel); D->C (finished other tasks); D -> E (making a call); E -> B}

Graphical

Tabular

1. define row and col meaning

The rows represent originating states and the columns represent ending states for specific transitions.

2. define cell

A null input or a null output is marked by “-”.

msg , NoC , call, and done to represent “paging channel message”, “unable to receive paging channel”, “making a call”, and “finished with other tasks”, respectively.

“na” or not marked (left empty), the corresponding transition is not allowed.

List

{A, B, - , -}

{B, C, -, -}

{C, B, “unable to receive paging channel”, -}

{C, D, "paging channel message", -}

{D, C, "finished with other tasks", -}

{D, E, "making a call", -}

{E, B, -, -}

Markov Chains as Enhanced FSMs

FSM+发生的概率 = Markov Chains

In the context that we use it for usage-based statistical testing, this Markov chain is also called a Markov OP, because it constitutes the specific operational profile (OP) for the system.

Musa’s operational profiles (OPs) for usage-based statistical testing using partitions.

Starting with a simple Markov OP example of your choice, convert it to the corresponding Musa OP. (Make necessary assumptions as needed.)

output sum should be 1

Musa OP: an operational profile, or an OP for short, is a list of disjoint set of operations and their associated probabilities of occurrence.

Unified Markov Models for Testing

统一马尔可夫模型

这样的 UMMs 使得模拟个别操作单元并将它们链接起来形成全局操作变得简单。更高层次的操作可以扩展到更低层次的模型中，以进行更彻底的测试。